Death

The "that" of death (for instance), the fact that men die, cannot be treated as an unproblematic cultural universal.10 We have only to reflect on beliefs in various modes of symbolic death to see that here, as so often elsewhere, there may be wide cultural divergences and substan-

tial difficulties in matching actor and observer categories.11 A fortiori what counts as disease or illness and what as mental illness or madness vary strikingly between cultures. Yet so far as ancient Greek views of death go (the subject of another distinguished contribution to the Sather lectures),12 a resolute acceptance that men die is strongly marked in Homer,13 even if there is afterwards a shadowy existence in Hades, and even if some exceptional individuals escape that fate and achieve semi-divine status as heroes.14 But acceptance of the brute fact of death gives no consolation for, indeed may even heighten, personal bereavement. That acceptance does not qualify, rather it lends resonance to, Achilles' anguished cry that he would rather be a bondsman on earth than rule among the dead.15

On the how of death, Greek physics eventually had, as usual, a multitude of theories to offer. Yet they provided little understanding and no reassurance. There was Aristotle's suggestion, for example, that death is the extinction of the vital heat, which may take place, he believes, either from cold or from an excess of heat.16 That theories that appeal just to the hot, the cold, and the like are quite inadequate had already been argued in the Hippocratic treatise On Ancient Medicine . There the writer criticises those who use such newfangled "hypotheses" in part on the grounds that to do so is to narrow down the causal principles of death and disease.17 What is needed, he believes, is a more complex account, taking into consideration all the manifold powers in the body and their combinations.18 Again even Plato had a suggestion to make on the subject in the Timaeus , namely, that the material cause of death is a deterioration in the structure of the atomic triangles that constitute the physical elements of which the body (and everything else) is made.19

To be sure, each of those, and many other, hardheaded naturalistic explanations entailed the denial of the literal truth of Hesiod's mythology of death as presented in the myth of the metals in the Works and Days , with its complex counterpoint on the way each race meets its end.20 Those of the Golden Age are as if overcome by sleep; those of the Age of Silver, who remain children for a hundred years, are "hidden" by Zeus and become the blessed ones of the underworld; the Bronze Age race destroy themselves; some from the Age of Heroes go

to the Islands of the Blest; and Zeus will destroy the last Age of Iron when men are born grey-haired.21 Again, theories of the physics of death were not compatible with a literal reading of Plato's own myth, in the Politicus , of the age of Cronos—the anti-cosmos when time flows in reverse22 —while they had no comment to make on the values implicit in the ideology of the "beautiful death"—the death while young, in battle, securing lasting fame.23 No prosaic naturalistic account of the how of death had, of course, anything to offer on the why, nor on how we as mortals should live with our mortality. They offered nothing to replace the lesson obliquely taught by Hesiod's myth: we must realise that, since we are born in the Age of Iron, there is an imperative upon us to accept death, along with toil and pain.

Such comfort as was on offer from the philosophers in the classical period, at least,24 came principally from a very different quarter, from the essentially religious belief in the immortality of the soul found first in the Pythagorean tradition, then in Plato and others.25 Yet that was certainly not science replacing earlier attitudes or patterns of belief.

On the contrary, in Plato at any rate, it was often what was now self-consciously recognised as myth doing so. The substance of the eschatological accounts in the Gorgias, Phaedo, Republic , and Phaedrus is accepted by the character Socrates, and no doubt by Plato, as true or at least as like the truth:26 there would presumably be no wavering on the underlying principle of rewards and punishments, the ultimate justice of the regulation of the universe. Yet on each occasion the account is expressly said to be myth, or its status is otherwise undercut.27 In the Phaedrus , for instance, Socrates begins by offering a "demonstration,"

ments on the immortality of the soul, he turns to describe its character

Disease

This first round is, then, no real contest: there is no scientific takeover, no real engagement in the classical period between the study of nature and what myth and religion afforded, whether they did so self-consciously or otherwise, and whether as developed and presented by philosophers or otherwise. But there is more to be said on what might otherwise seem the similar topic of disease, and more on mental illness or madness. In the case of disease, too, the study of nature offered no answer to the naive question of why disease in general should occur: Why do we not live in continual perfect health? Yet it certainly effectively, and in some cases deliberately, blocked any move to explain diseases—both particular types of diseases and individual incidences of them—by invoking divine or supernatural agencies.31

To see this in the right perspective is more complicated than might appear. First it is as well to stress that not all physical ailments and disabilities were deemed by the ancient Greeks—or have been by anyone else—to be the products of divine or demonic forces. Medical anthropologists have, to be sure, only comparatively recently begun to insist that there is much more to the map of most societies' beliefs about physical ailments than the parts that have generally received most attention in the ethnographical accounts, that is, those that relate to the severest diseases and the most dramatic ones, such as epilepsy.32 For many minor ailments, as it might be the common cold, minor stomach upsets, bruises, or bunions, many societies have no recourse to supernatural explanation. Homer has no occasion to talk about the common cold. But apart from the fact that there are many straightforward accounts of wounds and lesions caused by men in battle33 there is an important contrast between the plague sent by Apollo in Iliad 134 and references to diseases that are not directly attributed to a god, such as, for example, the "long disease" contrasted with the arrows of Artemis at Od. 11.172.35

However, this is not to deny that notions that diseases are often sent by the gods or that diseases are themselves semi-divine creatures stalk-

ing the earth36 are widespread and deeply entrenched in archaic times and after.37 Whereas the fact of death in general (as opposed to the ideology) did not, on the whole, need demystifying in Greece,38 the topic of diseases undoubtedly did; and in a remarkable, unprecedented move, some of the Hippocratic writers made a deliberate and self-conscious bid to secure such a demystification, even if it was one accompanied by its own elements of paradox and obfuscation.

First as to the elements of paradox. The move consisted in deeming all diseases natural, not subject to divine intervention, divine only in that the whole of nature is.39 They all have natural causes, a

causes of diseases are physical ones but allow for a norm or model of a healthy living body, by reference to the nature of which diseases can be assessed, and to secure a return to which the doctor exercises his best efforts. The doctor must help nature to effect its own cure, even though the disease to be cured is itself natural and has its nature.43

Health and disease are both thereby located in the domain of what is, the doctors claimed, in principle investigable. The success of the naturalistic framework thus provided for understanding depends, however, on the pathological theories being accurate or at least helpful, on the diagnoses being reasonable, and on the treatments being at least to some extent apparently effective. We shall be returning in chapter 3 to discuss the arbitrariness and dogmatism of many of the theories proposed. For our present purposes I may simply note that it is characteristic of a good deal of Hippocratic medicine that the writers overstate their cases. From the observation that bile and phlegm may be pathogenic substances, there were those who leapt to the conclusion (as in the treatise On Affections ) that all diseases came from bile and phlegm.44 From noticing prominent changes in temperature

and humidity in many patients, some became convinced that the hot, the cold, the wet, and the dry are themselves the causes or bring about changes in the elements or humours in the body and thereby give rise to diseases.45 Yet against the view that those four opposites are the sole causes of death and disease one can range the treatise On Ancient Medicine , which I have already mentioned, the author of which protests that that is to narrow down the causal principles. He objects to those who invoke these opposites on the grounds that they are trying to base medicine on unverifiable postulates where "it would not be clear either to the speaker or to his audience whether what was said was true or not"46 —even if this author himself then goes on to develop some physiological and pathological theories of his own that are, we might say, not much less speculative than those he dismisses.47 The point need not be elaborated further, since the elements of bluff in many Hippocratic theories of disease are obvious enough. We clearly need to suspend disbelief, if not our critical judgement entirely, when

we are solemnly told, as by the author of On Breaths , that air is the cause of every illness,48 or, by the author of On Regimen , that fire and water ultimately are.49

On the question of diagnosis and treatment, however, if we turn to those treatises that stay closer to clinical practice there is much that is sensible and sober and much that is perceptive, alongside much that perhaps needed no special Hippocratic skill to perceive. The why and how of particular types of diseases have become a possible subject of study, even if progress towards adequate answers was slight. Deploying pathological notions that were, in many cases, entirely superficial, research was generally directed at what we should call symptoms, and the causes often remained undiscovered, and not just when the causes that modern medicine would invoke depend on severely modern conceptions such as that of microorganisms. Yet research is the right term for the sustained effort to obtain a typology of diseases, to chart their progress and outcome, to establish correlations between apparently relevant factors, to move towards hesitant epidemiological generalisations.

Epidemics 1 conveys the tone: "Painful swellings near the ears which accompanied fevers did not always subside nor suppurate when the fever was resolved with a crisis, but they were relieved following bilious diarrhoea or dysentery or by the formation of sediment in the urine, as happened in the case of Hermippus of Clazomenae."50 Or again:

We are evidently far from the world of Apollo sending the plague or of Hesiod's diseases randomly roaming the earth.52 Interestingly enough, however, a feature that provides both a link and a contrast with earlier patterns of thought is the residual moralising tone of some Hippocratic comments on the causes or predisposing factors to diseases. Epidemics 1.9 gives a list of the types of persons who died in a particular epidemic. They include: "boys, young men, men in the prime of life, those with smooth skins, those of a pallid complexion, those with straight hair, the black-haired, the black-eyed," and so on, but also "those who had been given to reckless and loose living."53

One of the case histories in Epidemics 3 begins: "Nicodemus took a fever at Abdera as the result of sexual indulgence and drinking,"54 and another: "at Meliboea, a young man who had been heated for a long time as the result of drinking and much sexual indulgence, took to his bed"55 (unlike Nicodemus, who had a crisis and recovered, the youth at Meliboea died). Immorality or at least intemperateness leads here (as in archaic thought) to sickness. Yet the difference should be remarked: it is not Apollo who strikes you down for offending him or his priest. The damage you do to yourself has no supernatural cause, only a natural one for which you are yourself solely responsible—namely, your own self-indulgence.56

On the topic of treatment, similarly, Hippocratic prophylactic recommendations were generally of more help than the treatments they prescribed for their patients once sick. Those treatments were often ineffectual (though that did not prevent some extravagant claims being made on their behalf)57 and they were sometimes more dangerous

than the condition they were used to remedy, whether it was a matter of the drugs employed (which included hellebore, Spanish fly, black nightshade, and a variety of compounds of arsenic)58 or of the surgical procedures used (such as succussion upside down on a ladder,59 forcible straightening on the bench,60 cauterisation, trepanning). The value and importance of plain living, simple foods, regular exercise are stressed in many works, though again, to get the record straight, one must add first that there were doctors who went to extremes: Herodicus, who is famous from Plato, is said to have killed his patients by excessive exercise,61 and there were others whose idea of simple

food was a starvation diet, for which there was even a technical term,

The topic of physical illnesses offered one of the clearest openings for the rationalist takeover. There are plenty of signs of the hubris of Greek rationalism in the Hippocratic treatises, as also of its tendency to run to excess. Yet one of the strengths of the new conceptual framework they present, and one of its originalities, lies in its absolute, un-

compromising character. The assumptions to be made (about the naturalness of diseases) and the way forward in research are confidently sketched out, even if the elements of promise are greater than those of fulfilment, for in practice delivery fell short both in the matter of understanding and in that of control—that is, the cures achieved.

Madness

Mental illness posed problems for the rationalists that were at points importantly different from those of physical illnesses.65 While physical sickness was never exactly celebrated (though the case of Philoctetes illustrates that it could be viewed with awe),66 there were what Dodds called, after Plato, the blessings of madness,67 especially the gift of prophecy and the inspiration of poetry. There is no need to rehearse the rich variety of phenomena to which Dodds drew attention other than to recall that they included not just the star examples of the statement of the power of Dionysus in the Bacchae and the exceptional recognition of the positive manifestations of madness in Plato's Phaedrus , but much else besides in Greek religious belief and practice as well as in Greek literature.68 The question I wish to address is, rather, the following: in the face of these proofs of the hold, so to speak, of madness

on the Greek imagination, how did the would-be rationalists fare? Among those would-be rationalists the pre-Socratic natural philosophers were the first in the field,69 but I shall concentrate once again on the fuller material available in the medical writers.

Their ambition to naturalise mental illness as well as physical, to treat it both conceptually and in practice no differently from physical, is clear, but we must ask with what success they did so, and at what price. First some of the material that is important to us, much of it less familiar now than the texts on which Dodds focused, should be set out, and we may begin with another of the case histories from the Epidemics , the account of a condition that was evidently taken to be at least in part psychological in origin:

As this and many other examples show, Hippocratic accounts of symptoms move in a continuous gradation from thirst and nausea,

through anorexia and insomnia, to despondency and depression, or from high fever, to the delirium that so often accompanies it, to the patients being out of their minds, or from twitching and convulsions, to agitation and anger, to hallucinations.71 As we noted before, attempts are made to establish correlations. For example, the third constitution in Epidemics 1 chap. 9 states: "High fever attended the start of the illness along with slight shivering fits, insomnia, thirst, nausea, slight sweating about the forehead and over the clavicles (but in no case all over), much random talk, fears and despondency, while the extremities such as the toes, and especially the hands, were chilled."72 The doctors were concerned to collect cases of cold toes along with those of fear and despondency: all formed part of a total homogeneous epidemiological picture.

The strength of the Hippocratic approach to madness lies, as before, in its naturalism.73 There is no question of any of these writers

thinking of madness as the result or the manifestation of

While the resolute matter-of-factness robs of its purchase any attempt to glorify madness, there seems no recognition that some modification in approach when dealing with mental illness might be called for. Treatments are, in any case, not often discussed in the case histo-

ries in the Epidemics , but one theme is not reassuring. Several of the patients (as in the case cited) "lost control"—

a limited endorsement.81

When we turn back to the Hippocratic treatises that attempt theories of madness, the impression they give is very much one of their authors whistling in the dark. Dealing with different kinds of mental disturbance, On the Sacred Disease , for example, states: "The brain may be corrupted both by phlegm and by bile, and you can distinguish the two types of disorder thus: those whose madness results from phlegm are quiet and neither shout nor make a disturbance; those whose madness results from bile shout, play tricks, and will not keep still, but are always up to some mischief. Such are the causes of continued madness. But fears and frights also occur from a change in the brain. Such a change happens when it is warmed and that is the effect bile has when, flowing from the rest of the body, it courses to the brain along the blood-vessels. Fear persists until the bile runs away again into the blood-vessels and the body, and then it stops. Pain and nausea are the result of in-opportune cooling and abnormal consolidation of the brain, and that is the effect of phlegm, and the same condition is responsible for loss of memory."82

This treatise has a well-deserved reputation for its often well-directed attacks on the ascription of epilepsy to divine intervention and on the charlatanry of those who claimed to be able to cure it by charms and purifications.83 Yet if the purifiers were indeed vulnerable to some of this writer's criticisms, the element of bravura in his own typology of mental illnesses, some due to phlegm, some to bile, is surely amazing. It is only those with unbounded faith in our author and already convinced of the correctness of Hippocratic naturalism who would believe that he knows much more about what he is talking about in that context84 than the purifiers who diagnosed one type of epilepsy as the work of Poseidon, another that of Ares, another that of the Mother of the Gods.85 True, his framework of explanation is naturalistic, not religious or supernaturalistic. Yet the operations of phlegm and bile to which he appeals, while in principle verifiable, remain at the level of pure speculation. Those operations are invisible entities too, if of a different kind. As for the treatment this writer recommends, it relies largely on the attempt to control the hot, the cold, the wet, and the dry by regimen. Having proclaimed that "the majority [of maladies] may be cured by the very same things from which they arise,"86 he goes on:

As in the attack on the topic of physical diseases, some of the rationalists are loud in their claims both to superior knowledge and to superior therapeutic efficacy, but in the case of mental illness the bluffing is even more transparent. The establishing of a naturalistic basis for the understanding of madness, the ruling out of references to the divine or demonic, is a release from one mystification. But it was achieved at the cost of the substitution of another of a different kind, at least when the theorists' own proposed explanations were quite unsubstantiated and imaginary. Nor did the positive and constructive help on offer amount to very much. To be told that your madness was not sent by the gods might (if you were convinced) be reassuring. At the same time the convinced rationalists cut themselves off from such support as had been available from traditional social, let alone religious, resources. But otherwise, to have any great expectations of improvement from adopting the anti-bilious or anti-phlegmatic diet of cold, or alternatively warm, food and exercise, prescribed in On the Sacred Disease , was clearly, and equally, principally a matter of faith.89

Dreams

On madness the Hippocratics generally refused to be moved by those who would have celebrated it in one or another of its forms. On the topic of dreams,90 however, many of them were persuaded by, or at least accepted, common Greek beliefs. Among those beliefs was a realisation that not all dreams are significant, not all are veridical: there is the Gate of Horn, but there is also the Gate of Ivory.91 Yet it was widely held that many dreams contain a message, even if not necessarily an obvious or direct one, but one needing interpretation. From the Hippocratics down to Galen and beyond many doctors, including some of the foremost spokesmen for the anti-irrationalist point of view, accept some role for dreams in diagnosis, even if they do not endorse particular practices such as that of temple incubation, the soliciting, as it were, of dreams from the god, including, especially, dreams relating to

the dreamers' illnesses or containing instructions about their cure.92 Thus Epidemics 1.10 includes "dreams, their nature and their time" among the items in the general list of factors to be considered in diagnosis.93 In the Hellenistic period Herophilus even includes "god-sent" dreams in his classification of the three main types.94 Galen not only tells us that his father was guided by a dream in deciding that Galen himself should take up a medical career, but also refers to therapies that he says were suggested to him by dreams.95

In time,96 as is well known, complex theories were developed not

only distinguishing the various types of dreams—predictive and non-predictive, allegorical and non-allegorical—but also setting out in detail how they should be interpreted. Many of the writers in question, such as Artemidorus,97 are sophisticated, at points quite cautious, restrained, even self-deprecatory. Many topics of interest might be pursued here. One we may note in passing is the extent to which the importance of wish-fulfilment is recognised by Greek dream-theorists: Freud himself remarked, rather defensively, in the 1914 edition of Die Traumdeutung , that those who attach any importance to such anticipations can go back to classical antiquity, and he cited Herophilus in particular in this connection, while he still insisted that no one before him had held that every dream is a wish-fulfilment.98 However, our chief concern here must be with the kinds of theories and explanations our early would-be rationalists offered to account for the phenomena.

Once again we have a whole Hippocratic treatise devoted to the subject, the fourth book of On Regimen (sometimes called On Dreams ), as well as an important discussion in Aristotle which (whether or not he knew On Regimen 4) develops a similar theory.99 Since Aristotle con-

fines himself largely to providing a general framework of explanation, it will be convenient to reverse the chronological order and take him first.100

Dreams correspond to movements in the body, notably in the sense organs themselves, these movements being transmitted to the soul.101 During the day many of these movements go unnoticed in the welter of impressions the soul receives. But at night, when the soul is less preoccupied, traces of some of the daytime impressions may be registered in it, provided the soul is itself in a stable condition.102 No dreams are sent by the gods, though Aristotle says that they are

revered.104 Most of what were believed to be prophetic dreams are mere coincidences, but some are signs, some causes, of future events:105 they are causes in that they may suggest a course of action that the dreamer then puts into effect; they are signs in the manner Aristotle has explained, when they provide information about movements and changes in the body—though even here, if the soul is not itself stable, the information will be garbled. It is skill in recognising similarities that makes the best interpreter of dreams.106

That dreams may thus indicate points relevant to the health of the dreamer is a view that Aristotle ascribes to the "more discerning doctors," and one he endorses himself.107 Whether or not it was written by one of those "discerning doctors," On Regimen 4 offers an elaborate working-out of that idea.108 After first setting out a psychological theory according to which (as in Aristotle) the soul is distracted by waking impressions but while asleep "it becomes master in its own house,"109 the writer takes pains to differentiate himself from others in the field:

In fact, in the subsequent discussion, prayer is recommended from time to time, and even the gods to whom it should be addressed are specified. "Pray to Earth, Hermes, and the Heroes," for instance, when the dream is of the earth looking black and scorched—which indicates excessive dehydration in the body.111 However, the writer is scrupulously agnostic about whether to go beyond prayer and engage in apotropaic rituals: when dreams are contrary to the acts of the day, this indicates disturbance in the body which may be severe or mild, but "on whether or not you ought to avert the act [that is, by appropriate rites], I pass no judgement."112 The burden of his thesis throughout is that each kind of dream corresponds to a particular physical illness or malfunction which steps can be taken to remedy.

While he dismisses rival interpreters with his curt "they do not know why it happens," no arguments are here offered for his own the-

ory, only assertions, although some of the underlying assumptions, and his use of symbolism, are transparent, and traditional, enough.113 Broadly and simplemindedly, to see good things in dreams is good, and bad things bad, and again it is good to see things that correspond to daytime thoughts and actions and that represent them as occurring in an orderly fashion.114 More specifically we are told that it is a sign of health if, in the dream, when a star seems to fall out of its orbit, it appears pure and bright and moves eastwards.115 Conversely, "when [a star] seems dark or dim or to move westwards, or towards the sea, or towards the earth, or upwards, these signify diseases. Upward movements indicate fluxes in the head; movements towards the sea, diseases of the bowels; and those towards the earth, usually tumors growing in the flesh."116

Moreover, confident recommendations for treatment match confident diagnoses:

Analogies with more modern health faddists are not hard to suggest.

The limitations of this rationalist takeover are twofold. First, the field of what is taken over is restricted. This writer is not concerned (though Aristotle was) with the whole range of predictive dreams, about some of which he is quite indifferent; he concentrates, rather, on what can be discovered about the state of health of patients from their dreams. He has an entirely naturalistic theory of the correlations between the two. No god sends these signs; they are the natural by-products of physical disturbances, a theory he elaborates with some persistence. But it is limited also in a second sense, in that, although superior knowledge is claimed, in practice the theory draws heavily on, and at points is merely a rationalisation of, popular beliefs. Yet the ambition to go one better than traditional views and even than specialist interpretations is evident from those claims to superior knowledge.119 The specialists are said not to know what they are talking about—whereas the Hippocratic writer, armed with his naturalistic theory of physical-psychical correlations, can, if you believe him, put the whole "science" on a firm footing.

Divination and Fate

The limitations, and pretensions, of the inquiry concerning nature emerge clearly once again in relation to the final pair of topics I mentioned, divination and fate.120 Here one might have expected the proto-scientists to have abstained from confrontation with the likes of Teiresias and Cassandra.121 Even if some dreams might be scrutinised for the diagnostic signs they might yield about the dreamer's current state of health, the idea of trying to predict the future, especially the individual's future, was, one might have thought, a palpably unpromising area for any kind of research that purported to involve the inquiry concerning nature, even if it might be the concern of a moral philosophy, whether deterministic or anti-deterministic.122

Yet first, the discourse of prediction, which is prominent in our scientific vocabulary when we talk of the predictive value of a hypothesis, encompassed in the ancient world too a wide range of phenomena. In two areas, especially, it is legitimate to talk of ancient scientific predictions. Whereas modern medicine is concerned with diagnoses, the ancients often focused, rather, on "prognosis,"123 especially the outcome of the disease, and we need not doubt that, drawing on a wide experience and sometimes despite some simpleminded theories, many Greek doctors were often able to anticipate not just the recovery or death of their patients but also the general progress of their ailments.124 Again,

and closer still to the modern analogue, once Greek theoretical astronomy had become established,125 the models proposed could be, and were, used to predict the positions of the sun, moon, and planets.

Secondly, the overlap between the better and the less well-grounded predictions was recognised by some of the ancient writers, both in medicine and in astronomy. Some Hippocratic treatises recommend the practice of prognosis in terms that are obviously reminiscent of the role of the prophet. When the writer of the work called Prognosis says that the doctor should "tell in advance, in the presence of his patients, the present, the past and what is to come to be,"126 or again when we find in Epidemics 1.5 the recommendation to "declare the past, determine the present, foretell the future,"127 the echoes of Calchas in Iliad 1 or of the Muses in the Theogony are obvious.128 Prognosis advocates forecasting in part so that the doctor will not be blamed for failure: he cannot be held responsible if he has foretold an unfavourable outcome to a case from the beginning.129 But in part the aim is to increase the

doctor's reputation. Patients will more readily entrust themselves to his care if he can tell them not just the outcome of the disease, but its past course and their present condition,130 and the doctor will "justly be an object of wonder."131 The surgical treatises, too, though wary of certain types of ostentation,132 occasionally endorse the practice of forecasting, and not just, for example, to warn the patient of the risks of treatment.133 Thus On Joints speaks of "brilliant and competitive forecasts" with approval.134

The writer of On Regimen in Acute Disease , however, sees the danger of medicine being confused with divination. The reputation of medicine is harmed by disagreements among doctors, which undermine the art to the point where some might even say that it resembles divination or the inspection of entrails and that doctors are like seers quarrelling about the interpretation of omens from birds.135 Prorrhetic 2 opens with an attack on the idea that "marvellous" and exact predictions are possible in medicine.136 The author says that he will not

engage in such "divinations" but will set out reliable signs by which one can recognise which patients will recover and which die.137 Other predictions should be made

The doctors thus evidently used their ability to foretell the future and to retrodict the past as a means of impressing their patients and indeed of building up their practice. Yet there was a risk of the doctor being assimilated to the soothsayer, a risk some Hippocratic writers try to guard against, and which much later Galen repeatedly tells us he still had to contend with.141 Some of the medical men actively sought a reputation for being able to predict the future,142 even while they dis-

sociated themselves from others who, in other contexts, had precisely the same ambition.143

The ambivalence of the relationship between—to use our terms—astronomy and astrology is more highly charged still, and many have simply dismissed the latter as an aberration. The fact that most prominent ancient astronomers, including Hipparchus and Ptolemy, also engaged in astrology is often taken to be irrelevant to Greek science and as evidence only of the failure of the Greeks to be scientific . Yet not to be guilty of gross anachronism, we must take as our explananda not just those parts of ancient mathematics and natural philosophy that we approve or consider fruitful, but the whole of the corpus of work of those who engaged in different branches of those complex and manifold traditions. To ignore astrology would be to miss the insights it can offer both about ancient controversies concerning what those traditions comprised and about the ambitions some theorists entertained concerning some areas that they were certainly eager to include.

That some parts of their work were better grounded than others goes without saying; it went without saying to the ancients themselves, even while they, like us, argued about the criteria of superiority. Ptolemy, for one, clearly distinguishes between the two types of prediction or prognostication to be made from the study of the heavenly bodies: on the one hand, predictions of their movements (astronomy in our sense); and on the other, prediction concerning events on earth.144 Moreover, he explicitly emphasises the conjectural nature and the difficulty of the latter study,145 criticising the excessive claims made

by some past and contemporary practitioners146 and limiting his own discussion to generalisations based on the supposed beneficence or maleficence of various heavenly bodies or their configurations.147 The validity of astrology as a whole was disputed,148 but we should remember that there were similar foundational disputes in many other areas of the inquiry concerning nature, including about astronomical model-building itself.149 Based on a belief in a connection,

The case for it seemed untenable to many,153 but others exploited what seemed to them a splendid opportunity to bring this area of divination too into the orbit of rigorous mathematical disciplines. Even though astrology began in Greece with vague ideas about the influences of the stars such as we find in Hesiod,154 it came to have, in Hellenistic times, an elaborate theoretical framework most of which it owed to astronomy.155 In this, astrology was importantly different both from divination by the consultation of books, for instance (as in the sortes Homericae or Virgilianae), which involved no study of natural objects at all, and from hepatoscopy, for there the marks on the surface of the liver that the diviner studies are, as Rufus gives us to understand, of no significance for the medical man.156 The use of planetary tables and of spherical geometry is common to astronomy and astrology, both of which engage in the determinations of planetary positions. Initially just impressionistic, astrology came to have claims to be, in some respects at least, an exact study. Certain assumptions (and they were of course the crucial factor) had to be made about what were claimed as the natural effects of different heavenly bodies or at least about how they could be used as signs; and the application of general rules to individual cases was always a matter of the astrologer's own judgement. Yet planetary configurations could be worked out with impeccable mathematical precision and deductive rigour. In that respect

the casting of horoscopes or genethlialogy could claim to be more exact than most areas of medicine or of natural philosophy. The symbiosis of the two studies of the heavenly bodies is remarkable, for on the one hand the aspirations of astrology helped to keep elementary astronomy alive, and on the other the prestige of astrology depended partly on its incorporating the same mathematical procedures used in astronomy. It was thanks, in part, to his mathematics that the "mathematician," as he was often known, won his reputation as a superior diviner.

Finally, the importance of astrology, for Ptolemy at least, was underpinned by its ultimately moral aim of helping us view the future with calm and steadiness.157 But this moral concern is in no way exceptional in the inquiry concerning nature in the ancient world. On the contrary, as we shall see in due course,158 it is a recurrent one. For now, we may simply note that, following Plato, Ptolemy held that astronomy too is good for the character,159 and that following Aristotle, Galen claimed that the study of the parts of animals reveals the wonders, beauty, and goodness of creation and instils in the student true piety towards its wise and benevolent creator.160

Our later investigations will give us ample opportunity to consider aspects of Greek science where traditional beliefs and attitudes are less prominent in the background or even—as often with Archimedes, for instance—quite irrelevant. This first study has been deliberately directed at a set of highly problematic and difficult topics for science, where myth, religion, and ritual provided the usual resources for stabilising belief. Those who engaged in the inquiry into nature—those who invented that inquiry—exhibit some well-grounded confidence in their ability to provide an alternative, naturalistic, rationalist framework for understanding. At the same time they often, it may seem to us, fail to recognise the limitations of what they had achieved or of what they could hope to achieve, both where the questions they raised are simply not amenable to their approach (certainly not in their day, and in some cases not even now) and where the answers they proposed are vulnerable, if in different ways, to criticisms similar to those they themselves brought against earlier beliefs.

Yet that recurrent phenomenon may be understandable in part at least in terms of the problems the new investigation into nature faced in establishing itself alongside and in confrontation with other more traditional sources of wisdom, comfort, and understanding. Some of the investigators themselves claimed that theirs was the way not just to understand nature, but to gain a correct apprehension of the divine:161

true piety consisted in the type of study in which they were themselves engaged.162 Others did not so much transmute as undermine traditional systems of belief, attacking in particular some of the authority figures who sustained them—the prophets, diviners, purifiers, and the like.163

But, implicitly or explicitly, the investigators into nature laid claim to a new kind of wisdom, a wisdom that purported to yield superior enlightenment, even superior practical effectiveness, and in part (though this can only be justified by the detailed studies that follow) they were surely right in their conviction of their own originality and their belief in the potentiality of the approach they adopted, even though their strengths had their corresponding weaknesses, especially in the excesses and exaggerations of many of those claims. They were wise men of a different kind, unlike the old seers in important respects, though again much closer to them in others than aspects of the self-image they projected would lead one to expect. They successfully demystified many a mythical, mystical, symbolic, or traditional assumption. For all that, the science they presented was, in some cases, no more than the myth of the elite that produced it. These are themes that will be explored more fully in the remainder of this book.

Comparative Perspectives

Innovativeness, let it be emphasised at the outset, is, of course, no prerogative of the ancient Greeks.3 Rather, it is manifested to a greater or lesser degree by every human society. This is not to deny the enormously conservative tendencies in what are often not inappropriately called "traditional" societies. Yet first, a measure of adaptability is, no doubt, a necessary condition for survival. Secondly, the rich store of detailed informal knowledge, for example of plant kinds and their uses, of animals and of animal behaviour—the whole of what Lévi-Strauss discussed under the rubric of "concrete science"4 —must be seen as gradually accumulated over extended periods of time. So too were the technological advances that brought about what Gordon Childe called the "urban revolution" in the ancient Near East.5 All of this presupposes sustained inquisitiveness and intellectual acquisitiveness, even though the additions made to the store of knowledge may well not be identified, let alone recorded, as such. Where the ancient Greeks eventually developed a minor genre of literature devoted to the "first discoverers,"

than to figures securely framed as what we should call historical personages—though we should note that the Greek "first discoverers" also include plenty of the former as well as of the latter: Prometheus and his like, as well as Archytas, Archimedes, and theirs.7

Even though, as I noted in Chapter 1, tradition is what is usually appealed to both to justify certain ways of behaviour and to block certain types of question, what is included in concrete science or as common knowledge is, nevertheless, subject to adjustment—to the tinkering characteristic of the bricoleur ,8 if not to planned or self-conscious revision. Even the actors' own protestations of the sacrosanctity of the tradition do not preclude the possibility of aspects of that tradition undergoing modification and scrutiny, even if not necessarily formal or institutionalised scrutiny. In two areas especially, recent anthropological work has thrown light on the degree to which innovations are possible, occur, and are even inevitable within what is still conceived as an unaltered tradition. First, such studies of oral literature as Goody's on the myth of the Bagre,9 Phillips' on Sijobang,10 and Finnegan's general analysis11 have demonstrated the tolerance of variation in what is still thought of, and unreservedly claimed to be, precisely the same nar-

rative.12 Secondly, using fieldwork in Thailand, Tambiah has recently investigated the outer limits within which rituals may be altered and adapted to new politico-religious ends and still be apprehended as unchanged.13

The inference to past innovation is even more compelling where its intellectual products are more obviously exceptional, as is the case with some of those of ancient societies, for example, the mathematics and astronomy of Babylonian civilisation or the mathematics and medicine of ancient Egypt. Here our evidence is written, though some of the extant didactic mathematical texts give glimpses of the oral situation of instruction within which they were presumably used. Thus in the Rhind mathematical papyrus from Egypt we read: "If the scribe says to thee '10 has become 2/3rds and 1/10th of what?' let him hear . . . " and there then follow the workings and the conclusion.14

Admittedly, we are usually in no position to chart the stages of the developments that occurred, let alone to identify individuals responsible for particular features of them. Nor should we Whiggishly assume that there was a single continuous development, a sustained onward-and-upward march, as opposed to periods of advance interspersed with others of retrenchment, stagnation, and regression. But even though we are in the dark about most of the circumstances surrounding the growth of mathematics, astronomy, and medicine in the ancient Near East, the documentary evidence we possess for the end

results is substantial, and those end results themselves certainly imply innovation at some stage. It is worth laying some stress on that feature of those great civilisations, since it tends to be brushed aside when attention is focused on their undoubted elements of conservativeness and of deference to traditional authority, both in the sense of deference to the customary authority figures and in that of deference to the past.

Those elements, too, are, to be sure, very prominent and they can be exemplified in many different aspects of Egyptian and Babylonian culture, ranging from the social and political sphere to medicine and astronomy themselves. True, our Greek sources typically exaggerate the contrast between, for instance, Greek and Egyptian attitudes. Herodotus,15 Plato,16 and Aristotle17 are among those in the classical period who remark on the conservative tendencies in Egyptian culture, on which Plato, especially, often commented with approval.18 Later, Dio-

dorus19 reported that Egyptian doctors ran a risk of legal sanctions—the death penalty, no less—if they deviated from what the sacred medical books laid down. Moreover, in the case of medicine we do not, of course, have to rely simply on what the Greeks tell us: the extant Egyptian medical texts themselves exhibit the enormous strength and authority of tradition. We have a striking example of this in the Edwin Smith papyrus, a text which preserves medical lore handed down over an extended period, where the glosses contained in the version we have represent the attempts by the final redactors to explain difficult points in the diagnoses of the cases and the treatments prescribed.20 Clearly the chief aim of later physicians was the conservation and faithful interpretation of the wisdom of their predecessors.21

Even so the point should not be over -emphasised. We may turn to another Greek text to suggest another side to the picture, a report in Herodotus which, despite its patent inaccuracy at certain points, nevertheless has a lesson to teach us. Herodotus says that, lacking doctors, the Babylonians take their sick down to the marketplace so that any passerby may comment and say how he or anyone else he knew recovered from a similar illness.22 Now it is just not true that the Babylonians had no doctors—though those who acted as such may have looked to Herodotus less distinctive than Greek or Egyptian physicians.23 Yet whatever the flaws in Herodotus' story as a historical report, it serves to remind us that even in generally conservative societies there may be, and often is, a certain open-mindedness about therapy, a readiness to canvass diagnostic opinion and to listen to suggestions concerning treatment.24

Greek Innovations and Egotism

I have been at some pains to suggest that a certain innovativeness may, indeed must, be supposed to have been at work in the ancient Near East—including in fields that are directly relevant to the understanding of what we call natural phenomena—even though we are usually in no position either to date the innovations or to identify their authors. But the significance of that point, in turn, should not be missed. Even though, obviously, innovativeness is no Greek prerogative,

that does not mean that the manifestations of innovation are everywhere the same. The extant remains of Egyptian and Babylonian medicine, mathematics, and astronomy can be combed in vain for a single example of a text where an individual author explicitly distances himself from, and criticises, the received tradition in order to claim originality for himself;25 whereas our Greek sources repeatedly do just that. Even where we can infer innovations in Egyptian or Babylonian texts, that is to say, it is not the style of their authors to publicise the fact or even to mention it.26

The contrast with Greek writers is striking, and we are dealing, of

course, with a phenomenon that extends well beyond the domain of the inquiry concerning nature. Homer's authorial personality remains discreetly veiled—though even Homer has Telemachus remark that it is the newest songs that men praise most.27 But Hesiod writes himself into his poems and states his credentials directly. He has learnt from the Muses, who know how to tell the truth—as well as lies that are like the truth.28 He has, moreover, been victorious, he says, in competition with fellow poets.29 Though certain reservations should, no doubt, be entered in connection with Snell's theses concerning the "discovery" of the mind and the "rise of the individual,"30 he successfully collected, under the latter rubric, a wealth of material relevant to the emergence of the Greek authorial ego , notably material from early lyric, from that set of strongly individuated and aggressively innovative poets that includes Archilochus, Sappho, Alcaeus, and their successors.31

Continuing and extending that tendency,32 the natural philosophers and medical writers emerge, indeed thrust themselves forward, as strong and distinct personalities. Even when Xenophanes tells us that no man can know for sure about the gods and the other things he discusses, he makes us aware that it is he who is talking:

goddess's instruction to Parmenides takes a form that marks a far greater distancing from that tradition, for she tells him to "judge by logos the much-contested refutation pronounced by me."37 It is, we should say, the strength of the deductive argument, not the appeal to divine authority, on which Parmenides depends to secure conviction in his hearers, even though he equates the latter with the former. In Ionian speculative natural philosophy, too, Diogenes of Apollonia begins his work by telling us about his method and again leaves us in no doubt that it is his : "it seems to me that every logos should begin from an incontestable starting-point."38

Egotism, to be sure, is not necessarily connected with innovativeness,39 but the two often go together in early Greek philosophy, especially in claims to set forth the truth that had eluded everyone else. One after another, the major pre-Socratic philosophers from Xenophanes onwards state or imply that no one else had got the answers right, establishing their own presence in the text with copious criticisms of other writers, their predecessors or contemporaries, named or unnamed, at the limit by criticisms of what everybody else believed. Xenophanes attacks Homer and Hesiod by name for "ascribing to the gods everything that is shameful and a blame among men, thieving, adultery, and deceiving each other."40 Heraclitus, in turn, hammers

Xenophanes along with Hesiod, Pythagoras, and Hecataeus for "much learning,"

These features of early Greek philosophical writing are well known and need no elaboration. The corresponding points in relation to early Greek medical texts are in some respects more complex, reflecting in part the heterogeneity of the extant treatises, but we can give examples of both egotism and innovativeness—and their conjunction—in works of very different types. We may take first such comparatively polished or pretentious exhibition pieces,

language and reality, no less,46 and the following chapter offers a definition of medicine with two more first-person-singular verbs: "first I shall define what I take medicine to be."47 And apart from his obsessive self-advertising, he lines himself up firmly on the side of innovation: "it seems to me that it is the aim and function of intelligence to discover what was unknown before, wherever such a discovery confers a benefit over ignorance."48

First-person-singular statements appear with great frequency also in treatises that display a much greater knowledge of actual clinical practice. On Airs, Waters, Places , for instance, gives us in the opening chapter a summary of what the medical student should consider, the effects of the seasons, the changes in the weather, the effects of warm and cold winds, the properties of waters, the position of the city, and so on, and then proceeds: "I shall explain clearly,

The severely professional Epidemics , especially, presents a particularly intriguing case. Thus in book 1, chapter 4, of the second "constitution," we read: "I know of no case of

careful not to conclude, from those references by themselves, that the "I" is the same individual in each case. These books generally reflect several physicians' experience: they were built up by a process of accretion and have been subject not so much to interpolation (for there is no definite original text into which interpolations have been inserted) as to a series of additions by authors who were no doubt seeking to improve their usefulness. The process may not have been too dissimilar from the way in which modern textbooks of pathology or physiology are subject to successive (if more easily identifiable) stages of rewriting and reediting in the light of what is taken to be the latest knowledge. Evidently some of those Greek doctors who inserted their contributions sometimes chose to vouch for a particular piece of information by indicating that it came from their personal observations. The chief point, in any event, is this: unlike the Egyptian case-histories in the Edwin Smith papyrus and elsewhere, where the authors do not intrude to vouch for their opinions or observations personally, just such claims punctuate our extant Greek clinical records.

But as in philosophy, so too in medicine first-person statements may point up claims for originality. Three treatises of rather different types that exemplify this are On Regimen in Acute Diseases, On Fleshes , and On Regimen . Thus the author of On Regimen in Acute Diseases , who holds forth on the shortcomings of previous writers, especially the authors and revisers of the work called Cnidian Sentences , begins his own positive account of diet in acute diseases with the claim: "it seems to me to be worthwhile to write down such matters as are not yet known to doctors even though they are of great importance and bring great benefits and injuries."54 On Fleshes draws a contrast between the opening chapter of the work, which sets out certain preliminary considerations for the study of the formation of the human body and where the author says he draws on "common opinions," and the sequel, expressing his personal views: "now I myself declare my own

opinions."55 On Regimen , especially, describes his theory of the balance between food and exercise as a discovery,

The surgical treatises, too, are often much concerned with innovation in surgical practice. On the one hand we find passages praising inventiveness57 and claiming or implying that the only correct treatment is that which the author himself sets out.58 On the other, these authors also frequently criticise some of their own colleagues for their misplaced striving after effects.59 The opening chapter of On Fractures ,

for instance, first criticises practitioners who "get a name for wisdom"60 for their over-sophisticated treatments of fractured arms, and then remarks on the general problem: "Many other parts of this art are judged thus: for men praise what seems outlandish before they know whether it is good, rather than the customary which they already know to be good; the bizarre, rather than the obvious."61

This is one of several treatises in which the new point that the authors present as their contribution is, precisely, the dangers of the newfangled in medicine: texts that are trebly suggestive, first because of the indirect evidence they supply concerning the positive value set—in some quarters—on originality in medical practice, secondly because of the way they exemplify the strong authorial presence that is such a distinctive feature of early Greek medical texts, and thirdly because they illustrate how the question of whether or how far to follow tradition was openly contested.

The treatise On Ancient Medicine , especially, takes as its chief theme the need to return to the tried and tested methods of earlier

medical practice, what the author himself calls ancient medicine.62 His main endeavour is to refute those who try to base medicine on the new 63 method of postulates (or "hypotheses") and who thereby, in his view, drastically oversimplify the problems. Yet while allying himself with the past, he constantly uses expressions that signify his personal view. "I at any rate have not thought" (

pages in the Heiberg (CMG ) text, this author uses the first-person-singular pronoun no fewer than thirty times, as well as first-person-singular verbs,

Several Hippocratic authors thus engage in an active debate on innovation in medical theory and practice. Their public, or at least parts of it, were evidently also much taken by the latest fads or fancies in treatment. On Regimen in Acute Diseases , for instance, criticises laymen for not appreciating true excellence in treatment but, rather, being preoccupied with praising or blaming strange remedies,70 and Precepts chides patients who ask for treatment that is outlandish or obscure, though this writer puts it that they should not be punished for this prejudice, merely disregarded.71 The writer of On Joints refers to the wonder and delight registered by patients and their friends at specially intricate techniques of bandaging (a new fad, presumably) though he goes on to remark that after a time the patients become bored with wearing their complicated bandages.72

Today we can understand a similar twentieth-century obsession with the latest fashion in treatment in part in terms of the effects of certain identifiable pressures, not least those from the sales forces of pharmaceutical companies. But in the ancient world there were no equivalent pressures, but just doctors trying to impress patients—or potential pupils—and patients in turn making demands on doctors.73 In these circumstances the phenomenon we encounter in Greece is more surprising, particularly since to justify the use of new therapies the ancients had only insecure analogues to the argument that appeals to the full apparatus of "modern medical science."74 Unlike in natural philosophy—where what was at stake was merely a matter of belief and not usually one of immediate practical consequence—the treatment a patient received from a Hippocratic or from any other type of healer might, at the limit, make the difference between death and recovery. In this context we might expect a reasonably deep-seated caution, if not conservatism, to prevail, and indeed some aspects of our Hippocratic evidence suggest just that.75 Yet the degree of innovativeness tolerated, even favoured, is striking, nor is this just a matter of

fancy bandaging, nor one where, the case being desperate, any remedy is worth trying. Among the surgical practices the Hippocratic doctors elaborated are some of the daunting, if not foolhardy, techniques I mentioned in Chapter 1, the forcible straightening on the Hippocratic bench,76 and the succussion of the patient, often upside down, used not just in certain cases of reduction but even, amazingly, in some of difficult childbirth.77 Some of those who practised succussion are accused of doing so just for the performance, "to make the crowd gape": that is the criticism made in chapter 42 of On Joints , although that treatise goes on itself to endorse and recommend a modified version of succussion in some cases.78

In the prominence of the authorial ego, the prizing of innovation both theoretical and practical, the possibility of engaging in explicit criticism of earlier authorities, even in the wholesale rejection (at times) of custom and tradition—in all these features there are marked contrasts of degree, if not also in kind, between parts of early Greek, and most ancient Near Eastern, speculative thought, for example, not just in styles of presentation but also in the substance of what could be presented and discussed. These are far from being the only contrasts that we might consider in relation to the study of nature, nor are they features that are confined to that general domain of inquiry. But they raise a set of problems that any evaluation of the early stages of science must confront, even if we must acknowledge that the issues stretch far beyond the range of our discussion here.

The Role of Literacy

One thesis already in the field—that aims to explain the growth of both critical and innovative attitudes, both in their ancient Near East-

ern manifestations and in their Greek ones—has it that the key factor is the development in techniques of communication. One influential statement of such a thesis is the article by Goody and Watt entitled "The Consequences of Literacy,"79 and Goody has subsequently returned to the issues on more than one occasion, modifying his thesis especially on the nature of the contrast between Greek and Near Eastern achievements and focusing increasingly on the latter.80 Thus Goody argues first that many of the pre-Greek achievements depend essentially on the existence of written texts, and secondly that so far as Greece itself is concerned, the spread of literacy made possible by the introduction of an alphabetic system of writing is all-important. Literacy by itself, of course, does not discriminate between those who composed Egyptian medical texts or Babylonian astronomical cuneiform tablets on the one hand, and Hippocratic authors or pre-Socratic natural philosophers on the other.81

Many questions raised by this thesis are controversial and beyond the scope of our discussion here, notably the historical problems surrounding the development of the alphabet itself, the contributions of various Semitic groups, and the range of possible intermediaries between them and the Greeks,82 as well as the thorny issues in dispute between Havelock and his opponents on the timing and extent of the spread of literacy within Greece itself.83 But three points can readily be

agreed. First, the existence of written texts obviously permits a different kind of critical inspection, more leisurely and more formalised than is possible with spoken discourse.84 It permits , though it does not necessarily dictate , critical scrutiny, since the existence of written texts may and often does positively inhibit it,85 a point that has been made often enough by anthropologists (for example, by Shirokogoroff in his study of the psychomental complex of the Tungus)86 and by Orientalists (for example, by Oppenheim in relation to Mesopotamian

medicine)87 and the validity of which for late Greco-Roman antiquity is obvious enough.88 Secondly, when recorded in writing, innovations have a greater chance of being recognised as such and of being cumulative.89 Thirdly, certain types of writing that are taken to be characteristic of early literacy (tables, lists, formulas, recipes) may stimulate certain types of question—for example, problems of classification—and thus affect cognitive processes themselves.90

All these are positive contributions to our understanding of these complex questions. Yet reservations about how far Goody's thesis, and others like it, go to resolve our main problems in relation to early Greek speculative thought must also be expressed. One area where some of the points Goody made can be tested, but about which he has so far had comparatively little to say in his three main discussions, is mathematics, where, as we have already noted, we have extensive Egyptian and Babylonian texts as well as Greek ones—the last beginning much later than the other two, of course.91 Each of these three cultures developed its own arithmetical notation or notations, the Greek, like the Egyptian, being a decimal, the main Babylonian a sexagesimal, system. But as Goody himself has remarked,92 mathematics rests on universal logographic symbols, not on restricted phonetic

ones. In that respect all three notations are equivalent. In any case none has any evident superiority over the others on this score that could be compared to the superiority of an alphabetic system of writing over syllabaries, let alone over pictograms. Indeed, if there are advantages, these lie with the Babylonians, for their notation incorporated the place-value system and so revealed what the Greek use of letters for numbers conceals, namely, the equivalence of operation involved in the multiplication and division by the base and by its powers, by 10 and by 100, or, in the sexagesimal system, by 60 and 60² .

The fact that in all three cultures the development of complex mathematical manipulations depended on the existence of some written notation can certainly be taken to confirm that element in Goody's thesis. The role of tables here is particularly clear. Like our multiplication tables, tables of reciprocals, for instance, such as we have from Babylonia,93 encapsulate knowledge that is itself decontextualised and that can be put to a variety of uses in various concrete situations. Yet Goody's thesis by itself does nothing to help explain certain major differences in the mathematics developed in these three cultures; it can hardly explain them since, as noted, the technical processes of communication involved, the notations, are in the crucial respect broadly equivalent.

Take one important development that is confined, so far as we know, to Greece, namely, that of the explicit notion of, and demand for, demonstration or proof.94 By proof I do not mean the confirmation or checking of a result that regularly occurs in Egyptian arithmetic, for example, and that is often translated into English, legitimately enough, as the "proof": the scribe works his way through to the solution of a

problem and then checks that his result is correct.95 What the Greeks eventually developed was the concept of proof in the more rigorous sense of demonstration by deductive argument from clearly identified premises: and the qualification "eventually" should be stressed, since this was a gradual and hard-won development and not a concept available to the Greeks in, say, the days of Thales or Pythagoras.96 There is accordingly no call whatsoever in this respect (or indeed in any other) to speak of the Greeks as endowed with some special natural characteristic, some distinctive mental ability, as those who fantasised about the "Greek miracle" liked to do.

Moreover, in connection with the development of the concept, and practice of, mathematical proof, there is already by the late fifth century B.C. a concern with foundational problems, not the famous Grundlagenkrisis postulated by some historians who saw Greek mathematics as brought to an abrupt standstill when the incommensurability of the side and diagonal of the square was discovered,97 but more simply an interest in the elements , that is, the fundamental principles

which the rest of mathematics presupposes and on the basis of which the rest of mathematics can be built up. From the very first—that is, from the work of Hippocrates of Chios, sometime around 430 B.C. —the attempt to systematise mathematics depended on decisions as to what to take as the elements. By the fourth century we know that Greek mathematicians were actively exploring the possibility of alternative starting-points to geometry,98 though not (despite what has sometimes been claimed)99 the possibility of alternative geometries: when Aristotle mentions the possibility of denying that the internal angles of a triangle add up to two right angles, it is not in connection with any proposal to construct an alternative geometry on the basis of this denial.100 After Euclid, too, the question of what should be included among the axioms continued to be disputed, as the particularly well-documented and famous controversy over the status of the parallel postulate illustrates sufficiently conclusively.101

None of these developments (some of course quite late) can be paralleled in extant Egyptian or Babylonian mathematics, even though, let me repeat, we can infer that they too were highly innovative in many other respects. None depends simply on technical advances in notation and the like. They do, however, all have fairly obvious affinities with the features I exemplified in early Greek natural philosophy and medicine. In mathematics, too, there is not just manifest disagreement between rival views and the demand for validation, but also, we may infer, a fair degree of egotism. To be sure, in this case, with fewer early primary texts at our disposal, we cannot cite extensive passages to illustrate the use of the authorial ego—not before Archimedes, at least.102 Yet even in the wreck of pre-Euclidean geometry we have enough reliable evidence for the individual contributions of named theorists—for example, on special problems such as squaring the circle or the duplication of the cube,103 or in the discovery of particular theorems or

their proofs104 —to be fairly confident that, like early Greek philosophers and medical writers, Greek mathematicians were often ambitious innovators and proprietorial towards their own ideas.

The Argument from Politics

Elsewhere, following Vernant and others, I have argued that in addition to other factors that must be held to be relevant, including the spread of literacy, the political dimension is crucial for our understanding of some of the distinctive characteristics of early Greek speculative thought.105 Dealing with some Greek attacks on magic in particular, and more generally with the development of a certain openness and dialectical acuteness in parts of Greek philosophy and science (and I stressed then as I do again now that it is not the whole of Greek philosophy and science that can be so characterised),106 I argued that

these reflect the very considerable experience that many Greek citizens acquired in the evaluation of evidence and arguments in the contexts of politics and the law. True, that experience is uneven, far greater in the democracies than in the oligarchies, but it extended also to the latter on a restricted scale, even though the proportion of the population engaged in decision-taking was smaller and the occasions when they did so were fewer.107 It is well known, however, that in some of the democracies that experience could be very extensive indeed, on jury service, in the Assemblies, and in any one of a wide range of offices held by lot or by election.108 Certain aspects of the Greek experience of the pro-

cess Goody called the domestication of the savage mind—a process never, of course, completed, transparently not so in Greece—depend less, I would claim, on technical improvements in communication than on developments in, broadly, the political domain; they owe more to the experience that many Greeks gained there in types of argument and scrutiny than to the spread of literacy among them.109

On the more general issues of the domestication of the savage mind, I shall not repeat my earlier arguments. But there is more to be said on the specific questions we are concerned with here, where the problem presented by the material we reviewed is not so much one of innovation tout court , for to some degree innovation is, we said, universal. Rather, it arises from the combination of the degree of contestability of tradition and of what we may call the pressures towards overt innovativeness, the fashion for, even the obsession with, the novel, familiar enough to us today, but scarcely to ancient civilisations.

Now there are very evidently political dimensions to this issue too. We shall need to come back to these in due course, but three of the most obvious points may be mentioned at once. Clearly, first, innovativeness is just as prominent, or even more prominent, an aspect of Greek political life as of Greek speculative thought, and in the former is no mere theoretical matter, as new ideas could be and were put into

practice in the framing and reform of constitutions and in legislative measures of every kind—a trait often disapproved of, and feared, to be sure,110 but also often greatly admired.111 Secondly, the possibility of dissent from deep-seated traditional views presupposes a certain measure of political freedom of speech, though that measure should certainly not be over estimated.112 Thirdly and most importantly, the revisability of political constitutions and of the laws of various Greek city-states not only parallels, but at points interacts with, the revisability accepted in such other areas as cosmology, religion, and moral philosophy.

Thus political and moral philosophical innovation are often intrinsically related, nor can we doubt, surely, that political revisability helped to release inhibitions about revisability in other domains of thought, even while there may also be feedback from those other domains of thought to political revisability. An extended text in Aristotle's Politics shows that he, for one, recognised the special importance of political innovativeness in relation to other manifestations of innovativeness in other fields, for he remarked on both the similarities and the differences in this respect between politics and such arts as medicine. So far as the similarities go, he notes the argument that the advances that have been made in both domains depend on innovative-

ness, putting it, very much with the voice of Greek rationalism, that all men seek the good rather than the traditional.113 At the same time he points to a contrast, in that politics deals with what is established not just by rules but by custom, so that frequent changes in the laws have the effect of weakening the capacity of the law. Thus in this regard "much caution is necessary."114 But the very contrast suggests that, like many other Greek theorists, Aristotle saw politics as a master art that controls the very framework within which the other arts are exercised. The reason why particular caution is needed as regards innovation in politics is, precisely, that it has such far-reaching repercussions.

To throw light on the problems presented by both the positive and the negative aspects of the pressures towards overt innovativeness in Greece we may investigate some of the contexts in which it is mani-

fested. In Chapter 1 I broached some aspects of the growth and transformation of rivalry in claims to wisdom,

and the Sophistic Debate

Both in the archaic and the classical periods the term

tation for sophia in general. They included seers, holy men, wonder-workers. Men such as Epimenides, Aristeas, Hermotimus,118 were consulted in crises or disasters, plagues or pollutions,119 which shows how wise men may be not just spokesmen of traditional lore but called in where that knowledge faces an impasse—though, to be sure, in offering a way forward any wise man may represent himself as the true exponent of tradition as much as the mediator of knowledge that goes beyond the common store. But already in the sixth century the variety of

The existence of more or less formalised competitions in "wisdom" of one kind or another from as early as the eighth century B.C. provides us with a clue concerning the eventual opening for the inquiry concerning nature.123 I noted that Hesiod already tells us that he won a poetry competition and that there is a similar allusion to such a competition in the Homeric Hymn to the Delian Apollo .124 Trials of skill at solving riddles,

cious early evidence of rivalry (though not in a formal

The "wise man" thus afforded some of the early cosmologists a category within which to work, one that was flexible enough to permit innovation.135 Thus far, extensive parallels for at least some of what we know about Greece can be found in other societies, for instance in the competitions in riddle-solving or in other aspects of wisdom reported from India, Sumeria, Babylonia, and many other parts of the Near East.136 But one important eventual difference in degree, if not in kind—as, again, others before me have stressed137 —is that some of the Greek competitions were a matter of public debate, adjudicated by lay audiences with (as we noted) considerable experience in evaluating arguments in such other contexts as the Assemblies and the law courts. In India, the contests reported in the Upanisads* , at least, are essentially esoteric.138 It was, in general, up to the wise men themselves to claim

victory or to acknowledge defeat.139 As for the ancient Sumerian wisdom debates, recently adduced by Frischer as parallels to the Greek material,140 in them the judgement of the contest is represented as in the hands of a god—Samas* or Enlil.141 However we interpret what that verdict means, it is firmly assigned to non-human authority.

In the Greek context, the speakers often addressed, and had to be intelligible to, a far wider public. The author of On Ancient Medicine , as we noted, insisted that it is "of the greatest importance that anyone speaking about this art should be intelligible to laymen."142 But that in turn involved the layman, in that case in making up his mind about medical theory, in others about physics or cosmology, in yet others

about aspects of morality or even religion.143 There are still rules about winning and criteria for success, but in principle, at least, those rules are entirely open. They are not made to depend on the authority of individuals, human or divine, let alone on the authority of some corporate notion of the past or of what is hallowed by tradition, even though what they do depend on chiefly, the appeal to logos , still cannot be totally dissociated from those who purported to be its representatives. In medicine that meant most of the Hippocratics, though other Greek healers, those in the temples of Asclepius or the itinerant purifiers,144 no doubt refused to enter that kind of debate, to play the

game by the rules those Hippocratic writers themselves laid down. The new wisdom did not, of course, drive out the old, in medicine especially, though it evidently proved its attractiveness at least to a certain kind of audience of those keen, in principle, to judge what was said by the case made out for it, rather than just by the standing of the speakers.145 The double bind on the new-style wise men was that they sought to be not just admired (like athletes) but understood, even while they insisted that what they offered to be understood was no merely common understanding.

In the open debates that we know took place each participant, striving to win, would naturally try to justify his own position and undermine those of his opponents, and one way he might attempt to claim superiority for his own ideas was by stressing their novelty. Moreover, the occasions for display that occurred (both in connection with contests of wisdom and independently of them) did not just permit, but must sometimes positively have favoured open, indeed ostentatious, claims to originality. We know, for example, that the pan-Hellenic games provided one context not just for music, drama, and poetry

competitions, but for other intellectual exhibitions—part education, part entertainment—of various types,146 including lectures not only on morally uplifting or cultural subjects but even on such topics as element theory or the fundamental constituents of the human body.147 We hear, for instance, of the frequent attendance of Hippias at the Olympic games. He took along, according to the evidence in Plato's Hippias Major and Minor ,148 his own poems and prose works and was ready to speak on any subject on which he had prepared an exhibition piece or epideixis , and to answer questions afterwards.149 Gorgias, too, we know, gave speeches at the Olympian and the Pythian games, and according to Plato was prepared to answer questions on any subject anyone cared to propose.150

Most of our specific evidence relates, to be sure, to well-known sophists151 such as the two just mentioned, and accepting the sophists as making any serious contribution to developments relating to science still presents difficulties, since discussion still continues to be concentrated rather narrowly on the work of a small group of the most famous individuals, beginning with Protagoras, and to be preoccupied with the criticisms that Plato brought against them. These criticisms pose a major obstacle to our understanding, since he figures so promi-

nently among our early sources of information.152 Yet we must recognise that there was far more to what is called the sophistic movement than the work of the named individuals Plato attacks or even of the generality he abuses. The category of sophist, in Plato himself, as well as elsewhere,153 is far from hard-edged, and there were important over-

laps not only between sophists and natural philosophers but also and more especially between sophists and medical writers or lecturers.154 There is a permeability in those categories, as well as a permeability in the audiences the individuals concerned took as their targets.

Certainly the extant medical texts yield excellent evidence that

some medical writers fought hard to differentiate themselves both from those they called "sophists" and from what they call "philosophy." The writer of On Ancient Medicine , as we saw, emphasises the point when he rejects speculative theorising about the nature of man, where he specifies that it is not just what he calls sophists but also doctors,

other reasons because the same man never wins the argument three times in succession, but whoever happens to have the glibbest tongue in front of the crowd: important, if well known, evidence for the existence of those competitive lectures on physiology judged by a lay audience.159 It is clear that some of the medical texts that seek to distance themselves from those that offered general disquisitions on topics marginally relevant to medicine have more in common with the works in question than might seem likely from the way they set out to stress the distance.160 Moreover, as we noted earlier, there are other texts that do not dissociate themselves from the sophistic epideixis , but follow that model and exemplify it. We have mentioned On the Art and On Breaths as the two most striking cases.161 The reaction of an earlier generation of commentators was to suggest that maybe either Protagoras or Hippias himself wrote On the Art .162 That is unlikely, in all conscience, but it was certainly not just foolish of Theodor Gomperz and others to entertain such a possibility.

On Breaths and On the Art may be taken to establish that the sophistic epideixis marks one extreme end of the spectrum that our extant Greek medical treatises represent. Those treatises do form a spectrum : there are important distinctions to be drawn between more, and less, popular works, between general lectures and practical manuals or

collections of notes (for instance), between authors with more, and less, clinical experience, or with none at all. But the extension of that spectrum as far as the sophistic epideixis can throw light on at least some aspects of our specific problem concerning what I called the pressures towards overt innovativeness. If we turn back to the sophistic epideixis , three features stand out. First and most obviously, in the context of an exhibition performance, whether at one of the great Games or on some other public occasion, caution and reserve are not likely to be the most highly prized qualities. On the contrary, every effort will be made to attract and hold an audience, to make the "sales pitch" as effective as possible. This was, after all, one of the chief ways in which teachers attracted fee-paying pupils.163 We expect, and we duly find, in examples of the genre, both from Gorgias and in the Hippocratic Corpus, a striving after originality as well as after effects of every kind.164

Secondly, from the side of the hearers, we may imagine that most were aware of, and so must surely to some extent have discounted, the elements of exaggeration in this kind of performance. Although the analogy should certainly not be pressed too far—and maybe Huizinga did press it too far165 —the occasion of the sophistic epideixis has some of the razzmatazz of the fairgound sideshow.166 Most of the audience at Delphi and Olympia were away from home, and all must have been

conscious of the contrast between festival and everyday experience. Certainly the element of playfulness is commented on directly by Gorgias at the end of his Helen .167 In Thucydides too, when in the Mytilenean debate Cleon is made to chide the Athenian Assembly for their lack of seriousness, he puts it that they are behaving like an audience at a performance of sophists,168 and Thucydides himself underlines the seriousness of his own historical enterprise by insisting on the contrast between it and the competition pieces of earlier writers of chronicles,

The point extends to the inquiry concerning nature and to medicine. Exploiting what became a standard device to put down opponents, the author of On Ancient Medicine contrasts his own serious interests in the art with their speculations, which, in his memorable phrase, belong rather to painting than to medicine.170 Plato too undercuts all attempts at accounts of the changing world of becoming—his own included—by categorizing them as a mere pastime,

whole of early Greek science just as fun—though that would suit Feyerabend as well as Huizinga.172 At the same time we should not ignore what the signs of speculative playfulness in parts of it can tell us about the aims of authors and the expectations of audiences.

Thirdly and more generally, it is worth emphasising that some of our Greek material relates to contexts, such as inter-state games, where at least some of the constraints that existed within any given city-state were suspended—though not all were, and some additional ones were operative. Again, of the main groups of "intellectuals" concerned, nearly all of the most notable "sophists," many of the doctors, and indeed quite a number of the natural philosophers too had spheres of influence that were not confined to a single state. They could and did move freely from one city to another, both simply to earn their living and, if need be, to avoid political trouble. That is, after all, what Aristotle was to do when he withdrew from Athens in 323 B.C. , and it was probably what most people expected of Socrates.173 Here too the link with politics is clear, and while this aspect of political pluralism no doubt facilitated, and may even have been a necessary condition of, intellectual innovativeness, we should not underestimate the possible influence in the reverse direction, the effect that such intellectual innovativeness could and did have on the development of political pluralism.174

Far more than their counterparts in most other ancient civilisations, Greek doctors, philosophers, sophists, even mathematicians, were alike faced with an openly competitive situation of great intensity. While the modalities of their rivalries varied, in each the premium—to a greater or lesser degree—was on skills of self-justification and self-

advertisement, and this had far-reaching consequences for the way they practised their investigations as well as on how they presented their results. To be sure, to stress the novelty of your own ideas was not the only possible tactic to adopt in such a situation. Some medical writers, as we saw, took the opposite stance, criticising newfangled theories and treatments and siding with what they represent as traditional methods: yet we also found that when the author of On Ancient Medicine takes that line, his arguments—and it is to be noted that he does argue —are punctuated by expressions that underline his own authorial presence. The temptation to claim to introduce new ideas and practices was there and often not resisted—it was, indeed, yielded to with some abandon. As I remarked earlier, new medical treatments could not be justified with appeals to the authority of "modern medical science"—to the outcome of laboratory tests and the like—even though some ancient doctors were certainly not above attempts to mystify their clients with esoteric talk of the supposed humoral or elemental analysis of drugs and other therapies.175 But since there were no legally recognised medical degrees or qualifications for them to cite as basic credentials, they had to start further back, as it were, and rely more on the force of direct argumentative persuasion to get remedies, new or old, accepted.

To win and hold an audience demanded a strong personality and the gift of the gab, whether in the surgery or in the public lecture or debate: while those contexts no doubt look very different to us , in Greece they were readily connected.176 You could not, or at any rate you did not, if you were an exponent of Hippocratic rationalism, simply

shelter behind, or assimilate yourself to, the "tradition"—at least not without justifying your so doing. We know from the treatise On Diseases book 1,177 as well as from a famous text in Plato's Laws ,178 —that some doctors might expect to have to justify their diagnoses and treatments not just to other doctors (behind the scenes, as it were), but to and in front of their patients and their patients' friends and relatives, sometimes with other doctors present seen as rivals eager to take over the case if the opportunity arose.179 Thus On Diseases 1 provides tips on how to deal with the veritable cross-examination you might have to withstand.180 There was no deference to the professional in the white coat. Yet externals were not irrelevant. Another Hippocratic work, Precepts , warns the doctor against the use of luxurious headgear and exotic perfumes to impress: that clearly indicates where the temptations lay, even though this particular author says firmly that they should be resisted.181

The natural philosophers did not similarly have to amaze their audiences to get them to take their medicine. They were not competing for patients, though they were for pupils—and fame. Yet Empedocles at

least, who was the only prominent early cosmologist, so far as we know, to have some of his work delivered by a rhapsode at Olympia,182 was certainly not easy to outdo in showmanship. "He liked," as Guthrie put it,183 drawing on Diogenes Laertius, "to walk about with a grave expression, wearing a purple robe with a golden girdle, a Delphic wreath, shoes of bronze, and a luxuriant growth of hair, and attended by a train of boys."184 But although the styles and contents of their speculations differ widely, what Anaxagoras, Democritus, and the rest have in common with Empedocles is that explicitly or implicitly they too claim to have found the solutions to physical and cosmological problems that had defeated everyone else. However much they differ in their other interests, they were rivals there, and were in business to argue that their own ideas were different from, and superior to, everyone else's.

Both in medicine and in natural philosophy the written text had an important and, as time went on, an increasing role as the object of critical reflection, though (as we noted) the texts, when read, were still usually read out.185 Yet overt innovativeness in speculative thought and the corresponding self-distancing from tradition stem not only from the spread of literacy (by itself no guarantee that such attitudes will be adopted), but also from a complex, pluralistic social and cultural situation. What may be particularly important there is the development of new modes of rivalry and competition, calling for new styles of self-justification. In philosophy too, as in medicine, the individual

often thought of himself as participating in—and sometimes literally participated in—a debate in which the personal contribution of each participant was clearly marked as his , even when he did not go out of his way (as so many did) to stress his originality explicitly.186 When we speak of Greek writers needing to win and hold an audience, audience is often the apposite term, and it may be to that interaction with audiences, and to the development of contexts for that interaction, that we have to look for the chief clues to the understanding of the particular positive and negative modalities of innovativeness in ancient Greece.

Conclusions

My theme has been that one of the striking and distinctive features of much of early Greek thought, particularly when we contrast it with what we know from some other ancient civilisations, relates to the degree of overtness of innovation and of the contestability of tradition. The actual measure of free speech that the political situation secured in different city-states, at different junctures, over different types of political, moral, religious, and cosmological subjects, poses problems of great intricacy that cannot be explored here.187 Yet in the grossest terms, there is certainly a gulf between Athens in the fifth century, even the Athens that prosecuted Anaxagoras and was to put Socrates to death,188 and the Babylonia of Darius or the Egypt of Amasis.189

Rivalry in claims to be wise starts almost as soon as we have any evidence to go on in Greece, and what counted as wisdom was an extraordinarily open-ended and negotiable question. Anyone could set himself up as a philosopher or as a sophist or, come to that, as a doctor. You depended not on legally recognised qualifications (there were none, we said, not even for doctors),190 nor even simply on accreditation—though that was undeniably important.191 What you had to rely on, largely, was your own wits and personality, and they were often judged by the verbal dexterity with which you presented your case, even when such verbal dexterity itself came to be suspect and so turned into a quality that had to be concealed to be fully effective.192 Plato makes the sophist Gorgias say that he could take on and defeat any ordinary doctor in argument, whether in front of the Assembly (in

competition for a post as public physician) or, indeed, at the bedside193 (where again we may remark the ease with which those two contexts are juxtaposed). No doubt Plato means his audience to see this as an exaggerated claim.194 But in ancient Greece, where what passed for medical knowledge was both far less technical and more widely shared than now, the point was not an extravagant one; one of the elements of exaggeration, rather, we might say, is that, to judge from some of our Hippocratic texts, there were doctors who would have been well able to look after themselves in debate, even with a Gorgias. Even those who there appealed to what they represent as tradition, to the good old ways of medical practice, for example, argued to justify doing so. Tradition by itself, in many of the areas we are concerned with, at least,195 carried little authority.196 Pre-Socratic philosophers do not assert that earlier ideas should be accepted simply because of the prestige of those who had first proposed them; no more do Plato and Aristotle. Even those Hippocratic writers who saw the danger as one of an obsession with the newfangled do not base their case simply on appeals to authority figures.

In time, to be sure, the balance between these two, tradition and innovation, was to change very drastically, though I cannot here go into the stages, let alone discuss the possible underlying causes, of this

complex process. We may simply note that from the end of the fourth century, increasingly, a series of great names—some, like Hippocrates, very largely the constructs of the commentators197 —came to be turned into just such authority figures, to whom appeals could be made as some kind of guarantee of the validity of the ideas associated with them. "Hippocrates," Plato, Aristotle, and later Ptolemy and Galen were transformed into such figures, and even though at an earlier period the written texts of Plato (for example) may well have helped Aristotle (for one) to develop and press home his objections to Plato's philosophy, the explicit aim of some of the late commentators was not to criticise those texts so much as to show how they contain the truth. Indeed, the sixth-century Aristotelian commentator Simplicius sought to show how Plato and Aristotle were in substantial agreement,198 just as in the second century A.D. Galen already often aimed to reconcile Plato and Hippocrates.199 One of the principal manifestations of that shift towards tradition200 was, indeed, the turning of the written text into a vehicle for the transmission of authority rather than one for

challenging it—thereby producing the opposite effect to the one Goody claimed for increasing literacy at an earlier period.201

Yet we should be careful not to suppose that the tendency to appeal to the authority of the past was uniform and all-pervasive in natural scientific inquiry, even in late antiquity. While when Galen cites Hippocrates it is almost always to agree with him,202 the reverse is true of Galen's slightly older contemporary, Soranus. On nearly all the occasions when he cites Hippocrates or his followers in the Gynaecology it is to criticise them and to expose their mistakes.203 Ptolemy, too, dissents from Hipparchus often enough, greatly though he admires him.204 Nor should we underestimate the originality of Galen and Ptolemy themselves, for all their repeatedly expressed deference to the past. To say, as was once fashionable,205 that they are just eclectic, is nonsense, though some of their own rhetoric tends to mislead in that direction. Their own contributions to their subjects, both as observers and as theorists, are of the highest order,206 even when they present these as the elabora-

tion of the work of those of their predecessors of whom they most approve.

Down to the sixth century A.D. and even beyond, a Kuhnian tension is still a feature of parts of ancient speculative thought, even though the balance had shifted after the classical period from innovation towards tradition—to innovation mainly within, and represented as faithful to, the tradition, or rather to one or another of the plurality of rival traditions that still continued in most fields of investigation. What in some areas of thought was to alter the balance irrevocably—indeed by the sixth century A.D. had already done so in those areas—was the appeal to a particular text, the Bible, as revealed truth. The shift from reference to the "divine Hippocrates," the "divine Plato," and so on, to reference to the word of God may seem not so great in verbal terms, but it reflects fundamental differences not least in the underlying institutional realities: the creation of a church, the constitution of Christianity as the official religion of the empire, and the availability of a new battery of sanctions that could be deployed against the deviant. But those topics, too, are beyond the scope of our discussion here. What this study has attempted, rather, is to sketch out some of the problems presented by the balance of the tension at the very earliest stages of the Greek inquiry into nature. There in the classical period one crucial development was the opening up of the possibility, precisely, of development—if the oxymoron can be excused, the initiation of a tradition of, precisely, the contestability of tradition.

To conclude that the bias towards innovativeness characteristic of parts of early Greek speculative thought just confirms a Kuhnian verdict207 that what we have here is, after all, not proper science—not "normal" science working within a dogmatic tradition or set of paradigms—is tempting and has an element of truth, but is one-sided and premature. On the matter of its one-sidedness, what that ver-

dict importantly leaves out of account is the stages through which proto-science itself passed. Fifth-century Greek speculative thought was no merely aberrant—rhetorical—interlude, intervening between tradition-oriented Egyptian and Babylonian medicine, mathematics, and astronomy, and again tradition-oriented Hellenistic science. The ancient Near Eastern evidence suggests some of the weaknesses, as well as some of the strengths, of the opposite bias towards conservatism—the negative effects, the constraints, of monolithic authority. By contrast, the early Greek material we have reviewed illustrates not just the excesses to which egotism often led (though it does that) but also some of the positive aspects of aggressive innovativeness, in the canvassing of alternatives and the development of criticism through competition, as debate is opened up between rival theories and attention is focused on their grounds and articulation, indeed, on the question of the nature and foundations of science, medicine, and mathematics themselves. While too much attention paid to such second-order issues may detract from the business of getting on with the inquiries themselves, to pay no attention at all runs the risk of leaving the inquiries blind. A certain self-consciousness in the investigations and an awareness of alternatives, at least of rivals, were tolerably durable legacies bequeathed by early Greek to Hellenistic science, part of what then became, for some, revered tradition. For those early developments themselves to occur, however, what was needed was not just written texts, texts in which the figure of the author may not be visible against the background of the tradition, but (among other things) texts that through a strong authorial presence implied a personal accountability for the claims they contained.

And as to the matter of the prematurity of that judgement, our exploration of the Greek experience in the following chapters will provide the basis for the expression of certain other reservations and qualifications.

Dogmatism in Early Greek Natural Philosophy

One of the first things that strikes a student turning to the beginnings of Greek speculative thought, and first to pre-Socratic natural philosophy, is its dogmatism.14 The wildest generalisations are offered with no suspicion that they may require qualification. True, this impression is partly one created by the doxographical sources on whom we often have to rely. They are concerned to record a sequence of positive theories ascribable to Thales, Anaximander, and the rest, uncomplicated by reservations or provisos.15 Yet this impression is often confirmed when, as for several of the later pre-Socratics, we have more substantial evidence, in the form of original quotations.16

It is not as if there is much divergence, on this score, between otherwise radically divergent figures, such as Empedocles and Anaxagoras. Empedocles, for instance, announces categorically that bone consists of a certain definite proportion of the four "roots" or elements, earth, water, air, and fire.17 Anaxagoras, who represents what is in many ways a quite different, Ionian, tradition of research, is sometimes just as positive in his assertions, for example, on the original state of the cosmos, when "all things were together" and "air and aether held all things,"18 or on the production of earth from water and of stones from earth under the influence of cold.19 Even those who were much later hailed as the forerunners of scepticism, such as Xenophanes and Democritus, were, on occasion, categorical enough.20 Xenophanes certainly states that "there never was a man, nor will there ever be, who knows the certain truth about the gods and all the other things about which I speak" and that "seeming is wrought over all things."21 But elsewhere he is prepared to speak of earth stretching down indefinitely below our feet, of the ocean as the begetter of the winds, and of our all being born from earth and water.22 Democritus, too, though quoted as saying that we understand nothing exactly,

The Hippocratic Medical Writers

For more sustained expressions of doubt and uncertainty we have to turn to our other and more extensive main early source, the medical writers—not that they do not also provide examples of dogmatism to equal or surpass anything we find in pre-Socratic natural philosophy. On this, as on so many other topics, the positions adopted in our extant fifth- and fourth-century B.C. medical texts vary widely—and initially rather puzzlingly—from extreme dogmatism on the one hand to a self-conscious anti-dogmatism on the other.25 How far, we may ask, are these apparently strongly contrasting attitudes to be correlated with different types of treatise, types of writer, types of audience, or a combination of some or all of these? In what respects are the attitudes in question indeed alternative and conflicting, or how far can we suggest a framework of explanation to cover both apparently opposed tendencies?

Dogmatism in the Hippocratic Corpus

We must begin with a fairly detailed review of the modalities and manifestations of dogmatism in the medical writers, since it is against that background that what I have called anti-dogmatism must be evaluated. The treatise On the Art , which we have considered before as an example of authorial egotism,26 shows to what lengths some writers went to protect themselves and the medical profession against any possible charge of incompetence or even of fallibility. Chapter 3 sets out what the author hopes to demonstrate, the word used being apodeixis . Medicine is first defined in terms of its aims, which include "the complete removal of the sufferings of the sick" and the "alleviation of the violences of diseases," and the writer claims that medicine achieves

these ends and "is ever capable of achieving them."27 Against those who demolish the art of medicine by citing the misfortunes of those who die from their illnesses, he counters with a passage that is worth quoting at length:

Chapter 9 proceeds to distinguish between two main classes of diseases, a small group in which the signs are easily seen—where the disease is manifest to sight or to touch, for instance—and a larger one where they are not so clear. In the former group "in all cases the cures should be infallible, not because they are easy, but because they have been discovered."29 So far as the second group goes, "the art should not be at a loss in the case of the unclear diseases too."30 The difficulty in achieving cures stems largely from delays in diagnosis, but this is more often due to the nature of the disease and to the patient than to the physician. The patients' own descriptions of their complaints are unreliable, for they have opinion rather than knowledge.31 "For if they had understood [their diseases], they would not have incurred them. For it belongs to the same skill to know the causes of diseases and to understand how to treat them with all the treatments that prevent diseases from growing worse."32 Again the writer's naive optimism comes out: the nature of our bodies is such that where a sickness admits of being seen, it admits of being healed.33

The breathtaking self-confidence of this treatise is far from unique. Drastically oversimplified pathological, therapeutic, and physiological doctrines—stated with apparently total self-assurance despite the manifest controversiality of the subjects in question—figure not just in

other exhibition pieces, such as On Breaths ,34 but also, for example, in On Affections ,35 On Diseases 1,36 On the Sacred Disease ,37 On Fleshes ,38 On Regimens 1,39 and so on. On the Places in Man , for instance, is a work chiefly devoted to a quite detailed account first of certain anatomical topics and then of a range of morbid conditions and their treatments. Towards the end of the treatise as we have it40 we find a chapter that announces: "The whole of medicine, thus constituted,

seems to me to have been discovered already. . . . He who understands medicine thus, waits for chance least of all, but would be successful with or without chance. The whole of medicine is well established and the finest of the theories it comprises appear to stand least in need of chance."41

On the Nature of Man , in particular, makes repeated claims to be able to demonstrate the theories it proposes.42 While his opponents add to their speeches "evidences and proofs that amount to nothing,"43 the author says that he will "produce evidences and declare the necessities through which each thing is increased or decreased in the body."44 Yet his own positive evidences turn out to be very much of the same general type as theirs, even though their monistic conclusions are more extreme than his. He suggests that what influenced the monistic theorists he attacks was the observation that a certain substance may

be purged from the body when a man dies. In some cases where a patient dies from an overdose of a purgative drug he vomits bile, in others maybe phlegm, and the monists, seeing this, then concluded that the human body consists of this one thing.45 But while destructively the author sets about demolishing monism with powerful dialectical arguments, constructively when he seeks to establish that the body consists of the four humours, blood, phlegm, yellow bile, and black bile, his own chief argument too depends on the simple observation that all four are found in the excreta. This shows, to be sure, that all four are present in the body, but spectacularly fails to demonstrate that they are the elements of which it is composed.46

Alongside the frequent use of the vocabulary of evidence and proof, one of the key terms this author employs is necessity,

same chapter we find: "necessarily, each thing returns again to its own nature when the body of the man dies, the wet to the wet, the dry to the dry, the hot to the hot, the cold to the cold."50 Chapter 4 argues that when the humours in the body are well mixed and in the right proportion, the body is healthy, but that pain occurs when one of them is in excess or defect or is separated off from the others. "Necessarily, when one of them is separated and stands by itself, not only the place from which it has come becomes diseased, but also that where it collects and streams together causes pain and distress."51 Again in chapter 5, having suggested that blood, bile, and phlegm differ to sight, to touch, in temperature, and in humidity, he goes on: "necessarily, then, since they are so different from one another in appearance and power, they cannot be one, if fire and water are not one."52

Clearly, logical and physical, conceptual and causal, necessity are not here differentiated. Many instances represent a conflation of one or more ideas that we might distinguish. Often the underlying idea seems merely to be the claim that something is always or usually the case. At the limit, the addition of the term necessarily appears to reflect little more than the writer's desire to assert his point with emphasis.

Similar uses of the term

including some which, as we shall see later, are otherwise remarkable for their undogmatic or anti-dogmatic traits. Examples could be given from Aphorisms ,55 On Ancient Medicine ,56 Wounds in the Head, On Joints , and On Fractures .57 The treatise On Airs Waters Places , too, frequently presents as matters of necessity the correlations it proposes

between the aspect of a city and the character of its water, or between both of those and the constitutions and endemic diseases of the inhabitants, or even between the political constitution and the character of the people. We may again illustrate very selectively from the rich fund of examples.

Thus we are told that in a city sheltered from the northerly winds but exposed to warm prevailing southerly ones, the water is "necessarily plentiful, brackish, surface water, warm in the summer and cold in the winter,"58 while in a city that faces the risings of the sun, the water is "necessarily clear, sweet-smelling, soft, and pleasant,"59 As for the effects of waters of different types, the writer states, for instance, that "stagnant, standing, marshy water is in summer necessarily warm, thick, and of an unpleasant smell, because it does not flow. But by continually being fed by the rains and evaporated by the sun it is necessarily discoloured, harmful, and productive of biliousness."60 Dealing with physical constitutions and endemic diseases, the writer claims, for instance, that in northerly-facing cities that generally have hard, cold water, the inhabitants are "necessarily vigorous and lean."61 Pleurisies and acute diseases are common, "for this is necessarily the case when bellies are hard."62 Correlating the character and changes of the seasons with the diseases to be expected in them, the writer says:

"If the winter be dry, with northerly winds prevailing and the spring wet, with southerly winds, the summer will necessarily be feverish and productive of ophthalmia."63 Finally, correlating political constitutions and characters, the second half of the treatise suggests, for example, that "where men are ruled by kings, there necessarily they are most cowardly. . . . For their souls are enslaved and they are unwilling to run risks heedlessly for the sake of another's power."64

Even though other generalisations in this treatise are quite often explicitly qualified as holding only "for the most part" or just as being "likely,"

Uncertainty

In diagnosis and therapeutics, in pathology, anatomy, and physiology, the overwhelming impression created by a very considerable body of texts in a wide variety of Hippocratic works is one of their authors overstating their cases, representing as incontestable assertions for which their ground were—and must even have seemed to many of their own contemporaries to have been—tenuous or nonexistent. Yet that is only one side of the picture. Alongside the dogmatic tendencies I have illustrated—sometimes, indeed in the very same treatises—there are signs of tentativeness and caution, a readiness to admit to doubts and to mistakes, a recognition of the rashness of unsupported claims, explicit qualifications concerning how far a general rule applies or about the limits of the writer's own firsthand knowledge, and statements insisting on the inexactness of the whole of medical practice.67 In some cases, where, for example, the healer deliberately records his own errors, we are dealing with what appears to be—to judge from the extant remains of ancient medical literature, non-Greek as well as Greek—a quite unprecedented phenomenon.

We have noted before that criticisms of current medical practice are common in certain works,68 but a critical attitude towards the mistakes of colleagues is of course quite compatible with and often accompanies overconfidence about the correctness of one's own ideas and procedures. In some Hippocratic texts, however, the author explicitly acknowledges that he was himself mistaken. Thus in Epidemics 5.27, which describes the case of one Autonomus who suffered from a wound in the head, the writer remarks: "It escaped my notice that he needed trepanning. The sutures which bore on themselves the lesion made by the weapon deceived my judgement, for afterwards it became

apparent."69 The following chapter refers to the case of a young girl who was also wounded in the head, where trepanning was recognised to be indicated and was in fact carried out, but in this case, the writer says, not enough of the bone was removed.70 The next two chapters describe two further cases where cauterisation was undertaken too late—in one case, we are told, thirty days too late—and both patients died.71

The author (or authors) of the surgical treatise On Joints not only describes some of his own mistakes but specifically notes that one such report is included so that others may learn from his own experience. Chapter 47 remarks on the difficulty of reducing humpback. "For my part . . . I know of no better or more correct modes of reduction than these. For straight-line extension on the spine itself, from below, at the so-called sacrum, gets no grip; from above, at the neck and head, it gets a grip indeed, but extension made here looks unseemly, and would also cause harm if carried to excess."72 He then proceeds:

That the author and his colleagues were at a loss as to how to cure or even help a patient is often admitted in both the surgical works and the Epidemics. Epidemics 3 case 9 of the first series ends an account of a woman who suffered from an attack of ileus with the grim note: "it was impossible to do anything to help her; she died."74 Case 5 of the second series remarks of a man who suffered from a sudden pain in the right thigh that "no treatment that he received did him any good."75 Chapter 8 in the Constitution in this book comments more generally that there was little response to treatment and that purgatives did more harm than good,76 and elsewhere writers in the Epidemics note that if

the treatment had been different, a patient might have recovered or survived longer.77

On Joints , too, often refers to surgical cases where no remedy is possible78 and repeatedly warns that the attempt to reduce certain intractable lesions does more harm than good.79 Elsewhere the surgical writers explicitly say they do not know what to advise,80 or withhold judgement.81 The difficulties and dangers of treatment are mentioned also in other treatises, either in general terms, as in the famous first Aphorism ("life is short, art long, opportunity elusive, experience dangerous, judgement difficult"),82 or in relation to particular remedies, as, for example, the administration of hellebore or the practice of cautery or that of venesection.83

Many works draw attention to the incurability of certain diseases, though the advice they offer differs. Some suggest that the doctor should at least do what he can to help,84 but others warn or instruct

him not to undertake such cases.85 On Fractures 36, dealing with fractures of the femur and humerus, illustrates the dilemma the doctor sometimes faced. "One should especially avoid such cases if one has a respectable excuse, for the favourable chances are few and the risks many. Besides, if a man does not reduce the fracture he will be thought unskillful, while if he does reduce it he will bring the patient nearer to death than to recovery."86 Yet if some of the Hippocratic writers register their unease on this topic, it is important to note that none recommends that those patients whom they cannot or will not treat should have recourse to other modes of healing: none suggests that the sick should turn to the cult of Asclepius,87 let alone try their luck with the itinerant sellers of charms and purifications.

The theme of the inexactness of the medical art is a prominent one in several treatises and of particular interest for our inquiry. We shall be returning later to aspects of this in connection with the use of measurement.88 Here we may simply note the recurrence of the motif in a variety of treatises. On Ancient Medicine , especially, develops the topic at some length. Exactness (

subject can be, and has been, made exact, but perfect exactness (

Other treatises, too, develop similar themes. On Diseases I, which presents a highly dogmatic general theory of diseases based on bile and phlegm,92 states nevertheless that there is, in medicine, no

time a patient will die, nor even whether this will be after a long or a short period."96

On the Places in Man , which asserts, as we saw, that the whole of medicine has been discovered already,97 also observes that there is a good deal of variability in medicine98 and remarks on the difficulties of determining the right moment for intervention.99 Despite the ultradogmatic tone of the physiological and pathological theories in On Regimen ,100 and despite the writer's claim that if one were present and could observe a man stripped and engaging in gymnastic exercises one could know just how to keep him healthy,101 the third book of the treatise opens with a chapter that emphasises that it is not possible to set out exactly the proportions of food to exercise for men in general—because of their differences in constitution and age, and because of such other factors as the positions of cities, the changes in the winds, and the differences in foods, for example between one wheat and another.102 No one, the writer says, has attained absolute exactness, though he claims he has got as close to this as is possible.103 Even the sophistic piece On the Art , which makes, as we saw, extravagant claims for what medicine can achieve,104 includes as part of its definition of medicine the refusal to treat cases "where the disease has al-

ready won the mastery"105 and ends by noting that it would not be fair to expect medicine to tackle the quite intractable diseases or to be unfailing in its remedies in those cases.106

The Purposes of Self-Criticism in the Hippocratic Writers

The material we have surveyed obviously presents difficult problems of interpretation. What are we to make of the different modes and degrees of dogmatism and tentativeness shown in different contexts and sometimes within one and the same treatise, the contrast between the apparently unhesitating self-confidence expressed in some texts and the caution and doubt, the readiness to admit bafflement and error, in others? One possible suggestion might be that the contrast is to be associated with, and explained in part in terms of, the varying aims and audiences of the treatises in question.107 Dogmatism and apparent self-confidence might be the stance adopted by those who addressed a lay public on general topics, whereas in treatises that represent the notebooks of working doctors and that were mainly directed to a professional audience of other practitioners, there would be a greater readiness to admit to hesitation or even to helplessness. Dogmatism would then be a tactic adopted in the context of a sophistic epideixis , often presented in a competitive situation where the winner was acclaimed by the audience of bystanders.108 Confessions of uncertainty, on the other hand, would be limited to, or at least typical of, communications by and for practising medical men, and not for the general public.

The importance of taking full account of the different audiences envisaged by the various types of writing extant in the Hippocratic Corpus needs no underlining. To elaborate some points from our discussion in Chapter 2: many suggestions that a medical man might make to his colleagues—and many ways in which he might wish to make them—would be totally inappropriate for a lay audience. This remains true, even though, as I stressed before, the lay/professional distinction was much less firm in ancient medicine than it is today, and there is ample evidence, from the fifth and fourth centuries, of an extended interest in medical topics—not just as a potential audience, but also as speakers and writers—among people who had no intention of actually engaging in medical practice. Plato would be one obvious example.109

Yet whatever features of this hypothesis we may wish eventually to retain, as stated it clearly will not do, for two main reasons. First we have seen that there are treatises (including some that are reasonably well-defined unities, not multi-author concoctions) that combine a certain dogmatism at some points with an apparent tentativeness at others. By itself this would not be surprising, for it might simply reflect the varying degrees of difficulty of the topics dealt with and the varying degrees of confidence of the authors in dealing with them.110 Yet to that, in turn, it must be said that in several of the cases we have considered, principally from On Diseases 1, On the Places in Man, On Regimen , and On the Art , it could not be claimed that dogmatism is confined to elementary or straightforward topics on which the authors might, with some justification, feel on safe ground. We have only to recall the claim in On the Art that for diseases with visible signs, "in

all cases the cures should be infallible" because they have been discovered. The combination of dogmatism and hesitancy in this and other works suggests a difficulty for any theory based on a clear-cut contrast between dogmatic treatises addressed to a general public and more cautious ones aimed at professional medical colleagues.

A second, more general objection to the hypothesis is that it is in danger of ignoring what most of the treatises we have considered have in common. Admittedly there are clearly identifiable differences between the two ends of what I referred to before as the spectrum represented by our extant texts—on the one hand the epideixis designed for public consumption, and on the other the almost exclusively technical notebooks. Yet there is a case for saying that, in their different ways and to different degrees, both types of production are exercises in persuasion.111 That is obvious enough in the case of the sophistic epideixis . But even those writers who mainly had their fellow-practitioners in mind were also concerned to win their confidence, or at least to make sure that their own credentials were going to be recognised.

There is no reason to doubt the good faith of the author of the chapter in On Joints that sets out his own mistakes so that other practitioners may learn from them. At the same time we should not rule out the possibility that deliberate self-criticism may occasionally be motivated by a desire to suggest a mature experience in the art. Admittedly it seems paradoxical that confessions of failure should be used in order to inspire confidence. Yet for a medical writer to demonstrate that he is well aware of the dangers of overconfidence would have a salutary effect. It would reassure prospective clients that they were dealing with a man who would not rashly undertake risky treatments nor raise hopes of cure unjustifiably. And it would help to persuade professional colleagues that the author was a man of experience conscious of the complexity and limitations of the art.

There is an important contrast here, not just between the more ten-

tative and the more dogmatic Hippocratic texts, but between the former and the claims for unqualified success that are characteristic of temple medicine. In the inscriptions set up in the shrine of Asclepius at Epidaurus it is 100 percent success that is recorded.112 Some Hippocratic writers might well have wanted to dissociate themselves from the implicit claims to infallibility made in religious healing, even while other medical authors represented in the Corpus adopt a tone that rivals temple medicine in self-assurance.

The idea that self-criticism was sometimes deliberately deployed with such an intention cannot be confirmed directly. But it is perhaps suggestive that the main context in which an apparent tentativeness is expressed in certain treatises is in general remarks concerning the inexactness or variability of medicine, as in On Regimen 3 and On Diseases 1. It looks as if the explanation of these apparently mixed cases is neither that the authors are simply expressing a variety of attitudes on different topics, nor that they are merely inconsistent, nor yet that we are dealing with divergent material in composite works. Rather, it may be that even in otherwise dogmatic works, the inclusion of some indication of the inexactness of medicine had become, or was becoming, something of a convention or a commonplace.

If so, we should accept the apparent paradox. Dogmatism is clearly a stance frequently adopted to impress people, especially a lay audience, and especially on such questions as the origins of diseases in general or the constituents of the human body. Yet professions of uncertainty may also have a certain persuasive role, and while detailed accounts of failure in individual cases are confined to the more technical works that record actual clinical practice,113 even more theoretical or philosophically oriented treatises occasionally include among their otherwise doctrinaire assertions a note to the effect that medi-

cine is not certain. With some authors it becomes part of the definition of medicine, and of its claim to be the art that it is, that it is inexact. The recognition that it cannot do everything is sometimes used as a genuine warning, but it is also sometimes used to bolster claims (and they might be extravagant claims) that it could do a very great deal. That certain diseases are incurable is sometimes not taken as a sign of the inadequacy of the art in its current state but is turned into part of the medical man's knowledge,114 part of what the medical man can be said to know.

Dogmatism and Uncertainty in the Fourth Century and Later

The continuing interactions of dogmatism and uncertainty have farreaching repercussions in many areas of Greek science long after the fifth century B.C. This is not just a matter of tone or style but relates to a deep-seated epistemological conflict where what are at stake are the answers to fundamental questions concerning the status of scientific theories and the possibility of science itself. With a wealth of material to draw on from philosophers of science, mathematicians, natural philosophers, and medical writers, our discussion must be even more drastically selective than ever.

Plato and Aristotle

We may begin with two central issues in the philosophies of science of Plato and Aristotle. When Plato comes to discuss the generation of the physical world, in the Timaeus , he refers to this repeatedly as a "likely story,"

, but quite how we are to interpret this expression or evaluate the account we are given has been and continues to be much disputed.115 Some suggestions that have been canvassed

---

136

need not detain us long. The alternative expression,

, immediately shows that

here need not carry the connotation of fiction, over and above that of narrative account.116 On the other hand, Taylor's claim that Plato was offering merely a provisional account117 falls foul of the objection that an account of the physical world can, in Plato's view, under no circumstances be converted from a merely probable into a certain one.118 Again, although Friedländer suggested that Heisenberg's uncertainty principle was in a sense anticipated by Plato,119 it is as well to recognise where it differs from anything for which Plato's authority could be claimed. Two points are fundamental: first, the uncertainty principle is precise, in that it specifies that it is impossible to determine both the momentum and the location of a fundamental particle; secondly, it is grounded on reflections on the circumstances of experimental observation and intervention.

Both the nature of the reservations Plato expresses and their scope need to be considered carefully. The fundamental ontological distinction that dictates the status of any account of the physical world is, of course, that between being and becoming. What comes to be, insofar as it comes to be, cannot be the object of certain knowledge. That is stressed at Ti. 27d5ff. and repeatedly in what follows. Yet in respect of

---

137

being itself no such reservation applies; on the contrary, concerning what is stable Timaeus makes the considerable demand that the accounts should "so far as possible" be irrefutable and unchangeable (or invincible) ones.120 Whenever the cosmologist or the natural philosopher has to do with the intelligible model—the Forms—after which the visible cosmos is constructed, there should, in principle, be no falling short.121

Moreover, the claim in respect to the particular cosmological account set out in the Timaeus is that it is "inferior to none in likelihood."122 The visible cosmos is not of course identical with the intelligible model. In the work of creation the Craftsman has to bring order into what is already in chaotic motion.123 He has to contend with the factor Plato calls necessity or the wandering cause.124 Yet he made the cosmos as like the model as he could. Four points are worth emphasising. First, the model the Craftsman uses is itself eternal and unchanging; the importance of this is spelled out at Ti. 28a ff., where the inferiority of any production based on a created model is stressed. Secondly, the product of his workmanship is good . The theme is a recurrent one and is given a triumphant climax in the final sentence of the Timaeus , where the likeness of the intelligible model is described as a perceptible god, greatest and best and fairest and most perfect.125

---

138

Thirdly, what the Craftsman does is to bring order into precosmic chaos or disorder, an order that the natural philosopher, for his part, can and should study and discover.126 Fourthly, the Craftsman's own work is indissoluble, even if that of the lesser divine Craftsmen does not share that characteristic.127

---

139

While the whole account of becoming is undercut as no more than a likely story, the particular grounds for hesitation expressed concerning particular items in the exposition vary. Timaeus baulks at a detailed discussion of planetary motion, for instance, in part for fear of making his account disproportionately long.128 Length is again a factor mentioned when he draws back on the question of why the half-equilateral is the fairest of scalene triangles.129 Here we are told that if someone is able to give a better account of the construction of the elementary bodies, his is the victory of a friend, not an enemy.130 The longer account that Timaeus refers to, but does not give, would not necessarily be an end of the matter: "should anyone refute this and discover that it is not so, we do not grudge him the prize."131 But that is certainly not to deny, but, rather, to assert, that the problem might be advanced.

To be sure, elsewhere the deflation of the value and importance of parts, at least, of the exercise is underlined, as, for example, at Ti. 59c–d when Timaeus speaks of probable accounts of becoming as a "moderate and intelligent pastime" undertaken "for the sake of recreation,"132 where the particular problems he is about to tackle concern the varieties and compounds of the simple bodies. Again at 68b–d we are told that to try to state the different proportions of the constituents that go to make up particular colours would be to betray an ignorance

---

140

of the difference between God's nature and man's, for on that question not even a probable account is possible.133

To take stock on the chief issues that concern us here, the first and most obvious contrast between Plato and most of his predecessors relates to the explicitness with which he confronts the question of the status of any account of the natural world. Secondly, on many topics on which both the pre-Socratic natural philosophers and many medical theorists had tended to express themselves dogmatically, implicitly making unqualified claims for the correctness of their assertions, Plato states his reservations, both general and particular, about the possibility of attaining certainty. But if in principle and in practice he is undeniably an anti-dogmatist on many questions in physics and cosmology, we should not underestimate the dogmatic elements that remain. If certainty is not possible concerning becoming, it is demanded "so far as possible" for being, including the intelligible order the divine Craftsman uses as his model. Above all, the issue of the goodness of the created world and of its creator is not a matter of doubt. In the Timaeus we are merely told that it would be impious to deny this,134 but in the Laws Plato was to treat those who denied that the world is the product of benevolent, rational order as a threat to the state he there describes and, as such, subject to sanctions of formidable severity, including death, if they do not modify their views.135 Teleology especially is not negotiable.

By insisting that physics deals with what is true "for the most part"136 as well as with what is true "always" Aristotle drew a distinc-

---

141

tion that marks his distance from Plato. Yet that very distinction points to a well-known crux in his thought, one that relates, broadly, to the tension between the demand for scientific theories to be certain and an appreciation that not everything in science is or can be. On the one hand Aristotle insists, in the Posterior Analytics , that

must fulfil some very tough conditions indeed. Understanding137 is of what cannot be otherwise than it is, and demonstrative understanding in particular depends on premises that are true, immediate, better known than, prior to, and explanatory of the conclusions.138 On the other hand, the study of nature is not limited to what is true "always" but includes also what is the case "for the most part." In practice, in his scientific treatises syllogisms are rare, and demonstrative ones fulfilling the criteria set out in the Posterior Analytics rarer still. At the same time, reminders of the provisional nature of the results, and of the need for further investigation, are frequent.139

Yet—an obvious question—how can a study that deals with what is true only "for the most part" conceivably be a science or yield episteme as Aristotle defines it? At least, if "for the most part" is interpreted in a statistical sense (more than half, but not all), then syllogisms that have both premises true "for the most part" will not yield conclusions that hold "for the most part," let alone universally. If most B's are A, and most C's are B, it will not follow that most C's are A; it will not follow that any are. Moreover, when only one premise is true for the most part, the other universally, they will not necessarily combine to give a conclusion that is true "for the most part." "Most B's are A" and "all C's are B" together do not yield "most C's are A." And when the

---

142

major premise is universal, the conclusion is again not "for the most part" if that is taken to exclude "universally": "all B's are A" and "most C's are B" together do not rule out "all C's are A."

In the light of the difficulties in Aristotle's opaque and elliptical discussions140 it has been suggested that "for the most part" is not purely statistical but is used, rather, as a temporal operator (i.e., "not always") or as a quasi-modal operator ("not necessarily") or corresponds to some admittedly unanalysed notion of what holds "by nature."141 Yet Aristotle himself, it must be said, nowhere elucidates the concept, nor does he explain how syllogisms incorporating propositions true "for the most part" meet the requirements laid down for understanding in the opening chapters of the Posterior Analytics , notably the requirement that it is of what cannot be otherwise than it is.

Some alleviation of the general problem is possible. The Posterior Analytics , it has been argued,142 has primarily a pedagogic aim: it presents certain recommendations about how a mature science is to be taught, or at least about how to set out a body of theorems in good deductive order so that their connections are revealed and the explanations they incorporate are grasped as the explanations they are. Manifestly, Aristotle has very little to say, in this work, on the problems of discovery, about how scientific understanding is acquired in the first

---

143

place.143 At the same time, the examples he gives show that his discussion is not restricted to the already well-established disciplines such as mathematics and the exact sciences. Although most of his illustrations are drawn from such fields, a fair number, particularly in the second book, relate to zoological or botanical questions.144 Presumably he has in mind an ideal that these studies can eventually attain, for certainly they had not done so in his day.145 Yet for that ideal to be realised, either we have to imagine that the studies as set out will deal solely with universal and necessary propositions, or the difficulties in extending the schema to cover propositions true only "for the most part" have to be resolved—with corresponding modifications, no doubt, to the ideal itself.146

The value of the model in the Posterior Analytics as a model of demonstration, however, remains. If we recall the complex and confused uses of the terms for necessity and demonstration in the Hippocratic writers, we can see the advances made.147 Aristotle stipulates precisely

---

144

what conditions have to be met to justify the claim that conclusions have been demonstrated. True premises and valid inference are not enough: the premises must be prior to and explanatory of the conclusions. In a sequence of demonstrations the ultimate starting-points (they comprise definitions, axioms, and hypotheses) must themselves be indemonstrable (on pain of an infinite regress) but known to be true.148 Whatever other obscurities remain, necessity as logical consequence is now deployed with confidence, and we have a whole subtle discussion of necessity as a modal operator, even though, again, the precise interpretation of many points in Aristotle's treatment remains controversial.149

But the clarity of the model has been bought at a price in terms of the range of its applicability. In mathematics and the exact sciences there is little difficulty in fulfilling Aristotle's criteria: a body of theorems can be presented in systematic order and their derivation from a set of axioms and definitions made clear. Yet the situation is very different in the natural sciences, and not just for the reason already mentioned, that these deal with propositions some of which are true only "for the most part." For the model to be applicable here we have also to be able to answer the thorny question of the nature of the indemonstrable starting-points. Over and above the general regulative principles that govern all discourse—the laws of contradiction and of excluded middle—what will count as axioms in zoology and botany, in meteorology or geology?150 Can we envisage the definitions in such fields having the status of such starting-points?

---

145

Definitions and demonstrations are, as Aristotle points out in his acute if often problematic discussions of their interrelations in the Posterior Analytics ,151 crucially interdependent. Take first one of his astronomical examples. Lunar eclipse is not just any loss of light that the moon suffers (a cloud obscuring it will not count), but loss of light due to the interposition of the earth. But if you ask for the explanation, you will receive the information packed into the full definition. Why does it suffer eclipse? Because the earth intervenes.152 Similarly, in one of the botanical examples alluded to:153 deciduousness is not just any

---

146

loss of leaf that a tree suffers (if it is diseased and drops its leaves, that will not count), but loss of leaf from the coagulation of the fluid or sap at the junction of the leaf-stalk. The fully fledged syllogism that sets out why broad-leaved trees are deciduous might run: all trees that have sap that coagulates are deciduous; all broad-leaved trees have sap that coagulates; so all broad-leaved trees are deciduous. This syllogism meets the criterion for a demonstration, for the conclusion is drawn through a middle term that is explanatory. But everything depends, evidently, on the truth of the definition.

From this point of view, all that the theory of demonstration does is to provide a set of rules for the proper articulation of propositions in such a way as to reveal the explanations as the explanations they are. But for the botanist in the field, obviously the chief task is the acquisition of the knowledge, not its articulation. As Aristotle's own practice in, for example, the zoological treatises shows, he is generally far short of being able to resolve the main problems he raises by demonstrations containing explanations proceeding from incontrovertible starting-points.

But whatever tensions remain between his theory and his practice, Aristotle did, as we said, transform the understanding of demonstration, and whatever the limitations of his model in other fields, the possibility of its application to mathematics and the exact sciences was clear. His formal logic differs in several fundamental respects from Euclid's practice in the systematic presentation of a body of geometrical theorems in the Elements. 154 In particular, Euclid's arguments are not syllogistic, and attempts to recast them in syllogistic form reveal the artificiality of that exercise.155 Yet what Aristotle's theory and Euclid's practice have in common is the conception of demonstration proceeding by rigorous deductive argument from indemonstrable

---

147

axiomatic starting-points. Here, one may say, was a new style of wisdom indeed. Moreover, the ideal thus jointly derived (very roughly speaking) from Aristotle and Euclid was to prove enormously influential156 and well beyond the exact sciences.157 Physical scientists and medical writers too often advocated demonstration more geometrico and in some unlikely contexts. Just what will count as the indemonstrable premises in element theory and meteorology, in physiology, embryology, and pathology, a difficulty already in Aristotle, does not become much clearer later in those such as Galen who also hankered after deductive certainty.158

---

148

Nevertheless, one strand of a dogmatic tradition thereby attained a measure of philosophical respectability in the wake of the development of the theory of demonstration and of its practice in the mathematical sciences, and one clear benefit from this was a greater awareness of the questions of the formal analysis and validity of arguments—though Stoic logic takes as much of the credit for this as Aristotle's.159 Yet over against that tradition, the recognition of the dangers of dogmatism, and a certain tentativeness and open-mindedness, can also be amply exemplified in some of Aristotle's successors, as they can in Aristotle himself. We may turn first to Theophrastus and to two works in the Aristotelian Corpus that are in the main the products of the Lyceum—the Problemata and the Mechanics —for excellent illustrations of the continuing tension between the dogmatic and the tentative.

Question-Posing in the Peripatetic Tradition

The question-posing style of discussion is widely developed in other works emanating from the Lyceum, whether or not this reflects the direct influence of Aristotle and Theophrastus themselves. The extant Problemata is not authentic, though we know that Aristotle wrote a treatise of that name.180 The work we have in the Aristotelian Corpus consists of thirty-eight books of "problems" not just on natural philosophical topics ranging from mathematics and music theory to medicine and biology, but also on questions of character and ethical issues. The collection as a whole displays a highly developed, even obsessive, curiosity, even if this is often directed at trivial issues or problems with little prospect of resolution—as when, in the book on justice, for instance, the writer puzzles over why wealth is more often found in the hands of the wicked than the good,181 or when, in the book on sympathetic action, he asks why yawning is caused by the sight of others yawning.182 Elsewhere, however, the problems are sometimes more suggestive, as when such questions are raised as why the ears of divers burst,183 or why substances kept in closely covered vessels remain free from putrefaction,184 or why the plague alone of diseases infects especially those who associate with the patients.185

---

156

Each chapter begins with a "why?" question, and the answers proposed often take the form of a further question: is it that so and so,

 . . .? We should not, however, exaggerate the extent to which this approach reflects any genuine tentativeness about the answer. Just as it appears that certain expressions of uncertainty become conventionalised in some Hippocratic texts,186 so too to propose a physical explanation in the form of a question could be no more than a matter of presentation.187 A sequence of problems in book 1 appears to be derived from the Hippocratic treatise On Airs Waters Places . Although that work is not mentioned, the writer of the Problemata appears to take as his starting-point propositions that had been asserted dogmatically in it. Chapter 10 of the Hippocratic treatise has been quoted already: "If the winter be dry, with northerly winds prevailing, and the spring wet, with southerly winds, the summer will necessarily be feverish and productive of ophthalmia."188 This supposed fact figures in Problemata 1.8: "Why is that, when north winds have been prevalent in the winter, if the spring is wet, with southerly winds, the summer is unhealthy with fever and ophthalmia?"189 The Hippocratic writer had gone on: "For when stifling heat succeeds while the ground is still wet with the spring rains and southerly winds, the heat will necessarily be twice as great."190 The Problemata chapter does not use the term

for necessity,191 and the explanation is introduced in the form of a question: "is it because . . . ?" But the explanation is an adaptation from the medical writer, notably in its reference to "stifling heat,"

---

157

,192 and the proposer shows no signs of not being totally confident that he has resolved his problem satisfactorily.193

Yet it would be a mistake to dismiss the whole question-posing approach as mere window-dressing, a superficial veneer masking what are essentially dogmatic attitudes. First, there are occasions when genuinely alternative answers are on offer. That so often none of those canvassed is very promising does not detract from this as evidence of a willingness to consider alternatives.194 Secondly and more importantly, on some problems it is recognised that no finally satisfactory answer is forthcoming and the writer admits to being left with some at least of his original puzzlement.

Two of the most notable instances come not from the Problemata but from the Mechanics .195 This too adopts a question-posing approach to the rather diverse mechanical problems it raises.196 Chapter 33, for instance, wrestles with the question: "How is it that a body is carried along by a motion not its own, if that which started it does not keep following and pushing it along?"197 Here the solution offered gets no further than a version of the idea that the impelling force continues to act via the medium.198 Chapter 32 is more remarkable still, in that it ends in self-confessed failure: "Why is it that objects that are thrown

---

158

eventually come to a standstill? Do they stop when the force which started them fails? Or because of being drawn in a contrary direction? Or is it due to the downward tendency, which is stronger than the force which threw them? Or is it absurd to discuss such questions, while the principle escapes us?"199

Schools of Medical Thought:
Dogmatism, Empiricism, Methodism

The texts we have considered illustrate some of the tensions between the dogmatic and the tentative, the speculative and the self-restrained, in post-Aristotelian natural philosophy. But in Hellenistic medicine, varieties of dogmatism and scepticism or anti-dogmatism are elevated into self-conscious methodologies. The so-called Dogmatic medical school

century B.C. ) and of Thessalus (first century A.D. )201 —set themselves apart from those of their predecessors and contemporaries whom they represented as having certain methodological principles in common.

The evidence we have to rely on is in many cases indirect and much of it comes from critical or hostile sources. Empiricism, especially, is poorly represented by original texts,202 and so too is Methodism until we come to Soranus in the second century A.D. Neither Celsus nor, more obviously, Galen is an impartial witness, and aspects of their reports are suspect as historical accounts.203 On the other hand, both are, obviously, evidence for the currency of certain ideas at the time they wrote,204 and we can analyse their interpretations of the debate even if we have to bear in mind that they are their interpretations and even if the evidence to confirm or refute what they attribute to some of the contending parties is often not available.

Celsus presents a particularly full picture of the alternatives as he saw them in the proem to the first book of his De medicina .205 The chief issues, as he reports them, relate to the aims, limits, and methods of the medical art. Those grouped together as Dogmatists are represented as holding that medicine should investigate not only (1) the so-called evident causes (such as heat and cold considered as causes), but also (2) hidden or obscure ones, as well as (3) natural actions (such as breathing and digestion, in other words, physiology) and, finally, (4) internal anatomy.206

Of these four inquiries the Empiricists are said to accept only the first, that into evident causes, alone. The other three are not just superfluous but impossible, since "nature cannot be comprehended"; the

doctor's task is to treat individual cases and for this purpose he must be guided by the manifest symptoms of the patient alone. Against the Dogmatists, the Empiricists rejected "reasoning" and accepted "experience" alone as the criterion. It is this that has suggested cures; it is from experience that medicine has been built up and on which it must continue to rely. It is not a discovery made following reasoning; rather, the discovery came first and the reason for it was sought afterwards. Moreover, where reasoning teaches the same as experience, it is unnecessary, and where different, it is opposed to experience and should be rejected.207

As Celsus makes the Empiricist argue:

Again, "even students of philosophy would have become the greatest medical practitioners, if reasoning could have made them so. But as it is, they have words in plenty, but no knowledge of healing at all."210

The third main medical group, the Methodists, had their own subtle and often rather maligned ideas about treatment,211 but on the essential topic we are concerned with here they are represented by both Celsus and Galen as agreeing with many of the criticisms that the Empiricists brought against the Dogmatists, for example, about their theorising about hidden causes.212 While Celsus reports the Empiricists as asserting that nature cannot be comprehended,213 Sextus makes it

appear that the Methodists withheld judgement on that issue.214 The inquiry into the obscure is to be rejected because it is useless, rather than (as the Empiricists are said to have held) impossible.215 If that is correct, then the distinction between these two medical groups would in certain respects be analogous to that between some of the Academic sceptics and such Pyrrhonian sceptics as Sextus Empiricus himself, in that the former asserted that the nonevident cannot be grasped (and so in that respect were negative Dogmatists) while the latter withheld judgement on that issue.216

Both Empiricists and Methodists thus appear to have combined in a withering attack on the speculative tendencies that had, in fact, been highly developed in Greek medicine from the first—even while other early texts, as we saw, emphasised the difficulty and tentativeness of medicine, resisting the ambition to treat it as an exact science and representing it as a conjectural or stochastic art.217 But faced with the inordinate array of pathological theories, based on humours, opposites, elements, the supposed disorders of the pneuma, the supposed blocking of the pores in the body, and so on,218 both Empiricists and Methodists may have agreed in concentrating on the practical aims of medicine. The great strength of their positions, as these are reported, lay in

both cases in the focus on what had proved to be successful in experience, even though our secondary sources press the difficulties of the rejection of "reasoning"219 and even though, no doubt, the interpretation of experience itself, and of the "appearances" to be relied on, may well have been more problematic than either group allowed.

Yet if the anti-dogmatic and anti-speculative tendencies in Greek medicine thereby reach their apotheosis, there was a price to pay. Both Empiricists and Methodists are said to have ruled out dissection and vivisection. In the latter case, human vivisection, as practised, according to Celsus,220 by Herophilus and Erasistratus on criminals "received out of prison from the kings," was repudiated by most people, including Celsus, with disgust221 —though Celsus mentions a Dogmatist justification in terms of the balance of advantage: the benefits accruing to "multitudes of innocent men of all future ages" justified the sacrifice of

"only a small number of criminals."222 But the Empiricists and Methodists are reported as rejecting human post mortem dissection as well, partly on the grounds that it is, if not cruel, at least nasty ( foedus ),223 but partly also on the basis of the argument that what is observed in the dead is not relevant to the living, since on death the body is changed.224

The obscure not just in the sense of the theoretical or the speculative, but in the sense of what is literally hidden, cannot or need not be inquired into. So far as anatomy went, Celsus has this to add about the Empiricist position:

Moreover, to judge from Soranus, the Methodists too showed a certain ambivalence on the question. Dissection is useless, Soranus says in the Gynaecology , but it is studied for the sake of "profound learning,"

it. "For we shall easily be believed when we say that dissection is useless, if we are first found to be acquainted with it, and we shall not arouse suspicion that we reject through ignorance something which is accepted as useful."227

Both Empiricists and Methodists thus went some way towards accommodating the findings of dissection. But both probably stopped well short of advocating the continued practice of the method. Here the rejection of dogmatism and speculation was also a rejection of new research. It was left to such a writer as Galen (who, even if he would himself have resisted the label, would certainly have been classed as a Dogmatist by his opponents)228 to recommend the method. This he does in texts whose very eloquence and passion testify not just to Galen's personal commitment to the method but also to his sense of the need to come to its support against its detractors. In On Anatomical Procedures he sets out no fewer than four kinds of reasons for studying anatomy:

Of these four, it is the last, the practical applications of dissection, that Galen chooses to emphasise here particularly, conducting, at this point, a war on two fronts. First he criticises many of those who practised dissection for concentrating on "that part of anatomy that is completely useless for physicians or that which gives them little or only occasional help," instancing the study of the heart and the bloodvessels communicating with it.230

Even the Empiricists, he proceeds, who "wrote whole books against anatomy," have to admit that such knowledge is necessary for physicians, but against the Empiricists in turn Galen pours out his critical scorn.232 Castigating the Empiricist claim that the doctor can learn all the anatomy he needs from the inspection of external lesions he writes: "One might well wonder at their temerity, for since even those who have devoted much time to anatomy have failed to bring the study to perfection, one could scarcely learn it from the contemplation of wounds. Perched high on a throne, a man can say these things to his pupils without being able to instruct them in the actual practice of the art."233 What is needed, he insists, is constant practice on many bodies, aided by the instruction he himself provides in his book.234 The chief motivation for this study and the book itself is clear: "What could be more useful to the physician for the treatment of war-wounds, the extraction of weapons, the excision of bones . . . than to know accurately all the parts of the arms and legs. . . . If a man is ignorant of the position of a vital nerve, muscle, or important artery or vein, he is more likely to be responsible for the death, than for the saving, of his patients."235

Conclusions

The controversy over dissection serves to epitomise one dilemma that ancient science faced. Unrestrained or arbitrary speculation, such

as ran riot not just in medicine but in many other areas of the investigation of nature, led in time to a reaction, the rejection of theorising of any kind that went beyond the "appearances."236 Where some Hippocratic writers had already rejected excessive claims for exactness and the use of arbitrary postulates, the Hellenistic medical schools evidently developed clearer and more powerful epistemologies that drew on the traditions of sceptical philosophy. Yet though the sceptic was an inquirer,237 his insistence on the need to withhold judgement and on the idea that it is either impossible or useless to seek to comprehend the hidden causes of nature could and did inhibit, even stop dead, a certain kind of research. The sceptic raised questions and saw that much—in fact he thought just as much238 —could be said on either side of disputed issues, but idle curiosity was pointless, and much that had been investigated, in an admittedly often over-sanguine way, had to be rejected as idle curiosity.

On the side of dogmatism, where the dogmatic Hellenistic philosophical sects met the sceptical challenge by upholding one or another positive view of the criterion of knowledge,239 most of the dogmatic

practising scientists took for granted an affirmative answer to the question of whether knowledge is possible. But inordinately speculative theories and excessive claims for their correctness, even their necessity, can be illustrated in every branch of the inquiry into nature. Many of those who engaged in that inquiry, as we said, pursued the goal of certainty in part under the influence of the models provided by axiomatised mathematics. In the process, much of the complexity of their subject

matter was sometimes ignored, finessed, elided; we shall return to that topic in Chapter 6.

At the same time the example of dissection, especially, shows how it was those who could be criticised for Dogmatism who upheld empirical research. Where the sceptical tradition could degenerate into defeatism240 (even if a defeatism that is readily understandable in terms of the impasse reached in many areas of physical and biological study), it was the more dogmatic and speculative theorists who offered more justification and incentive for further inquiry. It should, however, be stressed that they did so against the background of that challenge from scepticism. The dogmatism in question was, in this respect, still very different from the monolithic traditions exemplified from the ancient Near East in Chapter 2.

Some of the Greek work was, to be sure, undertaken within a framework of regulative principles approximating to what we might call a research programme, and so may be deemed to lend support to the claims of Kuhn and others concerning the role of such in normal science. At the same time we should acknowledge that much ancient speculation had always been and continued to be both more individualistic and more opportunistic than the title research programme would suggest or allow. In an ancient perspective, we have seen that whatever inhibiting effects tentativeness and anti-dogmatism came to have, they were also, especially initially, characterised by a notable

boldness and originality. In Hippocratic medicine, expressions of uncertainty, statements of the difficulties encountered and of the failures that could have been avoided, at least sometimes reflect a remarkably open and direct response to day-to-day clinical experience and a new commitment to the principle of recording mistakes so that others may learn from them—even if some of these attitudes were themselves in turn conventionalised and became part of the fund of rhetorical commonplaces used by authors who were otherwise unrestrained in their pretensions to knowledge.

Early Greek Poetry

Early Greek poetry provides plenty of examples where the stretch of a term seems particularly prominent, a feature that raises the question of how far and at what point the users themselves recognised this; it does not matter, at this stage, that the evidence comes from poetry,8 nor that there may be doubts about the exact connotations of particular Greek terms—if, again, we wish to assume that they have exact connotations. Talk about the unseen, the imaginary, the abstract (so often the locus, or the battlefield, of the revolutions of wisdom) is an area where there is bound to be especially heavy demands on semantic stretch. Neither we nor the Greeks can avoid conceiving or grasping the imaginary with the aid of terms whose stretch reaches back to the perceptible.9 Some of the topics we mentioned in Chapter 1 will serve to illustrate this. The Greeks commonly recognised that some

dreams are true, some false. But was there—where was there?—a Gate of Horn, a Gate of Ivory? The Fates spin and weave your destiny, but what sort of textile was that? Diseases roam silently among men, for Zeus has taken away their voices. Death binds or covers, sleep is poured over you.

The traditional question that such expressions provoked was: Is this a literal belief, or a metaphor? Yet it should be clear that it is simplistic to force that issue, even though such issues have repeatedly been forced, in ancient and in modern times, particularly when insufficient attention has been paid to differences between users' and observers' categories and to the question of the difference it may make to have some such explicit category as that of the metaphorical.10 Yet before the literal/metaphorical dichotomy is available, while a speaker may have a greater or a lesser sense of some difference between "pour" said of sleep and "pour" said of wine or water, it is truistic to say that the phrase will not be seen as a metaphor. It is that dichotomy that erects that particular would-be perspicuous and definite barrier, even though in practice those who wish to erect it generally find it hard to say precisely where it comes—as is shown by the interminability of discussions about the comparative deadness of dead or dying metaphors.

Pre-Socratic Terminology

Problems begin, however, to emerge, even before the terminology of such expressions as

come in this area, since discourse about the divine is bound to involve exceptional semantic stretch. That discourse cannot afford to do without the use of terms with straightforward applications in mundane contexts, yet just what was being asserted when they were applied to the gods immediately becomes a problem with Xenophanes' denial of the validity of their being so applied. Apart from the moral objections he brings against representations of the gods thieving, committing adultery, and the like,11 he attacks the whole idea of gods in the form of men. "Men think that gods are born and that they have clothes and voices and shapes like their own."12 "If oxen and horses and lions had hands and could draw with their hands and produce works of art like men, horses would draw the forms of the gods like horses, and oxen like oxen, and they would make their bodies such as each of them had themselves."13

Familiar as this polemic is, the point that concerns us here is the literalist interpretation of representations of the gods that it presupposes. While the belief that the gods form a society like that of men can be paralleled extensively (we need look no further afield than ancient Mesopotamia),14 the extraordinary detail with which the idea is worked out in Homer is exceptional. It is not just that the motivations of the gods—honour, glory, fame—are those of human beings: they engage in human occupations, including weaving and making armour; they scrupulously observe the customs of Homeric society, in the protocol of visits, for example, where a visiting god or goddess is offered a chair and footstool and given something to eat and drink, before being

expected to explain the purpose of the visit.15 They sleep, weep, and sweat, and when they fight they may be wounded and cry out, for all the world as if in physical pain.16 But this very detail, this passage to the limit of the conception of the gods as like humans, opened the way to a reductionist reading (not that such a reading is faithful to Homer): the more meticulous the parallelisms, the more "realist" the account might be taken to be, and so the more vulnerable to the criticisms of an admittedly starkly literal-minded Xenophanes.

By itself, the belief that Poseidon is responsible for earthquakes leaves very vague the answers to the questions of how he does it and why he did it on a particular occasion (though the form of the answer in the second case would naturally be given by the assumption of quasi-human intentionality, his more or less inscrutable will). But the more vividly Poseidon is imagined as sitting down to table on Olympus (even if to a meal of nectar and ambrosia) the more difficult the how question will be to answer or, rather, the harder it will be to ignore. For Atlas, similarly, to hold the earth up, he had better not be too anthropomorphic. Nor Zeus when he rains or thunders. At one stage, no doubt, all Greeks simply knew that Zeus rains. But when combined with anthropomorphism pushed to the limit, such an item of traditional religious knowledge could be challenged not just on the grounds of consistency, but also with a demand for clarification concerning precisely what was being asserted.

Xenophanes himself, we should recall, continues to describe god's behaviour in terms that are also used of men: god sees as a whole, thinks as a whole, hears as a whole, and he sways all things by the thought of his mind, without effort.17 But the important difference is that Xenophanes guards himself against a too literal interpretation of his religious propositions (even though we may still have questions

enough to put concerning both the meaning and the consistency of his statements about the gods). In the operations of the divine mind certain rules that apply to merely human thought are deliberately suspended; for we cannot change the world, or sway all things, just by taking thought. Fragment 23 is explicit on the point, for there the single god ("greatest among gods and men") is said to be unlike men not just in form but also in thought.18

After Xenophanes, what had been true of much early religion remains true of theology, of cosmology, and of other areas of philosophical thought where there is obvious pressure on the semantic stretch of terms, and already in the next generation of philosophers there are increasing signs of a conscious recognition of departures from common usage along with the beginnings of a far-reaching problematising of the relationship between language and reality as a whole. The general point is well known and need not detain us long. The paradoxes of Heraclitus provide many fine examples: war, we are told, is father of all and king of all;19 all human laws are nourished by the single divine law;20 nature loves to hide;21 thunderbolt steers all.22 From the Eros of Parmenides' Way of Seeming, through the Love and Strife of Empedocles and Mind in Anaxagoras, to Mind, again, in Diogenes of Apollonia,23 the history of pre-Socratic cosmological speculation is a history of what we find it tempting to assume we can straightforwardly call images, metaphors, or analogies,24 although, strictly speaking, it would be better not to use terms that might suggest that their authors viewed them as such or, indeed, that they had some clear alternative.

Quite how their authors saw them, and how far and how explicitly they recognised problems to do with the meanings of certain terms, are indeed crucial, if delicate and at points not ultimately decidable, questions.

Some direct problematising of language can, however, be illustrated already in Heraclitus, for whom "the one wise thing is not willing, and is willing, to be called by the name of Zeus,"25 and for whom the name of the bow is life (

Of all the pre-Socratic philosophers, Empedocles, perhaps, comes closest to an explicit recognition of the extension involved in his use of a term for a cosmological principle, for he says of Philia, Love, that while she is acknowledged as inborn in the limbs of mortals and is called by the names of Joy and Aphrodite, yet no man is aware of her as she goes to work on the elements.29 Yet however imperfect our ideas

may be, it is that cosmic principle that is at work in us. Cosmic Love would have to be said to be no mere metaphor, then, if we chose to press that question, but that just points to the difficulty of the stretch involved in the application to cosmology of any such term, and that in turn says something about what it is to do cosmology.

Plato

By the time we reach Plato not only is there an extraordinary proliferation of images and analogies (now often recognised as such) deployed in cosmology, psychology, politics, and ethics, but their use, or some of their uses, become the subject of explicit comment.30 Though the terms muthos and logos are not always contrasted, of course, they can be used, and were (notoriously) by Plato, to indicate a difference in the statuses of accounts.31 A logos can be, and in certain cases should be, incontrovertible, a matter of demonstration or at least of verification and argument: a muthos may be believed to be true and yet be incapable of proof (though many muthoi are presented as mere fictions).

Though muthoi have their uses, one refrain from the Socratic dialogues onwards is a demand for definition, for clarity, for the giving of

account. In texts in the Phaedo, Phaedrus, Theaetetus , and Sophist , especially, aspects of the use of images,

Plato's ambivalence on this whole topic emerges not just from his

own very extensive use of similes, metaphors, and analogies, but within those explicit comments on likenesses, for while some texts issue warnings about their deceitfulness, others recognise their usefulness. Paradigms, especially, are allotted a positive role,35 both for didactic purposes, to bring a student to an understanding of a difficult problem by considering first a simpler case or one analogous to it,36 and for heuristic ones, where the dialectician himself is supposed to use a similar method to discover the truth.37

Aristotle's Critique of Metaphor

In Aristotle, the shift in emphasis towards a more negative evaluation—at least in certain contexts—is marked. First, he frequently censures the metaphors and images used by his predecessors. Thus Empedocles' notion of the salt sea as the sweat of the earth is "adequate, perhaps, for poetic purposes" but "inadequate for understand-

ing the nature of the thing."38 Other images of Empedocles and other pre-Socratic philosophers are criticised on the grounds that they are based on superficial similarities—or on none, that the illustrations are obscure, or crude, or in need of qualification.39 Thus milk, he insists at one point, is formed by a process of concoction, not putrefaction, so Empedocles was wrong, or he used a bad metaphor, when he spoke of it as "whitish pus."40 Similarly, Plato's own theory of Forms as a whole is dismissed on the grounds that to say that the Forms are "models and that other things share in them is to speak nonsense and to use poetic metaphors"41 —where again we may remark that poetic is used as a term of censure.

Aristotle is especially uncompromising in his criticisms of the use of

should not argue in metaphors, it is clear that one should not use metaphors or metaphorical expressions in giving definitions."43 In the Topics , too, he repeats the criticism of definitions that contain metaphors on the grounds that "every metaphorical expression is obscure."44

There is, to be sure, another side to the picture. Elsewhere when he discusses style, especially,45 he approves of certain types of metaphor, particularly those that express a proportion, for these, he says, are vivid, witty, and clear46 (by which he does not mean to deny that from another point of view they are still "obscure"). He praises in the poet the ability to deploy metaphor and to discern resemblances; the latter is a skill that the philosopher too will need to exhibit.47 In the Topics , moreover, the "investigation of likeness" is said to be a useful means by which to become well-supplied with arguments and even also, in certain contexts, for rendering definitions, that is, in securing the genera for them.48 In the Sophistici Elenchi he is not above recommending

metaphor as a way of making an account difficult to refute without, he hopes, being found out—a backhanded recommendation, to be sure.49

Nevertheless Aristotle's appeal to the contrast between the "proper" and the "alien" or transferred uses of terms runs counter to some modern preoccupations. It leaves little room for any concession to an interaction view of metaphor or for the idea that a metaphor may create a similarity as much as show one.50 Indeed, the assumption in the background is that the comparisons implicit in proportional metaphora can be spelt out fully in literal terms without loss: his notion of metaphora already presupposes that there are two distinct, independently identifiable fields between which a transfer has taken place and in only one of which the term transferred is "proper." Finally, his analysis of analogical argument in the form of the paradigm concentrates on its shortcomings judged from the standpoint of the theory of the syllogism.51 It proceeds from particular case to particular case, whereas for the argument to be valid it must proceed first by a complete induction to a universal rule, which is then applied deductively to the particular case in question in the conclusion.52

The concessions that Aristotle makes, from time to time, to the usefulness of various modes of reasoning based on likenesses do not do much to mitigate an attitude that is otherwise strongly critical. But these formal condemnations provoke a series of questions. First, as regards Aristotle himself, how far does his actual practice tally with the implications of those formal condemnations, and insofar as it does not,

how can we explain the driving force behind his critique? Is it really the case that he entirely purges his speculative thought of metaphor, heeding his own warning that "every metaphorical expression is obscure"? Does he quite fail to recognise the role of models in both philosophy and science? What kind of impoverished science would it be that did without theoretical terms drawing, implicitly or explicitly, on models and even metaphorai? But if and when he in fact uses such terms, how could he square them with his theory of definition and demonstration? The questions may be raised in relation to Aristotle himself in the first place, particularly with regard to his contributions to the inquiry concerning nature. But this in turn will lead us to broach similar issues in relation to the use of theoretical and technical terms, and the role of metaphors and models, in Greek science more generally.

The Art of Nature

We may concentrate first on the inquiry into nature in Aristotle, and the term "nature" itself offers an excellent starting-point. As is well known, nature is defined in terms of an innate capacity for movement, and the power at work in what has that capacity (especially living creatures) is captured in a wealth of images, comparisons, and analogies. When Aristotle describes the growth of the embryo or the structure of the bones or the blood-vessels in the body or the way in which the blood is used as the material for the other parts in the body, he compares nature to a modeller in clay,53 to a painter (sketching a figure in outline and then applying the colours),54 to a housebuilder (laying out the stones along the foundations of the house),55 and to a good housekeeper (not wasting material).56 Several more images are borrowed directly from, or at least echo, those that Plato had used when describing

---

188

the work of the Craftsman in the Timaeus . Aristotle too compares the blood-vascular system to a system of irrigation channels,57 and he too compares the crisscrossing of the blood-vessels to a wickerwork structure.58 More simply, nature is repeatedly described as creating,

, devising,

, and adorning,

, living creatures or their parts,59 and most frequently of all, of course, her purposeful activity is expressed in the phrase "nature does nothing in vain,"

.60

For a philosopher who condemned all metaphor as obscure, Aristotle is, one might think, extraordinarily free with implicit and explicit comparisons of every kind between the role of

and the

. But the first-stage defence he would offer is not far to seek. It is above all in relation to the workings of the final cause that these comparisons are developed. Both domains, Aristotle would insist, exemplify finality, though its modality in each is different: he points out, for instance, that nature does not deliberate, just as he also recognises that there are exceptions to finality, failures to secure the good, in both artistic and natural productions.61 But in many of the comparisons he draws he would claim that there is no question of transferring conclusions from one particular instance to another directly (thereby encountering the difficulty he mentioned in his analysis of analogical argument). Rather, both particulars fall under a general rule for which he believes he has ample grounds. Art can be used to illustrate nature because both domains manifest certain general principles concerning, for example, the adaptation of form to function, the hierarchisation of ends, and the relationship between the end to be attained and the character of the matter necessary to attain it. To quote just one prominent example:

---

189

just as an axe, to be used for chopping, must be made of a hard material such as iron or bronze, so each of the parts of the body must be of a material suitable for the function it is to perform.62

But if, in general, we can see why art may be invoked as an analogue to nature, this does nothing to explain why in any given case a particular technological analogy should be used, let alone guarantee that it will not mislead. The crisscrossing of the blood-vessels may suggest wickerwork, but it does not show that they do indeed have the function of binding the front and the back of the body.63 Moreover, in this instance there is a fairly obvious negative analogy (or difference) that might have given Aristotle pause, in that the texture of the blood-vessels, the veins especially, might be thought ill suited to serve a binding function.

An even more disastrous example is Aristotle's theories concerning the role of the testicles, which he several times compares to the weights on looms.64 He believes their function to be, not to produce the semen but, rather, simply to keep the seminal vessels taut. It is true that he believes he has independent evidence that even after castration bulls can fertilise cows successfully, a supposed fact that he took to suggest that the testes do not produce seed.65 The tension of the seminal vessels, on the other hand, would—he thought—be released only gradually after the excision of the testes. The loom-weight idea offered the basis of an alternative theory, though the more immediately visible similarity it appealed to was—we should say—superficial.

Again, the general doctrine of the adaptation of the parts of living creatures to ends is expressed by Aristotle with the help both of particular comparisons with

, tools or instruments, and of the term

, instrumental, applied to such non-uniform parts as the hand. When he speaks of the organs of the body, the technological model plays an active heuristic role. A single text will serve to illustrate

---

190

the doctrine: "since every instrument (

) is for the sake of something, and each of the parts of the body is for the sake of something , that is to say, some action, it is clear that the body as a whole arose for the sake of some complex action. Just as the saw came to be for the sake of sawing, and not sawing for the sake of the saw . . . so the body exists for the sake of the soul in a way and the parts of the body for the sake of the functions that each of them naturally fulfils."66

Definition of Terms

In many of the cases so far considered, Aristotle would justify the implicit or explicit comparisons he himself uses by referring to the general rule, of which both items compared can be seen as instances, a rule which can, or should in principle, be supported independently. But the broader questions that Aristotle's theory of meaning and his demand for precision and the literal raise concern also his reaction to and criticism of many of the complex and problematic theoretical terms that his predecessors and contemporaries used in their natural philosophical speculation, whether or not Aristotle saw these as, or as involving, metaphor. In some instances he proceeds in the way we might expect from his criticisms of the obscurity of metaphor and the like and from his general statements requiring the strict use of terms: that is, he goes all out to purge the terms of ambiguity and vagueness and to establish a single clear-cut definition, even though the strain

that this imposes on some parts of his scientific enterprise are, at times, as we shall see, considerable. In other cases, however, he allows that a term may be "said in many ways,"

The pair heavy/light had been used in ordinary Greek primarily of what is difficult or easy to carry, though in both cases with a fair range of other meanings or applications as well, including difficult, and easy, more generally.68 But signs of the strain under which the naive conception was coming are already visible in pre-Socratic philosophy, where various correlations are proposed with other pairs of opposites (such as dense/rare) or with the elements as well as with movements,69 and

where Aristotle complains with some justice that the capacities in question were generally left undefined.70

Plato in the Timaeus first follows up the popular association with below and above and emphatically rejects the idea that this second pair relates to two distinct regions in the universe.71 The universe is spherical, so it makes no sense to talk of one part of the sphere being above or below another. Imagining—boldly—a thought experiment in which someone stands in the heavens at the interface of fire and air and forces a larger, and a smaller, quantity of fire towards the air (i.e., towards the centre), he says that it is obvious that the smaller quantity will be moved more easily.72 It then will be "lighter" and tend "upwards," the larger will be "heavier" and tend "downwards"—though "downwards" in this case is to the periphery, "upwards" away from it, whereas the ordinary Greek assumption was that, on earth at least, more fire is "lighter."73 What is light in one region, Plato is prepared to say,74 is the opposite of what is light in the other. Several aspects of the interpretation of this text remain highly disputed,75 but it is beyond doubt that Plato has radically redefined heavy and light: they do not just depend on the quantities of the material concerned but, like up and down, are relativised to where in the universe you are or to which element is in question.

Aristotle, in turn, is no less emphatic that certain conventional views are mistaken. Modifying Plato's idea of the importance of the element in which the real or imagined weighing takes place, he distinguishes between the two simple bodies that are heavy (or light) absolutely (that is, earth and fire) and the two that are so only relatively

(water and air: that is, relative to other elements).76 He is confident that air is light in comparison with earth and with water, but he raises as a puzzle the question of whether air has weight in air, deciding the issue positively by invoking a purported trial which, he claimed, showed that in air an inflated bladder weighs more than an uninflated one.77 Evidently here the possibility of carrying out a measurement was appreciated, though its difficulty and delicacy are reflected in the fact that when Aristotle's conclusion was challenged by later commentators, first by Ptolemy and then by Simplicius, they obtained quite different results from the same test.78

Aristotle further diverges from Plato in insisting that heavy (and down) are always to be defined in relation to movement to —and light (and up) in relation to movement away from —the centre of the universe, deemed to coincide with the centre of the earth.79 Plato too had held that the universe and the earth are spherical, but Aristotle now demonstrates the latter thesis with a battery of arguments.80 Some of these, it is true, are not independent of the issue concerning the nature of heavy and light, for they attempt to show the earth's sphericity as a consequence of the doctrine that the natural movements of the simple bodies are to, or from, the centre of the universe, where Aristotle assumes that heavy bodies do not move downwards in parallel lines.81

But some offer good independent grounds for his thesis, notably arguments that appeal to astronomical data, first, to changes in the visibility of the stars at different latitudes, and especially in the circumpolar stars that never set,82 and, second, to the shape of the earth's shadow in eclipses of the moon.83

The example of heavy and light vividly illustrates the meaning shifts that occur as theory develops, shifts that are similar in kind to those that have been explored from later science, where one example often cited is that between the notions of mass in Newton and in Einstein.84 While in assessing just how radical those ancient meaning shifts were it is fair to recognise that the theoretical framework within which heavy and light were entrenched in ancient debate was a good deal less sophisticated than many more modern examples, we should not, on the other side, underestimate just how much of Aristotle's account of both the sublunary and the superlunary region was at stake—a point not lost on some of his ancient critics such as Philoponus.85 Meanwhile Aristotle's own view of the matter was that he was providing heavy and light with clear, univocal definitions, and ones that incorporated the adjustments to popular notions necessary to take into account the doctrine of the spherical earth.

My second example was the pair hot/cold. Once again Aristotle

complains about the ambiguities of common usage—and about the disagreements among earlier theorists.86 Sometimes touch is invoked as the criterion, sometimes various effects (melting, burning, and the like) that the substance claimed to be hot, or cold, has on other things, and the conflicts between these criteria are discussed. Thus, boiling water imparts heat better than flame, but flame can burn; again, boiling water, he says, is hotter to the touch than olive oil, but cools and solidifies more quickly.87 The consequences of unclarity on this, and on the nature of the dry and the wet, are particularly drastic since, as he puts it, "it seems evident that [these four primary opposites] are practically the causes of death and of life, as also of sleep and waking, of maturity and old age, and of disease and health."88 More even than that, they provide the basis of Aristotle's own essentially qualitative element theory.

In the De generatione et corruptione he presents not only a very full discussion of issues connected with element theory and of rival views to his own, but also a set of definitions of the four primary opposites, to which he believes other qualitative differences (hard and soft, rough and smooth, viscous and brittle, and so on) can be reduced.89 "Hot," he says, is "that which combines things of the same kind" (

totle does not proceed per genus et differentiam , but he evidently aims to give clear and distinct characterisations of the four primary opposites. The somewhat abstract nature of his account is, however, striking. Moreover, as soon as we look at the range of types of case where he uses the four opposites, we encounter instances where his initial characterisations seem inappropriate and hard to apply.

This is particularly true when he is discussing the role of vital heat, one of the chief foundations of his whole biology. It is important, from his point of view, that it is heat in question, since this gives him his link with his general physical theory of the elements. But it is a quality that sometimes seems remote both from anything that might be suggested by the definition "that which combines things of the same kind" and from what might be thought to have some justification either in terms of popular usage or, indeed, of appeals to subjective impressions. Thus in one of his several discussions of the main groups of animals91 he arranges them in a hierarchy according to their methods of reproduction, which are themselves correlated with the four primary opposites. The most perfect animals, the Vivipara, are "hotter and wetter and less earthy by nature"; next come the ovoviviparous animals, the cartilaginous fishes (sharks and rays), which are cold and wet; the third and fourth groups are Ovipara that lay perfect, and those that lay imperfect, eggs, and these are hot and dry, and cold and dry, respectively; and the fifth and final group, the larvae-producing animals such as the insects, are "coldest of all."

We can see why he claims that the Vivipara, which include humans, are the most perfect creatures, and also why they are warmer than, for instance, fish. Yet it is a puzzle why he should claim that the oviparous

fish are cold and dry —though we may notice that he has already used the combination cold and wet for the (superior) ovoviviparous fish.92 The whole represents a schema that appears to owe more to Aristotle's preconceptions of the hierarchy of the animal kingdom, and especially to his views on the distance of the different groups from humans at the top of that hierarchy, than it does either to empirical considerations, or even to considerations derived from the general definitions of hot, cold, wet, and dry set out in the De generatione et corruptione .

Nor is it only in connection with animal taxonomy and vital heat that questions of this kind arise. At the very heart of the physical theory, some of the correlations proposed between simple bodies and pairs of primary opposites pose problems. Earth, Aristotle suggests, is cold and dry, air hot and wet, water cold and wet, fire hot and dry.93 The "wetness" of both air and water corresponds, of course, both to the range of the term

Focal Meaning, Proportional Analogy, and Homonymy in Aristotle's Science

Heavy and hot are, then, two terms of great theoretical importance where, diagnosing confusions in their use, Aristotle aims to establish and adhere consistently to a single univocal definition but in practice encounters difficulties in following through this programme. Elsewhere, however, as we said, he uses the concept of focal meaning, which preserves the centrality of a primary significance but allows a cluster of others to be related to it. We cannot do justice here, clearly, to the intricacies of this important concept, and of the related but distinct notion of proportional analogy, but one of Aristotle's canonical examples will serve as the briefest of introductions.95 "Healthy," we are told,96 is said primarily in relation to health itself, but also derivatively of signs of health (as when a blooming complexion is said to be healthy) or of what promotes or preserves health (as when regular exercise and a kind of climate are said to be healthy). "Healthy" is not to be understood and explicated in the same way when said of a climate or of exercise as when said of a patient who has recovered from illness, but the term is not merely ambiguous or homonymous, since all the other uses are to be connected with a primary one in relation to however we define health itself. This allows for what I have been calling semantic stretch, while it still privileges a primary application.

Here, then, is a device of great power and scope which Aristotle in fact uses repeatedly and to particular effect, as we noted, in connection with some high-level metaphysical principles such as essence and being. In his Physics and elsewhere such concepts as place,

in such a way.97 It is characteristic of his discussion to move outwards from a central, familiar, unpuzzling usage, gradually widening the range of what is to be included under the original rubric.

He proceeds in a similar way when clarifying the concepts of matter and form, and potentiality and actuality, for example, via the notion of proportional analogy, though this is not a kind of focal meaning so much as an alternative to it.98 Thus matter—where the term he coined,

trates—where whether the genus is matter, or is just like matter, is disputed104 —the point at which Aristotle is using the term in an "as if" way (that is, in a way he has to recognise as such) may be quite unclear and controversial.

Thus in a variety of contexts, dealing especially with the fundamental notions that underpin the whole of his philosophy and science, Aristotle offers a kind or kinds of analysis that while certainly not in direct contradiction to anything in his logic, nevertheless represent a certain relaxation of the requirements of univocity and universal, perse , predication laid down in his accounts of definition and demonstration.105 The balance between these two points is delicate—the more so as we do not have an extended formal discussion of focal meaning and so have to rely on the scattered comments that occur in texts that deploy the notion. But clearly, first, there is no question of Aristotelian metaphora being involved, in the sense of the transference of a term from one field to another. Nor, secondly, is focal meaning a matter of a comparison to be justified by reference to an (in principle) independently verifiable general rule exemplified in the particular cases compared. Thirdly, while the extent to which focal meaning is proposed by Aristotle as a tertium quid between what he calls synonymy (i.e., univocity) and homonymy is disputed,106 at the very least it is marked out

from other cases of homonymy in that a systematic relationship can be exhibited between primary and peripheral significances. Nevertheless, fourthly, despite his evident dislike of some modes of reasoning based on likenesses, and despite the demand for the strictest univocity in all terms used in demonstrative reasoning, focal meaning and proportional analogy tacitly mark a departure from that ideal in many key concepts. This is not the reintroduction of imagery, but it is a loosening of the straightjacket of univocity, an implicit recognition (maybe) that the requirements specified for definition and predication in the Posterior Analytics are an ideal .107

The tension here mirrors and indeed exemplifies a further deep-seated tension within Aristotle's divergent statements on the relationship between philosophy and dialectic. Often that relationship is expressed in terms of a series of contrasts: the philosopher works—or can work—on his own, the dialectician in conjunction with a partner;108 the philosopher deals with truth, the dialectician with opinion—for dialectical syllogisms reason from generally accepted views, demonstrative ones from premises that are true and primary.109 Yet on other, admittedly rarer occasions, Aristotle recognises a fundamental role for dialectic, in the sense of the critical scrutiny of received opinions, as a means of securing the primary principles of each science.110 But the snag is that the primary principles used in demonstrations, including definitions, are required to be better known than and prior to the conclusions.111 To get round the difficulty Aristotle would no doubt invoke his distinction between what is "better known to us" and what is "better known simpliciter,"112 but quite how the move from the first to the second is to be made, or how we are to recognise we have accomplished it when we have accomplished it, can be problematic113 —

particularly when we are dealing with cases that may involve focal meaning or proportional analogy. In any event the chief point that remains is that what is presented in the Posterior Analytics has to be seen as an ideal to which no more than approximations are to be expected in some key areas of inquiry.

Metaphor and the Development of Technical Terminology

I have so far focused largely on the evidence in Aristotle, since this offers by far the best opportunity to assess the match and mismatch between theoretical analysis and actual practice. But we should now extend the scope of our discussion to consider (once again, very selectively) some other aspects of the development and use of theoretical terms in Greek science more generally. Initially much of the inquiry into nature is almost entirely devoid of established technical terms: its discourse just is ordinary language and reflects—for better and for worse—its vaguenesses and unclarities. This is especially true of early Greek medicine, which takes over, more or less without modification, many popular terms for diseases.114 The usual generic word for fever,

widely agreed upon to justify the gloss in Liddell Scott Jones as "bilious remittent fever.116

The referential opacity of many popular, and newly coined, terms is particularly evident in words for diseases based on particular organs or parts of the body:

Similar points apply to many common terms in physiology. Both the advantages and the disadvantages of considerable semantic stretch can be illustrated in such a term as

the verb),119 then of cooking and digestion,120 it came to be applied to a wide range of physiological processes (including the production of semen and its action on the menses, the hatching of eggs, the development of the embryo, and the formation of blood, fat, suet, milk, and residues such as urine),121 as well as to various pathological changes, the formation of pus, catarrh, phlegm, and other humours122 (compare, in English, talk of the "ripening" of boils). Finally

This is a particularly clear example illustrating the difficulties of erecting definite boundaries between primary and derivative uses: there is no question of saying precisely where the term begins to be applied "metaphorically." As a portmanteau concept, it both enables a variety of different processes to be related and brought under the scope of a single theory, and it pays a price for this in the indeterminacy of the theory and a corresponding lack, at many points, of predictive or explanatory power.

But while large areas of Greek science, at every period, manifest a certain conceptual vagueness, there are important exceptions to this, cases where technical terms are coined and given clear working definitions. Anatomy, zoology,125 harmonics,126 and astronomy all provide examples, but we may concentrate on some from the first and the last of these. In anatomy, for instance, once some Greek investigators had begun to use dissection extensively,127 many structures were discovered

that had no popular names. Often the new coinages were constructed on the basis of analogies of one kind or another. What we call the retina, for example, was dubbed the net-like membrane (

Finally, astronomy, especially, developed a wealth of technical terminology, clearly defined words for zenith, meridian, apogee, perigee, parallax, colure, station, retrogradation and many others,131 let alone geometrical terms such as homocentric, epicycle, eccentric. Where imagery continued to play a more prominent and indeterminate part is, rather, in the sister discipline of astrology, where conclusions were drawn about the influences of planets and constellations from their

supposed masculine and feminine qualities, their commanding or obedient character, their being diurnal or nocturnal, beneficent or maleficent.132

The Category of Metaphor and the Criteria for Truth

A comprehensive study of "metaphor" in Greek science would be a comprehensive study of Greek science. But perhaps enough examples have been passed very rapidly under review to allow a certain perspective on the range of uses and to permit us to take stock of aspects of the polemic that some Greek philosophers directed against metaphor, myth, and other modes of reasoning involving likenesses or the non-univocal.

As we should expect, the Greek inquiry into nature is heavily dependent, in all periods, on every kind of more or less evidently stretched terms. Even those who might not accept that all language is in some sense metaphorical, will agree that it is often, even normally, through the generation of new, and the elaboration of old, models that science grows and acquires new ideas—and this is true, for sure, of ancient inquiries. The conceptions of concoction, of organ, and of matter itself provide examples, at different theoretical levels, of ingenious and surprisingly durable cases of creative semantic stretch from Greek science, even if we must grant that elsewhere such uses also permitted much merely wayward speculation.

Strong reservations are expressed first by Plato and then by Aristotle on the use of images, likenesses, myths, and metaphors, and the aggressiveness of their tone is a pointer to that underlying polemic. At the very earliest stages of the inquiry into nature, what it was replacing or attempting to replace was a view of the world put together (but not consciously) from elements relating to straightforward, concrete experience, and applied (again, not consciously) to the understanding of the otherwise inexplicable. The unexpected, the imaginary, the frightening, the occult, can only be comprehended within a coherent network of beliefs by some such extrapolation from the domain of the known, the familiar, the unproblematic—though that way of putting it runs the risk of representing the spiritual world as less well known, or at least less vividly apprehended in belief, than the world of tables and chairs, and that may well not be the case at all.133

The question of the status of ideas applied across a variety of contexts (as it might be, to the gods as well as to humans) was not an explicit issue until the philosophers made it such, until they made problematic the whole question of what counts as a variety of contexts. The effect of having an explicit category of the metaphorical was that it enabled issues of meaning and commitment to be brought into the open and, indeed, to be pressed—and the nature of the challenge to which the whole corpus of traditional beliefs might be subject was thereby transformed. It is particularly striking, in view of the way in which poetry was later viewed by some philosophy, that the fifth-century poets themselves, Pindar and the tragedians especially, can be seen as already frequently raising—more or less directly—problems concerning naming, meaning, understanding, and deception.134 Yet it was not their concern, of course, to develop explicit theories to do with the relationship between language and reality. The special sophia they often claimed was—naturally—heavily dependent on what Aristotle would

deem metaphor, when it was not also deliberately enigmatic.135 Above all, lacking an explicit concept of the metaphorical, they lacked also one of the literal, and the idea of tying the notion of truth to the latter would no doubt have seemed, to a Pindar, bizarre in the extreme.

Aristotle's invention of the metaphorical/literal dichotomy involved the stipulation of criteria for truth that at one stroke downgraded—even ruled out—poetry, most traditional wisdom, and even much of earlier philosophy. In his view most pre- or proto-cosmological thought is open to the charge of being mere "poetic metaphor," and where "metaphor" was diagnosed, the question of what the metaphor was a metaphor for was one that could always be pressed. When he separates

The polemic against metaphor and myth is thus part of the campaign waged by philosophy and science against poetry and religion—or at least against some traditional religious beliefs—although of

course the ancient forms of those battles must not be conflated with those they have taken since the advent of Christianity, let alone more recently. At the most general level, however, the ancient battles too related to the erection of boundaries marking the spheres of influence and the domains of discourse of those with varying claims to intellectual leadership and prestige.

To be sure, once the barriers were up, there were those who were prepared to try to exploit the possibilities offered by the category of the metaphorical to resist a certain type of challenge concerning the literal truth of their pronouncements, even though quite what claims they were making sometimes remained quite unclear. As can be illustrated already from within the texts of Plato himself, the category of myth could be used, on the one hand, to condemn the ideas so characterised but, on the other, to insulate a viewpoint from a certain type of criticism.138 Yet once the Aristotelian dichotomy between the literal and the metaphorical was available, to plead the defence of the metaphorical by claiming that a term was used just as a metaphor would by itself hardly do, for without overhauling and criticising that dichotomy itself such a defence was likely to seem merely evasive, leaving unanswered the Aristotelian demand for the literal account of which the metaphor was a metaphor. Meanwhile, on the side of the literal, the forging of that dichotomy was certainly one manifestation of Aristotle's confidence that literal truth was there to be attained, and while that was usually, no doubt, a sign of a certain simplistic overconfidence on his part, it provided, we may be sure, a powerful incentive to the pursuit of his style of scientific investigation.

Nor were the boundaries that were set up just a matter of sociology, to be accounted for by externalist considerations to do with the rivalry between different groups competing for prestige. Although we should now say that the differences between poetic, and scientific, discourse are less, and less clear-cut, than Aristotle, for one, often sought to in-

sist, the constraints on language in the two areas are not identical . In particular, the natural scientist is bound to have to explore, and at points to delimit, the implications of his "metaphors" with one eye on the need for his theories to come eventually (and no doubt not one by one)139 to a distinctive type of empirical or pragmatic test. The contrast with the way in which poetry works or is effective is obvious. So too, to take another field to make an analogous point, in law the lawyer will need to define and clarify his terms, though, again, without hoping for complete precision: Aristotle could be used to illustrate the recognition of the need,140 Lysias the resistance to a demand for precision.141

So far as the sphere of the understanding of nature goes, the positive features of the conceptual moves we have been studying (and it is important to recognise that there are some positive features) may be said to lie in the favouring of the explicit over the merely allusive, of comparative determinacy over interdeterminacy, obscurity, even fudge. Suggestive though it may be to view sleep as poured over you, or to speak of the "channels" of communication as just that,

nisms of the transmission of movement and sensation (as opposed to descriptions of the courses of the nerves)143 remained extremely vague. There was a long way to go.

But the—more obvious—negative features of this polemic include especially the rejection of, or at least lack of sympathy for, much that was heuristically fruitful in imagery, analogy, myth. Nor were these three by any means always characterised by—and they certainly had no monopoly of—obscurity, fudge, and the allusive. Moreover, the expectations of transparency and univocity that the philosophers generated were not ones they were usually or even often in a position to fulfil, even though they were, up to a point at least, useful expectations to raise, if only to focus on the ideal or the limiting case. The vocabulary of muthos and logos and of metaphor enabled a distinct type of challenge to be pressed, that of specifying the limits of the commitment to a theory, even though, maybe, in the strictest versions of the tests, with the emphasis on the precision of the limits, they were ones that science itself (then and now) was bound finally to fail—at least if it continues to use natural language or, rather, because it has to do so.

Some of the most outspoken condemnations of metaphor come in the context of Aristotle's discussion of the conditions for episteme , understanding, in the Posterior Analytics . Only universal, per se, predications using univocal terms will do for the purposes of demon-

stration, and accordingly there is no way to make room for metaphorai here. Yet to have confined the scientist to what would meet the requirements for demonstration according to the official programme in the Analytics would have been massively restrictive. Nor is there any question of Aristotle in practice actually so limiting the domain of physics. In fact, however, when, under the influence of that programme or not, he attempts precise definitions of complex concepts, the result is sometimes a certain arbitrariness (as we saw with his definitions of the four primary opposites). More often he is more tentative as he moves towards the delineation of fundamental concepts, especially when he uses the notion of focal meaning in their explication, even though that notion remains (we said) in a somewhat anomalous position in relation to the official programme.

The programme is a part, in a way the culmination, of that aggressive attack mounted by the new wisdom, at this point, against the old (and against some rivals from among the new) in a bid to supplant them. Yet once again, in practice, the new had, and continued to have, more in common with the old than the form that the attack took might lead one to expect. Certainly the effect of the forging of an explicit terminology to distinguish different types of discourse and different claims for truth was to raise the most radical questions with the most far-reaching repercussions, reverberating to the present day. Yet although Aristotle's desideratum for the well-ordered presentation of a mature science is that it should limit itself to strictly univocal terms, aspects of the actual science he does are evidently a good deal less rigorous—to their advantage. While there is no way in which he will allow poetry back into science ,144 in acknowledging the role of dialectic he recognises that the language of the scientist will often remain some distance from the ideal formalisations of the Analytics .

Dynamics

In the field we call dynamics, the study of moving bodies, it is well known that up until Aristotle the Greeks had not progressed much beyond general statements of such vague principles as that "like" seeks "like," a principle applied by the fifth-century atomists, for example, to animate as well as to inanimate phenomena, to birds as well as to pebbles on a beach.6 Notoriously, Aristotle himself attempts no theory of the factors influencing the speed of moving bodies, whether in "natural" or in "forced" motion, but merely introduces a number of general statements on that topic in the course of his discussion of other problems, such as the existence of the void or that of an infinite body, in the Physics and De caelo .7 Many of these statements are quite indeterminate. For example, several suggest merely that in natural motion the more there is of a heavy body the faster it moves downwards, and, similarly, that the more there is of a light body, such as fire, the faster it moves upwards. Thus at Cael. 277b3ff., for instance, in the course of an argument denying that the natural movement of the elements is due to an external force, he says simply that "it is, on the contrary, always

the case that the more fire there is the faster it moves, and the more earth likewise to its own place."8

Sometimes, however, he refers to certain proportions. Thus in natural motion he suggests that the increase in speed is "according to the ratio" of the increase in the weight or the impulse (

The principal problem of interpretation that these texts pose is the extent to which Aristotle should be seen as committing himself to precise general laws of natural motion stating a relationship of the form V µ W.13 The references to proportions have often been taken, in ancient and in modern times, to imply this. Yet as Owen and others have shown, that is in certain respects clearly, and in others very probably, an overinterpretation. First and foremost, Aristotle's interest in these passages is not in the factors governing the speed of naturally moving bodies at all. Rather, he is concerned to develop arguments in the first passage to disprove the existence of the void, and in the second to refute the possibility of an infinite body with infinite weight. His argument, in both cases, rests on the fact that there is no proportion between a finite magnitude and an infinite one,14 or between a finite magnitude and zero ,15 and so all he needs is to point out that there is a proportion, some finite relationship, between speeds or times and "impulses" or weights. Not only does he not state a formula of the form V µ W, he shows no interest in describing clearly under what conditions the increase in speed he refers to takes place. Some increase with weight/lightness is taken as common knowledge,16 and no attempt is made to specify this exactly, let alone to determine it by measurement.

Further references to proportionalities occur also in some of Aristotle's remarks concerning "forced" or "artificial" motion, and here, even more clearly, a weak interpretation is preferable—indeed, at

points, required. Thus in Physics book 7 chapter 5, especially, he considers the effects of "powers" of different strengths on the speed of the objects they move, where he has in mind, among other things, such familiar cases as a gang of men hauling a ship.17 At Ph. 249b30ff. he says: "if A, which causes the motion, moves B a distance C in a time D, then in the same time the same power A will move half B twice the distance C, and in half the time D it will move it [half B] the distance C. For thus it will be proportional. And if the same power move the same object a certain distance in a certain time and half the distance in half the time,18 then half the strength will move half the object an equal distance in an equal time; for example, let E be half the power A, and F half B, then the proportion of the strength to the weight will be the same, and so they will move an equal distance in an equal time."19

Thus far it might appear that we have here the makings of exact general laws of forced motion. Yet Aristotle immediately proceeds, at Ph. 250a9ff., with a statement that qualifies the field of application of the principles he has just sketched out. "And if E moves F a distance C in a time D, it is not necessary that E moves twice F half the distance C in the same time. If indeed A moves B a distance C in a time D, half A—that is, E—will not, in a time D or in any fraction of it, move B a part of the distance C which is in the same proportion to it as A is

to E. For it may be that it will not move it at all."20 Otherwise, as he goes on to say, "one man might move a ship, since both the strength of the haulers and the distance they all cause the ship to move are divisible by the number [of the men]."21

This exception strongly suggests that the proportionalities adumbrated in this chapter are not intended to apply strictly as universal rules .22 This becomes clearer still when we consider the range of phenomena that Aristotle believes to exemplify such proportionalities.23 Ph. 250a28ff. states that growth or increase, and even qualitative changes, are generally subject to similar rules, for example, that "in

twice the time, twice as much alteration will take place."24 Again, in the De caelo , 274b34ff., when he proposes a similar analysis for a variety of modes of change, he begins by specifying "heating" and "pushing" and then generalises his point to apply to any affection or movement whatsoever. If we bear in mind Aristotle's essentially qualitative conception of the hot/cold spectrum, there is clearly no question of the proportions or ratios in such a case being expressible in exact quantities.

For anyone on the lookout for the first signs of an ambition to arrive at strict quantitative laws of motion, Aristotle's statements about how objects move, in natural or forced motion, are a disappointment. But then Aristotle clearly had no such ambition. Certain proportionalities are stated that might, at first sight, be taken to be part of such a general theory, set out in the form of exact equations governing the speed of moving bodies. Yet these statements are generally made en passant in the course of his discussion of other topics, where he has dialectical, often destructive, ends in view and is certainly not concerned with the positive development of any exact general theory of motion—and where the statements in question are intended to apply only loosely or subject to exceptions which are themselves not specified precisely.25

Aristotle's views were influential, but he was, of course, far from being the only theorist to discuss aspects of the problem of motion. Several later writers implicitly or explicitly contested his statements, and some certainly made some attempt to broaden the empirical base of the discussion. A passage in Simplicius shows that the third head of the Lyceum, Strato, tried to adduce evidence for the phenomenon of acceleration (as we call it) in natural movement. Yet as reported by Simplicius, at least, Strato's observations are typically imprecise: "If one observes water pouring down from a roof and falling from a con -

siderable height , the flow at the top is seen to be continuous, but the water at the bottom falls to the ground in discontinuous parts. This would never happen to it unless it traversed each successive space more swiftly."26 Again: "if one drops a stone or any other weight from a height above the earth of about a finger's breadth , the blow made on the ground will not be perceptible, but if one drops the object from a height of a hundred feet or more , the blow it will make will be a powerful one."27

Much later, in the sixth century A.D. , Philoponus, the most devastating ancient critic of Aristotle's views on dynamics, certainly sought to refute those views by appeal to what he represents as empirical as well as to logical considerations.28 He takes Aristotle's doctrine of natural motion to imply that in motion through the same medium, the times required for the movement will be inversely proportional to the

weights or impulses of the moving bodies.29 To this he then comments: "This is completely false, and this can be established by what is manifestly evident more powerfully than by any sort of demonstration by arguments."30 He envisages the possibility of a test to refute Aristotle's theory, and yet the imprecision of this, as he goes on to describe it, is remarkable. "For if you let fall at the same time from the same height two weights that differ by a very large measure , you will see that the proportion of the times of the motions does not correspond to the proportion of the weights, but that the difference in the times is a very small one . So if the weights were not to differ by a very large measure, but the one, for example, were to be double the other, there will be no difference in the times of the movements, or if there is one, it will be imperceptible, although the difference in the weights is by no means such, but the one has the ratio of double the other."31

Although elsewhere in his discussion Philoponus occasionally refers to some specific weights, distances, and times for purely illustrative purposes,32 no attempt is made to report precise results of actual tests.

Even in these texts, which offer probably the most sustained ancient discussion of dynamical problems, Philoponus is content to show quite generally that the proportions he takes to be implied in Aristotle's statements are wide of the mark—without recording the exact measurements obtained in a series of particular trials (if, indeed, he carried these out).33

Yet this should not be said to be just a matter of a conceptual block. A technical factor is certainly at work, though the importance we attach to it may be a matter of some disagreement. The association of movement and time with number is already found in Aristotle, who calls time "the number of motion in respect of before and after."34 Yet in practice neither Aristotle nor anyone else in the ancient world had any means of exactly measuring short intervals of time.35 The day was divided into hours of variable length, an hour being a proportion of daylight or darkness. Shorter periods were measured by such devices as the water clock or sundial. But even after Ctesibius had introduced an improved constant-flow water clock in the third century B.C. , accuracy in measuring short periods to within an interval corresponding

to a second—or even to ten times that amount—was neither, usually,36 sought, nor was it obtainable.37

The evaluation of this technical consideration is, as I noted, problematic. After all, some of Galileo's own experiments in the Discorsi involve timing devices that are not markedly superior to—some are even cruder than—Ctesibius' water clock.38 Yet that it provides part, at least, of the answer to the lack of exact measurements in ancient terrestrial dynamics is surely clear, even if this technical failure to advance beyond Ctesibius itself poses a set of problems concerning ancient motivations and interests. We should certainly not ignore the fact that some attempts were made to bring empirical data to bear on dynamical problems in antiquity, even if not precisely measured data. But before agreeing to any wholesale conclusions about a lack of any such measurements in ancient science we have quite a number of other fields to consider.

Element Theory

The second example I mentioned as favourable, on the face of it, to Koyré, was element theory. What were the factors at work here? The dominant strand in ancient theories concerning the fundamental constituents of physical objects is represented by doctrines that refer to earth, water, air, and fire, or to hot, cold, dry, wet, and their like, whether singly or in combination, as the ultimate elements.39 Admittedly, atomism in each of its ancient Greek forms40 has a quantitative

aspect. The fundamental indivisible particles are differentiated by shape, size, arrangement, and (sometimes) weight.41 But though in part mathematical, no ancient atomic theory is anything but impressionistic in its application. It is not just that there are no strict correspondence rules, as in Hempel's schema, to get from initial hypotheses to observation statements; rather, the link between these two is left massively indeterminate. Precise measurements are not, in any case, normally deployed in such observation statements as are cited by way of illustration of the theories—which appeal, rather, to some fairly vague physical analogies.42 It is striking, then, that when Aristotle criticises the atomists for failing to account for alteration and for the interaction of bodies, he is objecting in part to their attempts to reduce qualitative differences to quantitative ones.43 Yet no ancient atomic theory succeeded in deriving the former from the latter.

Meanwhile in the predominant, qualitative element theories, such as Aristotle's own, opportunities to undertake direct measurements are rarely taken. Like the dry and the wet, the hot and the cold themselves are not, in any case, deemed to be capable of measurement. The gadgets described in Philo and Hero that are sometimes called thermoscopes fall well short of being measuring devices.44 Certainly they

show that in some contexts, at least, it was recognised that gases expand with heat. In Philo, a sphere containing air and hermetically sealed is connected by a bent tube to a vessel containing water. When the sphere becomes hot "on being left in the sun" (though Philo notes that the same effect is obtained as well when the sphere is heated in other ways),45 the air bubbles out of the vessel, and when the sphere cools, water is drawn back up the bent tube towards and into the sphere. Such an instrument might have been adapted to give rough measurements of temperature. Yet neither Philo nor Hero gives any hint that they appreciated this possible application. Their devices (like so many others described in their works) serve merely to illustrate a striking effect.46 Again when in later writers, such as Galen, we encounter talk of grades or degrees of hot and cold, wet and dry,47 this is no more than a theoretical elaboration; the grades are not thought to be measurable.48

Aristotle's own view of the explananda, and his explanations, are both resolutely qualitative. The problems that are to be resolved49 concern the qualities of perceptible substances—such properties as whether they are or are not capable of solidification, or of being melted, or of being broken—and he is satisfied with an account of compounds that specifies merely which of the simple bodies predominates in them.50 He does not attempt to state the precise proportions of the elements in various compounds, despite the fact that in an earlier four-element theory, that of Empedocles, some admittedly hesitant steps were taken in that direction.51 The fourth book of the Meteorologica refers often enough not only to a wide variety of compounds but also to such phenomena as evaporation and combustion.52 Yet there is not a single

exact measurement in the whole book.53 Here, in weighing and measuring compounds and their ingredients, there is no technical obstacle of the kind presented by the lack of exact time-keeping devices (and we shall be returning to consider examples where weighing is used).54 But the overriding consideration favouring qualitative theories over quantitative ones is clear: the explananda themselves are conceived in qualitative terms, and any reduction to the quantitative looked vulnerable to the objection that that involved a category mistake.

Evidence for Measurement

Alongside the fields we have taken so far, which tend to support Koyré's judgement, there are others that show that it must be substantially qualified. We may review very briefly some examples from four inquiries in turn, geophysics, astronomy, harmonics, and optics, before pursuing the issue further afield.

Harmonics

Two other areas of investigation, neither of which is tied to superlunary phenomena and both of which are regularly hailed as mathematical, will enable us to test the points I have just made. In harmonics there is a long-drawn-out dispute over the status of the perceptible phenomena, where the positions adopted range from an extreme empiricism all the way to the bid to reduce harmonics to pure number theory.99 How far a particular investigator was committed to a search for exact quantitative data would depend on his position in that overall epistemological controversy. But, as is well known, Plato already knew a tradition in which the measurement of the phenomena was fundamental. In the seventh book of the Republic , 530dff., Socrates first agrees with a view he ascribes to the Pythagoreans, that harmonics and astronomy are sister sciences, but then he goes on to criticise as "useless labour" the business of measuring (

, 531a2) audible sounds and concords against one another. This contrasts, rather—at least at first sight—with the approval of measurement to deal with certain optical effects expressed later, in Republic book 10.100

---

242

Moreover, elsewhere Plato provides some of our best early evidence for a recognition of the point that the exactness of sciences varies with their use of measurement, when, in the Philebus , branches of knowledge are stratified according to this criterion.101 But in Republic book 7, after Socrates' critical remark, Glaucon too speaks of those who "lay their ears alongside" the strings, "as if trying to catch a voice from next door; and some state that they can hear another note in between and that this is the smallest interval which is to be used as a unit of measurement , while others contest that the sounds are the same, both parties preferring their ears to their minds."102 Socrates distinguishes

---

243

these ultra-empiricists from the Pythagoreans,103 but the latter too are criticised for "looking for numbers in these heard concords and not ascending to problems."104

Plato's testimony here is all the more impressive in that he is, at this point, a hostile witness. He disapproves of the methods he describes, at least for his present concerns, and insists that it is only the completely abstract study (the consideration of which numbers are concordant with one another and which not)105 that is to be included in the educational programme of the Guardians. But measurement is an integral part of the procedures he criticises, indeed, both those of the ultra-empiricists who were engaged in an attempt to establish an audible minimum which could serve as a unit of measurement,106 and those of the Pythagoreans in their search for numbers in heard concords. In the latter case we have other evidence concerning Pythagorean investigations—for example, on the monochord107 —and it is clear that they had a particular motive for this study, namely, the bid to illustrate and

---

244

support the doctrine that "all things are numbers."108 Yet the contrast between the Pythagoreans and the ultra-empiricists shows that Plato had others in mind as well. Here, then, in an admittedly simple case, we can say that empirical inquiries involving measurement were undertaken before Plato—and we can follow their fortunes (not always auspicious fortunes, to be sure) in a long line of writers on harmonics from Aristoxenus down to Ptolemy, Porphyry, and beyond, though—to repeat—the importance attached to such investigations and the status accorded to the information obtained vary from one writer to another.109 Harmonics is, however, certainly one of the first examples of the successful quantitative explanation of certain qualitative phenomena.

Optics

The evidence we have for the early stages of the development of optics relates mainly to certain purely geometrical aspects of the study.110 Euclid's own optical treatise first sets out certain assumptions about

---

245

Figure 1
After Cohen and Drabkin, edd., 1958, p. 269 n. 1.

light rays and then proceeds deductively, more geometrico .111 However, empirical tests confirming the laws of reflection are described, for instance, in Ptolemy's Optics , although we cannot pinpoint the date of their discovery.

He first sets out the three elementary laws (3.3.88.9ff. Lejeune): (1) objects that are seen in mirrors are seen in the direction of the visual ray that falls on them when reflected by the mirror; (2) things that are seen in mirrors are seen on the perpendicular that falls from the object to the surface of the mirror and is produced; and (3) the position of the reflected ray, from the eye to the mirror and from the mirror to the object, is such that each of its two parts contains the point of reflection and makes equal angles with the perpendicular to the mirror at that point. With reference to Figure 1, where MR is the mirror, A the eye, B the object, B' the image, O the point at which the visual ray

---

246

strikes the mirror, and TO and BP perpendiculars to the mirror, these three laws state: (1)B' lies on AO produced; (2) B'lies on BP produced; (3) Ð TOA = Ð TOB. He then provides experimental confirmation of these (3.4–13.89.4ff. Lejeune).112

For our purposes the evidence for investigations of refraction is particularly important since, to judge again from Ptolemy, they included not just general discussions of the phenomenon but also measurements of its amount for different pairs of media carried out with apparatus that he is at pains to describe (Optics 5.8 [227.5ff. Lejeune]). The tables in Optics 5.11, 18, and 21 (229.1ff., 233.10ff., 236.4ff. L) setting out the amount of refraction for angles of incidence at 10° intervals from 10° to 80° first for air to water, then for air to glass, and then for water to glass, are remarkable from several points of view. They provide one of the clearest cases of an ancient scientist doctoring his results. Ptolemy has evidently adjusted these to fit his general law, even though that law itself is not stated. This takes the form r = ai – bi ² , where r is the angle of refraction, i the angle of incidence (the incident ray being that from the eye to the refracting surface), and a and b constants for the media concerned.113 Nevertheless, the complexities of that general law are quite unmotivated unless Ptolemy has made some (and we may believe quite extensive)114 empirical investigations involv-

---

247

ing the measurement of angles of incidence and of refraction for these media—even if those investigations did not yield quite the results that were claimed.115

Weighing

So far I have concentrated exclusively on the exact sciences. But one simple measuring technique used in a wide variety of contexts was weighing ,116 and this will now take us further afield, including into what we call the life sciences. Heavy and light were often cited as, or among, the differentiae of natural substances in both physics and physiology, but we must be careful, since they are sometimes understood in purely qualitative terms, on a par with wet and dry, or sweet, salty, and bitter.117 Thus when in certain contexts in his mineralogical work On Stones Theophrastus differentiates varieties of pumice or of

---

248

metal-bearing ore by "heaviness,"118 no actual quantities are mentioned. "Pumices," he says, "differ from one another in colour, density, and heaviness. They differ in colour inasmuch as the pumice from the Sicilian lava-flow is black, while in density and heaviness it is quite like a millstone. For pumice of this kind does indeed exist, heavy and dense and more valuable in use than the other kind. This pumice from the lava-flow is a better abrasive than the kind which is light [in weight] and white in colour, although that which comes actually from the sea is the best abrasive of all."119

Elsewhere, however, direct reference is made to weighing to distinguish heavier and lighter kinds of the same substance. The Hippocratic treatise On Airs Waters Places is much preoccupied with the differences in the waters that occur in different places, distinguishing those that are "hot" and "cold," "hard" and "soft," stagnant and free-running, turbid and pure and bright, as well as—frequently—those that are "heavy" and those that are "light."120 The opening chapter

---

249

suggests that here we are dealing not just with vague general impressions, but with something measurable, for there we are told that waters "vary both in taste and 'on the balance.'"121

Measurement is also clearly involved in Archimedes' famous hydrostatical investigations. The story of how he detected the adulteration of

---

250

a gold crown by observing that it displaced more water than the equivalent weight of pure gold may well be inaccurate in the form in which we have it from Vitruvius.122 But the extant treatise On Floating Bodies shows that he had a clear working conception of—even if he does not explicitly formulate—what we call specific gravity.123 In book 1, chapters 3ff., he distinguishes between solids that are "equal in weight" (

) with a given fluid, those that are "heavier" and those that are "lighter" than it, where he clearly has in mind not absolute weight but weight in relation to a given volume,124 and in chapter 7 he enunciates the principle since named after him: "solids heavier than the fluid will, if placed in the fluid, be carried down to the bottom of the fluid, and they will be lighter in the fluid by the weight of the amount of fluid that has the same volume as the solid."125

Further evidence from the medical writers shows that they referred readily enough to weighing and measuring in particular contexts. For instance, in their pharmacology, the proportions of the ingredients in compound drugs, and the dose to be used, are often—though certainly far from invariably—specified by weight or otherwise by exact quantity, that is, by dry or liquid measure.126 Thus On the Diseases of

---

251

Women book 1 gives this prescription to promote parturition: "one obol of dittany, one obol of myrrh, two obols of anis, one obol of nitre: pound these till they are smooth, pour on them a cyathus of sweet wine and two cyathi of hot water; give to the patient to drink and wash her in warm water."127 Many similar examples could be given—though

---

252

so too can others where the quantity of one or more of the ingredients, or the dose, is not specified exactly,128 and after the Hippocratics, references to the problems of the standardisation of weights and measures and of correlating those used in different parts of the Greco-Roman world appear in the pharmacological sections of such writers as Celsus, Scribonius Largus, and Galen,129 while tables of weights and measures begin to become common in specialist metrological writings.130

---

253

A twofold contrast suggests itself. On the one hand, the simpler notion, found already in Empedocles' element theory,131 that a compound consists of certain proportions of the constituent substances may be contrasted with the more precise idea that the quantities of the constituents are to be determined by weight .132 Yet on the other, despite the progress made towards exact quantitative specification, that progress was still very incomplete. Moreover, quantitative specification when we find it—even when all the relevant quantities are stated—was often no more than window-dressing.

In interpreting this evidence we have to bear in mind, first, that the ingredients used are not chemically pure substances, and, secondly, that ancient doctors are frequently urged to modify the drug and the dosages in relation to particular patients .133 Thirdly, as we noted in Chapter 3, some early medical writers insist that medicine, though a genuine techne , art or skill, cannot be made an exact study,134 and

---

254

some object specifically to appeals to such a procedure as weighing. When the writer of On Ancient Medicine protests that exactness in the control of diet is difficult to achieve, he says that "one should aim at some measure,"135 but he then goes on: "but as a measure you will find neither number nor weight by referring to which you will know what is exact, and no other measure than the feeling of the body."136 The treatise On Sterile Women , too, writes that treatment should be adapted to the particular patient, having regard to her condition and strength, which are not a matter of weighing ,

.137 The question of when it is appropriate to have recourse to weighing was, in fact, a matter of dispute, for some writers were for making medicine exact, or at least for representing it as such,138 while others were suspicious of attempts to do so and critical of what I have just called window-dressing. Nevertheless, some reference to weighing and measuring in pharmacological contexts is common enough, even if often the concern is not so much with exact formulae as with the proportionalities between the "strength" of the drug and that of the patient.

To these pharmacological cases we can add an admittedly limited number of other examples from medical writers at different periods where quantitative reasoning is in play in various physiological or pathological contexts. In the general description of the climatic and

---

255

epidemiological conditions encountered that is set out in the Constitution in Epidemics book 3, it is remarked, at one point, that the urine discharged was out of proportion to the fluid drunk, though here no specific quantities are mentioned.139 In one of the case-histories in Epidemics book 7, however, we are told that a patient discharged more than a chous140 of fresh blood in his stool and then, after a short while, a further third of a chous of coagulated globlets.141 Specifications of the quantities of the lochial discharge or of the menses are also sometimes given in the gynaecological and the embryological treatises—though in several cases the quantities reported appear fanciful.142

Then Erasistratus, in a remarkable experiment recorded in Anonymus Londinensis,143 tried to prove that animals emit invisible effluvia, by keeping a bird in a closed vessel without food for a period and then weighing the bird and its visible excreta. Comparing this with the original weight, he found, we are told, that there had been a "great loss of weight"—another case where, in our source at any rate, an observed difference in weight is remarked without any actual weights being reported.144

---

256

Galen, especially, uses quantitative arguments on several occasions. In On the Use of Parts he remarks generally on the proportionalities between the fluids and solids taken into the body and those discharged or lost,145 and elsewhere he specifies actual amounts of, for example, pus expectorated.146 In On the Natural Faculties the difference in size between, on the one hand, the vena cava (together with the right auricle) and, on the other, the pulmonary artery is cited among the arguments to support the conclusion that some blood must pass directly from the right ventricle to the left through invisible pores in the septum, though—unlike Harvey—Galen does not attempt to measure the quantities or flow of blood exactly or even approximately.147 Most notably of all, perhaps, a quantitative argument is adduced in the refutation of Lycus' view that urine is the residue from the nourishment of the kidneys.148 That cannot be the case, Galen claims, if one considers the amounts discharged, which in exceptional cases may be as much as three or four choes.149 If that is produced from nourishing the

---

257

kidneys, one would expect even greater amounts of residue from the nourishment of the other principal viscera, where there is no sign of this.

Counting

Exactness in the medical writers is sometimes a matter not of weighing or measuring, but of counting .150 Great importance is attached by many Hippocratic authors to the study of numerical relationships in connection with the determination of periodicities, notably in two types of context: (1) pregnancy and childbirth; and (2) the phases of diseases, especially their "crises," the points at which exacerbations or remissions are to be expected. In both contexts some of the ideas expressed have a solid basis. The normal time of gestation in humans is fixed to within fairly well-defined limits.151 Before the advent of anti-biotics, studies were carried out that went to show that certain acute conditions such as certain pneumonias and malaria manifest quite marked periodicities.152 In both fields, however, the proposals about periods and relations made in some Hippocratic texts go far beyond the range of what could be justified fairly straightforwardly by appeals to readily accessible evidence. Here the search for exactness led not to Koyré's "universe of precision" but to spurious quantification and ad hoc numerological elaboration.153

---

258

Number lore in Greek medicine must be interpreted in part against a background of Pythagorean beliefs, not just the general doctrine that "all things are numbers" but also more particular ideas concerning, for example, the importance of odd and even numbers and the correlation of that pair with other pairs of opposites. Odd is associated with right, male, and good, and even with left, female, and bad in the Table of Opposites reported by Aristotle, and we have other evidence that suggests that above/below, front/back, and other pairs were also sometimes incorporated into similar schemata.154

Yet the patterns of beliefs to which the medical theories we are interested in can be related include much besides Pythagoreanism. Many of the ideas attributed to the Pythagoreans are, in any case, widespread in popular belief. The positive and negative associations of some of the pairs of opposites included in the

certainly antedate Pythagoras.155 The classification of numbers into odd and even is general throughout Greek arithmetic. The idea that the days of the month may be good or evil can be traced back to Hesiod.156 Among other aspects of number lore, the idea of the special significance of the number seven occurs in sources before Pythagoras, notably in a famous poem of Solon's, not to mention the more controversial question of possible non-Greek influences dating from earlier still.157

---

259

We must recognise at the outset, therefore, that the pattern of beliefs against which Hippocratic numerological ideas are to be judged is complex. Moreover, those ideas themselves are extraordinarily heterogeneous. We may begin with some of those connected with pregnancy and childbirth. It would, of course, be futile to attempt to determine at what stage the Greeks were aware of the approximate time of gestation of the human embryo. When we reach the classical period, the view that babies born in the seventh, ninth, or tenth month are viable, whereas those born in the eighth month generally die, is widespread.158 But many other beliefs in periods and relations are also found. Thus the idea that the male embryo moves first in the third month, the female in the fourth, appears in the gynaecological treatises.159 On the Nature of the Child , to which we shall be returning, states that the male foetus takes thirty days at most to form, the female forty-two days, and also maintains that the lochial discharge lasts thirty days for a boy and forty-two days for a girl, a view also expressed in On the Diseases of Women book 1.160 On Sevens , a treatise of admittedly doubtful date, claims that the human seed is "set" in seven days,161 and On Fleshes states that it takes seven days for the embryo to acquire all its parts and elsewhere develops other theories of periodicities based on the number seven.162 On Regimen puts forward an obscure theory

---

260

about the concords or harmonies to which the movements of the developing foetus must correspond.163 Epidemics book 2 section 3 chapter 17 suggests that the pains in pregnancy occur every third day when there is movement after seventy days, and, further, that they occur on the third day after the fiftieth, and on the sixth after the one-hundredth, and in the second and fourth months.164

It is not the case that suggestions about such topics as when a male or a female embryo begins to move in the womb invariably take the form of a proposal of a definite number. Epidemics book 6 section 2 chapter 25, for instance, probably suggests merely that males move earlier, and develop more slowly after they are born.165 But references to particular numbers of days are very common, even though there is considerable disagreement about which are the significant ones. In some cases we may assume that the proposals are intended to be interpreted flexibly, merely as approximate suggestions of what may, in general, be expected.166 But in others the theories are stated without qualification. Often the role of symbolic schemata is obvious enough, though, again, in other cases we can do no more than guess on what basis certain numerical relations were proposed. We may, for instance, compare the suggestion that male embryos move in the third month, females in the fourth, with the correlation of male with odd and female with even in the Pythagorean Table of Opposites. Again, it has been suggested that a figure of thirty days for males in On the Nature of the Child corresponds to a musical interval of a fourth (two-and-a-half tones, with each tone as twelve days), while one of forty-two days for females is equivalent to a fifth (three-and-a-half tones).167 That is

---

261

conjectural, but more transparently that treatise maintains that the basis for the difference between the sexes here is that the female seed is weaker.168

Some insight into these theories can be gained from passages where the Hippocratic authors themselves are more tentative or reflective about their proposals. The writer in On the Eighth Month Child raises the question of whether women report their experiences in pregnancy correctly. "One should not disbelieve what women say about childbirth," we are told in one context.169 Yet on the difficulties experienced in the eighth month the writer says: "Women neither state nor recognise the days uniformly. For they are misled because it does not always happen in the same way; for sometimes more days are added from the seventh month, sometimes from the ninth, to arrive at the forty days. . . . But the eighth month is undisputed."170

The writer's own view is that the principal phases of pregnancy consist of periods of forty days, and he is at pains to calculate the beginning of the seventh month with some precision: it begins after 182 days and a fraction, that is, half a solar year.171 He endorses, in the main, the general view of the difficulties of the eighth month but at the same time claims superior, more exact, knowledge of how to calculate it. It is notable that he does not seek to contradict, so much as to make

---

262

more precise, the traditional conception, including that of the danger to any child born in the eighth month, and indeed he continues to talk of the "eighth month child" even when his own theory is that, strictly speaking, this is inexact.172

On the Nature of the Child is another treatise that is critical of what women say about their pregnancies, flatly denying that they can be right when they assert that a pregnancy can last longer than ten months.173 When he proposes his theory about the periods required for the formation of the male and female embryo the writer first argues on the basis of the analogy of the equivalent periods taken for the lochial discharge,174 but when he recapitulates "for the sake of clarity" he cites what he calls a piece of research,

, to support his view. The first consideration he mentions is that on the receipt of the seed the flow of blood into the womb is least, though it subsequently increases (while the reverse is true concerning the lochial discharge) where direct observation of such changes in the flow of blood is clearly out of the question.175 But he goes on to refer to what might have been the far more impressive evidence of miscarriages. "Again, many women have miscarried with a male child a little earlier than thirty days, and the embryo has been observed to be without limbs; whereas those that were miscarried at a later time, or on the thirtieth day, were clearly articulated. So too in the case of female embryos which are miscarried, the corresponding period being forty-two days, articulation of the limbs is observed. Hence both the earlier and the later miscarriages

---

263

show both by reasoning and by necessity, that the period of articulation is, for a girl, forty-two days, and for a boy, thirty."176

What is so striking about this passage is the disparity between the impeccable statement of method, and what the writer provides by way of the results of its purported application. He recognises very clearly that miscarriages would, provided the time of the miscarriage is known, yield telling evidence about the various stages in the development of the human embryo, male or female. Yet what he claims as his result is simply the complete and total endorsement of his theory. His statement of what miscarriages reveal is suspiciously vague and general, and although it may be too much to say that he has no actual evidence at his disposal at all, at least he does not here provide detailed documentation of any single case.177

Finally, the continuation of the text already quoted from Epidemics 2.3.17 shows that, within limits, questions could be raised about some of the periodicities that were proposed. After advancing his theory about pains on every third day when there is movement after seventy days, the writer proceeds: "Should the nine months be numbered from the [last] menstruation or from conception? Do the Greek months amount to 270 days, or is there an addition to these? Does the same apply for males as for females, or the opposite?"178 Yet it is significant

---

264

that even when, as here, certain questions are raised about accepted beliefs, those questions are formulated within the framework of those very beliefs. The writer clearly assumes that pregnancy generally lasts "nine months"; that is not in doubt. What is in question, rather, is how the nine months are to be calculated, that is, to put it bluntly, how the presumption of the nine-month period is to be validated.

There is thus a fair degree of disagreement both about what the significant periods in pregnancy and childbirth are and about how they are to be calculated. But that some calculation of days for some relations is correct is common ground to many authors. Theories about the periods at which the child born is or is not likely to survive are, in the main, based on popular beliefs which we may suppose to have originated in many cases long before the earliest Hippocratic treatises. The Hippocratic writers, for their part, are often critical of such beliefs, and sometimes they support their criticisms with appeals to what is claimed to be direct evidence. The importance of such empirical support is, we may say, certainly appreciated in principle. Yet in practice, in this context, what the Hippocratic writers offer is often little more than a more or less elaborate rationalisation of popular beliefs. In many cases the criticism is not that some popular assumption is too dogmatic and too precise, but that it is too imprecise—where the Hippocratic writer claims more accurate knowledge of the periodicities in question.

The second main area in which the medical writers develop complex theories of numerical relations concerns the periodicities of diseases, especially of "acute" diseases, that is, those accompanied by high fever. Here less is owed to popular assumptions, or at least there is no good evidence that the development of the classification of fevers into tertians, quartans, and so on antedates the period in which the Hippocratic writers themselves worked, although such a notion is not, of course, confined to them.

As already noted, certain diseases do in fact exhibit marked periodicities, and it is not too difficult to see this as one important and continuing stimulus to the elaboration of Hippocratic theories on the subject. Naturally enough, many writers share the general classification of acute diseases according to their periodicities: there were not

---

265

just tertians, quartans, quintans, septans, and nonans, but also semitertians, and as fevers that did not fall into any other category could be termed "irregular,"

, the classification could be made exhaustive. But in addition a wide variety of specific proposals are made concerning complex periodicities, especially doctrines associating groups of even, or of odd, days together. Thus Epidemics book 1 chapter 12 states:

Where paroxysms are on even days, the crisis too is on even days. Where the paroxysms are on odd days, the crisis is on odd days. The first period in those with crises on even days is 4, then 6, 8, 10, 14, 20, 30, 40, 60, 80, or 120 days. In those with crises on odd days the first period is 3, then 5, 7, 9, 11, 17, 21, 27, or 31 days. Further, one must know that if the crisis is on other days than those mentioned, there will be relapses and also it may prove a fatal sign.179

Offering a theory about the days on which sweating is beneficial in fevers, one of the Aphorisms repeats the same sequence of odd days, though adds to these the fourteenth and the thirty-fourth day.180 The treatise On Humours recommends that if the paroxysms occur on odd days, the patient should be evacuated upwards on odd days, and that if the paroxysms are on even days, the evacuation should be downwards on even days—although if the periods of the paroxysms are different,

---

266

evacuation should be upwards on even days and downwards on odd ones.181 On Diseases book 4, however, expresses a different view when it sets out to explain why deaths occur on odd days. "Thus the pain happens especially on odd days. Everyone knows that. . . . Those suffering from continuous fever who have been purged on even days have not been over-purged. But those who have been given a strong drug on the odd days have suffered from excessive purgation and many of them have died from this."182

Elaborate theories are not confined to sequences of odd or even days. Prognosis chapter 20, for instance, states

Fevers have their crises in the same number of days whether the patient survives or dies. The mildest fevers, and those that give the surest indications of recovery, cease on or before the fourth day. Those that are the most severe and accompanied by the worst signs cause death on the fourth day or earlier. The first attack of fever ends in this period, the second lasts until the seventh day, the third till the eleventh, the fourth till the fourteenth, the fifth till the seventeenth, the sixth till the twentieth day. In the case of the most acute diseases, the attacks continue up to twenty days, each one adding four days at a time, and then end.183

---

267

Aphorisms , too, at one point, proposes a mixed theory, where the fourth, eighth, eleventh, and seventeenth days are particularly significant and the ones for the doctor to consider with special care.184

Some of the more complex theories relating to extended periods are quite fantastical. Yet it is certainly not the case that all that these Hippocratic writers were doing was giving free rein to their speculative imaginations. On the contrary, alongside the apparently dogmatic schemata put forward in some texts, others—especially in the Epidemics —show that even while their authors continue to be preoccupied with the problem of periodicities, they were prepared to recognise variations in the patterns of those experienced and to qualify the generalisations they proposed. First, it is worth noting that the detailed case-histories in Epidemics books 1 and 3 rarely concern diseases that fall exactly into a clearly defined category, such as quartans with exacerbations on every fourth day (calculated Greek style, including both first and last days of each period) or septans on every seventh—even though there are occasions when the case-history incorporates a note, for example, to the effect that the pains generally occurred on the even days.185 Moreover, in the Constitutions in these books plenty of attention is paid to the differences between some individuals' experiences and those of others. Thus in Epidemics book 1 chapter 9 we read:

The circumstances of the crises by which we distinguished them were sometimes similar and sometimes dissimilar. Thus, two brothers who lay near the summer residence of Epigenes fell sick together at the same time. The elder reached a crisis on the sixth day, the younger on the seventh. Both relapsed at the same time, with an intermission of five days.

---

268

After the relapse they reached a complete crisis together on the seventeenth day. In most cases the crisis was attained on the sixth day and, following an intermission of six days, a second crisis was reached on the fifth day of the relapse. In some the crisis took place on the seventh day, the intermission lasted seven days, with a crisis on the third day after the relapse. In others the crisis occurred on the seventh day, the intermission lasted three days, with a crisis on the seventh day after the relapse. In others a crisis took place on the sixth day, the remission lasted six days and this was followed by three days' relapse, a remission of one day, a relapse of one day, and finally the crisis. This happened to Evagon, the son of Daitharses. In others a crisis took place on the sixth day, the remission lasted seven days with a crisis on the fourth day of the relapse, as happened to the daughter of Aglaidas.186

Moreover, the treatise Prognosis , which proposes, as we have seen, an intricate theory concerning the periodicities of fevers, goes on to raise certain questions in this connection. "None of these periods," the writer remarks, "can be numbered in whole days exactly." Rather, they are like the solar year or lunar month, for neither of them is "such as to be numbered in whole days ."187 Apart from this important reser-

---

269

vation about the calculation of periods by days, the writer observes that "it is very difficult to distinguish at the beginning between those fevers which are going to reach a crisis in a long period, for they are very much alike in the way they start. But you must pay attention from the first day, and reconsider as each four-day period is added, and thus the way the disease will develop will not escape you."188

In such texts from the Epidemics and Prognosis we have impressive testimony both to the doctors' determination to carry through a sustained programme of clinical observations and to the caution and open-mindedness with which they evaluated their data in their attempts to determine the phases of diseases. The outer limits to that open-mindedness are, however, apparent. Practitioners are advised not to jump to conclusions about the nature of the particular case they are dealing with: they are warned to expect that the exacerbations and remissions of different individuals in the same epidemic may vary; al-

---

270

though counting the days is the usual method of measuring the periods, they are sometimes told not to assume that periodicities will consist of multiples of whole days.189

Yet all this excellent advice is given on the basis of the assumption that the periodicities are there to find. They may be hard to identify: many fevers may simply be "irregular." But the presumption is that the periodicities will usually be determinable, and even that complex cycles of exacerbations and remissions will be. The more care and attention the doctors devoted to establishing the times of the crises, the more confident they could feel in their conclusions, not just in particular cases but in general. The grounds themselves of the general theory, however, were not examined critically, or not critically enough, and reflections on the causes at work generally presupposed that theory.190 It was enough for the more cautious doctors that periodicities could sometimes be spotted. Meanwhile the more speculative theorists had no compunction in making the most extravagant proposals concerning complex numerological relationships.191

---

271

The Underlying Epistemological Factors

The evidence we have reviewed is enough to show that no simple hypothesis to the effect that the ancients totally failed to make use of measurement will do. But we must now raise the question of the underlying epistemological factors at work. There was, of course, no orthodoxy on the question of the foundations of knowledge in antiquity, whether in the investigation of nature or elsewhere—no one standard set of views shared by all who engaged in that investigation, any more than among those who were more purely philosophical in their interests.192 But how far can we go towards identifying the factors that militated for and against the appeal to measurement?

For Koyré and no doubt many others, the key factor would be the influence of Platonism. To be sure, the dichotomy between reason and perception and the preference for reason over perception—even for reason to the exclusion of perception—have strong roots already in the pre-Socratic period.193 But the theme of the untrustworthiness of perceptible phenomena is associated particularly with prominent statements in Plato, especially the Plato of the middle dialogues,194 where the doctrine takes various forms. The emphasis is sometimes on the simple fact that such phenomena are subject to change,195 but more often also on the further point that particulars bear the predicates they bear in a qualified or relative fashion: what is beautiful in one respect may be said to be ugly in another, appear beautiful to some people but not to others, at one time but not at others, and so on.196

No one can doubt that Plato's views were extremely influential, and not just among ancient writers who represented themselves as his followers. But it would be nonsense to conclude that the whole of the ancient inquiry into nature was hamstrung by Platonic or Platonising inhibitions about the inadequacy of all perceptible phenomena. That would be to ignore, first of all, that there were plenty of philosophers who took a radically different view from Plato's in the epistemological debate. It is not just that Aristotle (following, in some cases, hints and indications in Plato himself)197 restores an important role to perception and insists that nature is investigable.198 In the Hellenistic period, both major positive schools of philosophy, the Epicureans and the Stoics, took perception to be, in some sense, the ultimate foundation of knowledge.199

The positions adopted by many of those who were primarily engaged in the inquiry into nature are difficult, sometimes impossible, to specify with any precision, since many of them do not enter the epistemological debate directly nor even necessarily reveal clearly their epistemological assumptions.200 Yet if we consider some of the major

figures and investigations in the exact sciences we have mentioned—Eratosthenes and Posidonius in geophysics, Hipparchus and Ptolemy in astronomy, Aristoxenus, Ptolemy, and Porphyry in harmonics, Ptolemy again in optics—there is nothing to suggest that they entertained radical sceptical doubts about the value of sense perception for their inquiries—that they believed that perception would provide no reliable information at all about what they were investigating.

There are certainly differences in the comparative importance attached to, and in the comparative use made of, reason and perception, between one theorist and another, between one field of inquiry and another, even between one set of problems within one field of inquiry and another set,201 and many texts—as we saw—draw attention to particular difficulties of observation in particular circumstances. But it is precisely because normally observation is not subject to such difficulties that they are worth drawing attention to where they exist. It would be pointless for Hipparchus and Ptolemy to criticise their predecessors for their "rough-and-ready" astronomical observations if there were fundamental epistemological reasons for treating all astronomical observations as unreliable, including those of Hipparchus and Ptolemy themselves.

Yet even if these points are conceded, other objections or worries about the possible effects of a Platonising influence might remain. There is no difficulty in showing that many ancient researchers do not

ignore nor dismiss the empirical phenomena entirely. But it might still be argued that the search for exact data was inhibited by a general expectation that any data gained from observation will fall far short of the true reality. The problem can be stated simply, but it is of the very greatest complexity, and it would be foolish to try to generalise about the expectations of ancient investigators even within a single discipline. Obviously, those expectations will vary, depending on, among other things, the individual's view of the difficulties encountered in conducting observations, whether with or without instrumental aids, and especially on the confidence he had in his theories.202 Yet—to take our best-documented example again—although Ptolemy often acknowledges inexactnesses in the astronomical data he uses, it is not that he is indifferent to their magnitude. It is not that he has a metaphysical principle that allows him to disregard such inexactnesses. On the contrary, his concern is always to insist that the inexactnesses he tolerates are minor and fall within the bounds appropriate to the particular problem in question.203

Paradoxically, perhaps, the very fact that he engaged in some selection and adjustment of his data in the light of his theories reveals his expectation that the fit between them will, in general, be a good one. This is true in certain contexts in the Syntaxis , but the evidence we considered from the Optics is even more striking in this regard. There, in the tables of refraction for the three pairs of media studied, the results are given as correct to within half a degree.204 But they all tally exactly with the underlying general law. Yet this very feature of his account—which shows that Ptolemy has adjusted his results—also reveals that his assumption is that a perfect fit between the observed data and the theory is possible, not just a perfect fit between the generalisations derived from the observations and the theory but one between

what he represents as the observed results themselves and that theory. Here there are no signs of inhibitions stemming from a belief that the data are bound to prove intractable. On the contrary, this example shows very clearly that the error is, at least on occasion, on the side of expecting, or assuming the possibility of, too close a fit between theory and data rather than on the side of the opposite assumption.

Thus far I have concentrated on aspects of the epistemological background that might be thought, or have been thought, to work against a realisation of the importance of quantitatively precise data. But one other influential idea that tells, rather, in the opposite direction is the Pythagorean doctrine that "all things are numbers." This was admittedly a highly obscure, at points perhaps even obscurantist, principle. The relationship between "numbers" and "things" is expressed in different, even incompatible, forms in our sources for early Pythagoreanism, for sometimes things are said to be numbers, sometimes merely like them.205 More important still, the examples cited to illustrate and support the principle include many that have nothing to do with natural philosophical inquiry, as when justice is associated with the number four, or marriage with the number five (the sum of three and two, identified with male and female, respectively).206 Again, we noted that other symbolic associations (not confined to those made by the Pythagoreans) appear to underlie many of the complex numerological relationships found in Greek medicine.207 Moreover, Aristotle reports and criticises overenthusiasm for the number seven: to the reflection that there are seven vowels in Greek, seven notes to the scale, seven

Pleiades, at seven years children lose their first teeth—or at least some do—and that there were seven who fought against Thebes, Aristotle's reaction is to say that such theorisers are like the Homeric scholars who see small resemblances but neglect important ones.208

While in many contexts the interests shown by Pythagoreans and others in the classification of numbers209 and in proportions, concords, and harmonies210 reflect ethical, symbolic, or aesthetic considerations, in others the theory that "all things are numbers" could and did act as a stimulus to find those numbers, by measurement, in the phenomena. The Pythagoreans, we said, had no monopoly of interest in the numerical relationships investigated in the study of harmonics. But the expression of the concords of octave, fifth, and fourth in terms of the

simple ratios 1:2, 2:3, 3:4 ranked for them, we may be sure, as a paradigm of the application of numbers to things. The exactness here is a matter of the simplicity of the mathematical relationships: the ratios are either multiplicate or superparticular. Yet those ratios had broadly to be confirmed, if not discovered, by reference to measurable data,211 and various investigations involving measurement were attempted, not just on the monochord but also, for example, measuring lengths of pipe or the quantities of water in jars that gave different notes when struck, and even weighing hammers that did so.212

As is well known, the stories that report some of these inquiries contain many elements of pure fantasy, especially concerning the results that were supposed to have been obtained.213 Yet that does not affect their value to us as evidence for the aims and methods of such investigations. Sometimes the inquiry involves working back from the results expected: thus in the story where predetermined quantities of water are poured into jars, the quantities are chosen to yield the harmonies. Sometimes the investigation proceeds from what is already given: thus in the story about the hammers, they were clearly not made by anyone to give the notes they were supposed to have done. But what the two types of inquiry have in common is the attempt, or

the ambition, to reveal the "numbers" in the "things" by measurement . Such measurements as were actually carried out in this field may often have been cursory or careless, under pressure from preconceived opinions and reflecting the desire for simplicity.214 Yet whatever else has to be discounted in the stories as we have them, they clearly indicate how the general doctrine that "all things are numbers" could promote quantitative investigations of the phenomena.

Conclusions

To attempt anything like an overview of such a manifold and complex issue as the use and abuse of measurement and the quantitative in ancient science is, no doubt, foolhardy, but some concluding remarks may serve to set out some of the results of our discussion. It is easy enough to see that blanket condemnations—the charge that ancient science is never quantitative in character—are well wide of the mark. The ancients' performance in different contexts and at different periods varies, and each field and period must be judged on its own merits, guarding, as always, against what are, in this case, the particularly prominent dangers of distortion that arise from expectations that reflect our knowledge of the eventual successful exploitation of measurement in various domains.

The first fundamental point is the negative one: it is not the case that the epistemological and methodological assumptions at work in the inquiry into nature were always and everywhere hostile to the pursuit of exactness in either of the two forms we are concerned with, that is, (1) the formulation of rigorous theories, and (2) the collection of precise data. Rather, those epistemological and methodological assumptions were, like their actual practice, very much a patchwork quilt of competing and opposing tendencies. But as regards the first form of exactness, the formulation of rigorous theories, we have noted

that the application of mathematics to the understanding of natural phenomena of various kinds was one of the most important and fruitful preoccupations of ancient science.

Then as regards the second issue, the collection of precise data, we have seen that while the perceptible phenomena were not usually going to be as exact,

The criticism of an ancient failure to pursue precision in the data discounts much important work in the exact sciences. In some other areas that criticism is positively wrong-headed, both misrepresenting what is the case and misjudging where the chief weakness of the an-

cients' approach lies. Far from being inadequately quantitative, some areas of ancient inquiry were excessively so,218 in part under the influence of the very successes obtained in such fields as harmonics and astronomy. An important recurrent phenomenon in Greek speculations about nature is a premature or insecurely grounded quantification or mathematisation. The excessive elaborations of numerical relations in theories concerning the periodicities of diseases and in embryology are examples of this. Another instance is Galen's attempt to distinguish four different grades of hot, cold, wet, and dry. In various versions of atomism, too, atomic shapes are manipulated in a way that is interesting geometrically, but almost wholly arbitrary. Numbers and geometrical relations could be the key to the understanding of the phenomena, but they were often merely the focus of symbolic attention—as on many occasions, notoriously, in Plato.219 The mathematical rigour of an entire inquiry—as in the casting of horoscopes, to revert to an earlier example220 —could be impeccable, but the inquiry remains with too little purchase, with too little grip, on the phenomena. The appeal to the mathematical often gave a spurious air of certainty, the precise

being confused with the accurate.221 Yet this very feature of some ancient work, the pursuit of exactness where it is in appropriate, is itself the subject of critical comment by other ancient authors, as for example, by the medical writers who protest against some bids to turn medicine into an exact science.222

Yet although the characterisation of ancient science as essentially qualitative stands in need of drastic modification, it has a certain limited validity. Appeal to measurement is rare in dynamics and in element theory, and even where it occurs, actual measurements are generally not recorded. In some fields the way the ancients usually formulated the problems directed attention to qualitative, rather than to quantitative, aspects. The instruments available to carry out exact measurements are of varying accuracy (a symptom as well as a cause of the problem), adequate enough for weighing and measuring mediumsized lengths and volumes but not, for instance, for measuring short intervals of time. The example of astronomy shows that when there was sufficient motivation, the ancient Greeks could develop some quite sophisticated instruments,223 but in general the improvements made in measuring instruments were modest. Outside astronomy, the weighing and measuring of the ingredients of drugs was the chief context in which ancient investigators were repeatedly engaged, as a matter of

course, in measuring procedures, and we may remark, first, that this is a simple application of procedures familiar from the marketplace,224 and, secondly, that this is also an example where a good deal of spurious exactness is in play.

It is too simple to say that what ancient science needed was a greater appreciation of the value of exact measurement: such a judgement would ignore the point that in some contexts counting and measuring were over valued, and some ancient scientists were rightly suspicious of phoney precision. Rather, what was needed was measurement directed, and confined, to determinable issues, or a clearer awareness of the importance of that question of the directedness of measurement—though of course no scientist, ancient or modern, could tell in advance which were the problems that would yield to this method of attack.

One final example will serve to underline that last point. The discovery of the diagnostic value of the pulse, ascribable to Praxagoras of Cos working around 300 B.C. , was undoubtedly of the greatest importance to medicine. Yet already in the generation after Praxagoras, the theory of the different kinds of pulse was brought to a high pitch of elaboration by Herophilus. He and his followers undertook a systematic classification of these according to "magnitude," "speed," "intensity," "rhythm," "evenness," and "regularity."225 He clearly understood that pulse rates vary with age and he distinguished a variety of abnormal pulses, such as the "ant-like,"

like,"

Three remarkable features of this endeavour (which is one that continues down to Galen himself and beyond)229 stand out. First, there is the difficulty of carrying out exact measurements of the short intervals of time in question. According to a report in Marcellinus,230 Herophilus,

undeterred, invented a special kind of water clock that could be calibrated according to the age of the patient, although we do not know what degree of accuracy he obtained or expected from this. Secondly, there is the evident ambition to make the inquiry an exact one, to construct pulse theory on the model of music, the successful mathematisation of harmonics. If the main concords are expressible in terms of simple numerical relationships, why not also the main ratios between the dilations and contractions of the arteries? But, thirdly, it is clear that we have yet another example of premature or insecurely grounded quantification. As in the Hippocratic study of the periodicities of diseases, there is, to be sure, some basis for the investigation. But that basis could not sustain the elaborate theoretical superstructure erected upon it. The attempt to reduce the data concerning the pulse to mathematically expressible relations like those of music theory shows how the ancients sometimes exercised considerable ingenuity and persistence in exploring such possibilities, but it also illustrates how in practice that ambition could turn out to be, in part, misplaced.

The Development of the Notion of Explanation

The validity of that interpretation of areas of ancient inquiry will be examined in due time, but certain preliminary remarks should first be made on the development of the notion of explanation itself. In a sense myths too, as I noted in Chapter 1, provide explanations—of a sort—of the subjects they deal with, but only in a sense, and only attenuated explanations. The myths in question range from major quasi-cosmological statements about the origin of the universe or of man's place in it, through particular aetiological accounts, down to "just-so" stories about "how the leopard got his spots." In interpreting these the first important point is a sociological one, namely, the context of delivery. Anthropologists themselves took some time fully to come to terms with the problems of context and intentionality in their material. Many stories do not record what adults seriously believe, only what adults habitually say in response to—and maybe in the hope of blocking—a certain kind of inquisitive questioning, from children, for example, or even from anthropologists. It is not as if we seriously believe that babies are brought by storks or found under gooseberry bushes. It is not as if many of us believe that the century plant does actually bloom only once in a hundred years.2

But apart from the question of whether such stories are claimed to be true , the extent to which they are or contain explanations is problematic. They may contain the equivalent of explanations, that is, the answers to "how," "why," or "what" questions. But in two ways especially, they are likely to be defective. First, the problem may not be made explicit, and, secondly, the proposed solution may consist of a set

of arbitrary assertions, the range of applicability of which is left quite indeterminate. This applies not only to tales told to children (under what circumstances storks bring babies is not discussed) but also to quasi-cosmological myths, about the origin of the world, or of humans or animals, or about how fire came to be used or skills discovered. Under what circumstances Marduk split the primeval water goddess Tiamat to make the sky with its celestial waters on the one side and Apsu, the deep, and Esharra, the "great abode," on the other, just does not occur as a question: 3 no more does why the stones thrown by Deucalion and Pyrrha became men and women.4 That this happened is simply asserted, and it is understood that this was an exceptional occasion with a special outcome. But why thrown stones do not usually metamorphose is not an issue, though it is known that they do not. That very way of querying the story presupposes a framework of natural causation that became self-conscious and explicit only with difficulty and with time—even though that realisation could and did build on what was, in a sense, already common knowledge, or at least commonly assumed.5

The emergence of what can begin to be called fully fledged explanations of classes of natural phenomena is an important new development, though a hesitant one, in early Greek philosophy, with the practice of such explanations preceding the theory. The sequence of ideas that Aristotle reports in De caelo 2.13 about the shape and position of

the earth and on the question of why it does not move illustrates both the advances and the limitations of pre-Socratic natural philosophical accounts, even if it is evidence that must be used with caution.6 For one thing, it was Aristotle who chose to present these ideas as a sequence of replies to the same set of questions, and that may well distort the original context in which they were proposed. Even so, although it would be quite wrong to represent later theories as progressively more sophisticated (let alone truer or in some sense more correct) than earlier ones, some of the constraints on what counts as an answer appear to be grasped more fully as time goes on.

Three features are worth remarking very briefly. First, there is the phenomenon of the regression of the explanandum . A common suggestion was that the earth does not move because it is supported on something, such as water (according to Thales) or air (as in Anaximenes).7 That resolved one difficulty by raising another: what keeps the water, or the air, itself in place—a point that was evidently appreciated by Aristotle and may already have been by Anaximander.8

Secondly, in Anaximander's suggestion—that the earth does not move because it is equally balanced on all sides and there is no reason, then, for it to move in one direction rather than in any other9 —we

have an example of suspending some of the commonly assumed data. A clod of earth, as Aristotle was prosaically to insist, moves in a certain direction, "downwards." Aristotle, with a spherical earth, defined that as towards the centre of the universe, deemed to coincide with the centre of the earth.10 That answer was not available to Anaximander, who thought the earth flat.11 But then in his case that truth about pieces of earth has to be assumed not to apply to the earth as a whole, for his suggestion to be an answer to the problem of why the earth does not move.

Thirdly, we find in the same chapter an example of the denial of the data that are supposed to generate the problem. The full motivation of the suggestion that Aristotle ascribes to certain Pythagoreans, namely, that the earth is like a planet,12 is unclear and controversial, but the effect of the suggestion is to make the earth move in space. The question "Why does the earth not move?" thus gets answered by denying the assumed fact: "But it does move"—though we evidently have another case of the regression of the explanandum, since how it moves and how, on the hypothesis of its movement, other phenomena are to be accounted for involve a series of other problems a stage further back.

These first attempts to resolve questions concerning the position of the earth may look indistinguishable from myths, or at least subject to criticisms that are similar in kind to those I made of the types of

explanations that are offered in myths. But apart from the well-known point that the philosophers' accounts are naturalistic ones,13 they are in principle subject to open challenge. A new suggestion on an old topic implicitly claims superiority to others in the field and has, accordingly, to give an account of itself. It is in that crucible of debate on contested issues that clearer working notions of what will count as an explanation, and of what an explanation should be, come to be elaborated.

For the first more explicit discussions of that topic we have to wait until Plato, though several of the Hippocratic writers made, rather more incidentally, important contributions to the understanding of such distinctions as that between causal and merely coincidental factors.14 Two of the key ideas for which Plato himself appears to have been responsible are, first, the explicit distinction between necessary condition and cause or explanation, and, secondly, the more general contrast between essence and accident. The first distinction is made in the Phaedo , where reference to what is true merely of the material conditions of a situation (without which, to be sure, it would not be the situation it is) is contrasted with reference to the

in terms of what a thing is for or the good it serves—that is, that explanation must be teleological—was fraught with significance for the future, and we shall be returning to it later.16

The second, more general distinction between essence and accident is crucial for the theory of Forms but is present already in the Socratic search for definitions. The Euthyphro puts it that definition is directed at the

These points are all very familiar. My aim in recalling them is simply to stress the moral they convey, that an explanation—in science or anywhere else—must focus on certain aspects of the phenomena in preference to others (causes, not preconditions) and to the exclusion of yet others (that is, must focus on the essential, not the accidental).

Mathematics and Physics in Plato and Aristotle

Further pressure positively to discard certain features of the phenomena comes from the side of the model of mathematical knowledge—it, too, prominent in Plato. The nature of mathematical truths and of the objects that mathematics studies had become, already by Aristotle's time, topics of intense controversy.18 Where Platonism construes mathematics as to do with separate intelligible objects and

accepts and insists that the truths of geometry, for instance, are never unqualifiedly instantiated in physical objects (the diagram on the blackboard, for example), Aristotle argued that mathematics had no separate entities as its objects: mathematics studies certain features of physical objects taken in abstraction from certain others, namely, the features that make them the physical objects they are.19 Mathematical truths are, then, truths about the mathematical properties of physical objects. Indeed, it has recently been argued, with some force and sophistication,20 that Aristotle does not merely not deny , he even requires that there are physical straight lines that fully and perfectly instantiate the geometrical truths about straight lines. It is true that the line drawn in chalk on the blackboard will not do as an example, nor even its outer edge, but, then, it would be wise to say that they are not straight lines. The truths about straight lines will nevertheless be instantiated in any of a number of straight lines that are present in any physical object.21 That interpretation is disputed, but at least it can be agreed that there is no need for Aristotle to say that in principle it is impossible for physical objects to instantiate mathematical truths; they certainly will not fail to instantiate truths of arithmetic,22 and he certainly has some perfect spheres—in the heavens.

Whatever the disagreements between Plato and Aristotle in the philosophy of mathematics, both held that mathematics is exact, and that point is fundamental, even though it requires as a gloss that pure mathematics also has to admit approximations in certain contexts (for the values of surds, for example).23 But in a bid for exactness, applied

mathematics too will discard, even for the Aristotelian, some, at least, of the physical aspects of the phenomena.24 Although the precise conditions under which the procedure called abstraction,

"Saving the Phenomena"

After these rather cursory preliminaries concerning the philosophical background, we may now turn to our principal concern, the kinds of idealisations found in the ancient inquiry into nature. We are told by Simplicius that Plato set as a problem the saving of the apparent wanderings of the planets, by means of regular, orderly—we are to understand, circular—motions.27 But the question of the conditions un-

der which it could be considered that certain phenomena had been saved —or that an adequate account had been given—is an issue not just for the Platonic or Platonising tradition, and not just for astronomy.28 We find a variety of expressions used in a number of contexts: saving the phenomena or appearances (

ever, many of the explicit references to such slogans (generally in late authors) are vague and leave the requirements on the "saving" indeterminate;36 our best policy is, rather, to study the actual practice of Greek investigators at work, and we may start with some fairly straightforward cases from the exact sciences.

Optics

In theoretical52 optics, too, there were disagreements about such physical issues as whether the visual ray departed from the eye or travelled to it from the object seen,53 and whether light was a movement,

(or transport,

) or should be interpreted as an actuality,

---

300

, or a tension,

.54 Divergent positions were also maintained on the further fundamental question of whether visual—or light—rays form a continuum (as, for example, Ptolemy insisted)55 or are discontinuous (as appears to be assumed in Euclid's Optics ),56 and this in turn affected beliefs concerning how far the programme of geometrising optics could be carried through and on the constraints on such a programme. Since it is quite clear that in the Elements Euclid assumes that geometrical magnitudes are infinitely divisible,57 it was presumably not for purely geometrical reasons that he would have departed from that assumption for optical phenomena in his Optics , but, rather, for reasons to do with problems connected with the visibility of objects at a distance.58 Yet some geometrisation of optics is common ground to most investigations of perspective, reflection, and refraction—including those of both Euclid and Ptolemy—to the extent at least that it was assumed, first, that visual/light rays can be treated as straight lines,59 and, secondly, that for some purposes the eye

---

301

can be considered as a point, the vertex of the visual cone.60 Moreover, we have good grounds for supposing that the second of these assumptions was clearly recognised by some as an idealisation —since on certain occasions the fact that vision takes place not from a point but from a certain area was acknowledged. Archimedes, in particular, provides a sophisticated discussion of the allowance that has to be made for this in the context of his determination of the angular diameter of the sun in the Sand-Reckoner .61

Astronomy

It would be easy to conclude, on the basis of some of the examples considered so far, that the problem with ancient science is more often too little abstraction than too much . Yet that would be premature. If we turn to astronomy, we see how much more complicated the issue is. Early on in the development of Greek astronomical model-building we find what appears to be a striking example of discounting part of the known data. According to Simplicius,72 the differences in the apparent brightness of particular planets had already been taken, in Eudoxus' day, to indicate that the distance of each planet from the earth is not constant. Simplicius reports that Eudoxus and Callippus failed to deal with the problem and, indeed, that other astronomers down to Autolycus of Pitane also did—not that Autolycus himself was successful in resolving the difficulty.73 There was, of course, no way in which such varia-

---

305

tions in the distance of a given planet could be accommodated within a theory based on combinations of concentric spheres, with the earth at the centre of the system. Yet it appears that Polemarchus of Cyzicus, for one, recognised the difficulty but, not being prepared to sacrifice the assumption that the earth is at the centre, chose deliberately to ignore it, representing the variation in distance as "imperceptible."74

Better still than such instances where we depend on secondary reports, we have some fairly explicit texts in Ptolemy that both show that he is aware of some of the problems and give some insight into how he hoped to overcome them. In Syntaxis book 9 chapter 2, he sets out the main difficulties that any account of the movement of the planets faces. He appeals to these difficulties as his excuse for allowing himself certain moves or devices. One that he mentions is that he will have to make certain primary assumptions that "do not stem from any readily apparent principle," though they are assumptions arrived at from continuous trial and application.75 His introduction of the equant, or centre of uniform motion, distinct from both the centre of the earth and the centre of the deferent circle, would be one example of such an assumption, though he does not specify it as such here.

The first device he refers to is even more interesting for our concerns. This is the use of certain assumptions he describes as "paradoxical" or "counter to reason,"

, and here he does ex-

---

306

emplify: "as when we carry out our proofs—to make them more easy to follow—as if the circles described by the movements in the spheres are bare [widthless] circles, and as if they are all in the same plane, namely, that of the ecliptic."76 Now, he recognises both that the circles are not, in fact, widthless and that they are not in the plane of the ecliptic. Yet for the sake of his first analysis of planetary motion Ptolemy isolates their longitudinal movements (their motion along the ecliptic) and focuses on them to the exclusion of any consideration of their movements in latitude (that is, north and south of the ecliptic). That achieves a formidable simplification of the problems. Yet it is one for which Ptolemy has a twofold justification. First, as he tells us in 9.2 when commenting on such procedures in general, there can be no objection to them where no appreciable difference, no

, results.77 Although he has no worked-out, indeed no explicit, theory of levels of significance, he is clearly exercising his judgement on whether the differences he is discounting are important, and the claim is that those arising from his "paradoxical" assumptions are negligible.

Secondly, and more importantly, even though he discounts movements in latitude in his initial discussion of the models of the planets in book 9, he returns to that very problem in book 13, where he modifies the models in an attempt to account for the observed deviations from the ecliptic. There is no question, then, of his simply ignoring the difficulties presented by movement in latitude or of his forgetting that he introduced the simplification in book 9. On the contrary, it is clear that what he borrows for the sake of argument there he pays back in full in book 13.78

---

307

Parallax Cases

The issue of the negligibility or otherwise of what is discounted takes us to some more complicated cases, such as the various assumptions made by different astronomers in different contexts about parallax. We can distinguish between three main types of case. First, there is the assumption that in relation to the sphere of the fixed stars, the earth may be treated as a point: it is of negligible size, and so it does not matter, in this context, that an observer is not at the centre of the earth, but on its surface, at some distance from that centre.79 This assumption is set out in Euclid's Phaenomena , for instance, and in the elementary textbook of Cleomedes.80 It also figures in Syntaxis book 1 chapter 6, where, moreover, Ptolemy offers a particularly clear statement of the grounds to justify it: the fact that the configurations of the constellations remain unchanged from whatever point on the earth they are observed indicates the very great distance of the stars.81

A second and far more controversial assumption is that made in

---

308

Aristarchus' heliocentric theory, as reported by Archimedes, namely, that not just the earth but the circle in which the earth moves around the sun is as a point in relation to the sphere of the fixed stars (see Figure 2).82 Archimedes' own comment is that that is, strictly speaking, impossible, since a point has zero magnitude and the fixed stars would then be at infinite distance83 (a similar point applies, of course, to the first type of parallax case as well). What Aristarchus needs is not that the stars be infinitely, only that they be indefinitely, far away.

The interesting feature is that he evidently incorporated this into his assumptions , in part in order to meet a possible objection to heliocentricity. If the earth moves in a circle around the sun (rather than the sun around the earth) there should be, one might think, observable differences in the shapes of the constellations as viewed from different points in the earth's orbit—from the points representing the spring and autumn equinoxes, for instance, at opposite ends of the same diameter of the orbit. Yet no such variation was observed; indeed, stellar parallax was not confirmed until well into the nineteenth century, with the work of Bessel and others around 1835. Aristarchus seems to have appreciated that this otherwise very damaging objection to heliocentricity was no objection at all provided that the stars are sufficiently far away. If the diameter of the earth's orbit around the sun is negligible in comparison to the diameter of the sphere of the fixed stars, then you would not expect observable variations in the relative positions of the stars, certainly not within the limits of ancient techniques of observation. Unlike Ptolemy's discussion of the size of the earth in Syntaxis 1.6, the assumption in the form adopted by Aristarchus was not itself justified by reference to independently observable phenomena; there was no way in which it could be. Rather, this reveals precisely what has to be accepted among the assumptions in order for an apparent objection from the side of the phenomena not to be the objection it seems. No doubt Aristarchus could have argued that the

---

309

Figure 2
Three cases of discounted parallax. In each case circle B is treated as a point.

inability to confirm an assumption directly does not make it untrue—and Copernicus would have said the same.84

The third type of case again comes from Aristarchus, this time from the extant treatise On the Sizes and Distances of the Sun and Moon . The second hypothesis set out there is that the earth is as a point, not in relation to the sphere of the fixed stars, but in relation to the moon's orbit .85 In this form the assumption involves discounting lunar paral-

---

310

lax—as if the position of the observer on the surface of the earth makes no difference to observations of the moon. Yet of course it does. The contrast with the careful and complex discussions in the Syntaxis where Ptolemy attempts to determine the allowance that has to be made for lunar parallax86 is striking and points up the difficulty that the second hypothesis in Aristarchus' treatise presents, indeed, its complete unacceptability if we are concerned with trying to establish the actual size of the moon and its actual distance from the earth.

Yet we should not be misled by one possible way of taking the title of Aristarchus' treatise (On the Sizes and Distances  . . . ) into thinking that that was his aim. Both the hypotheses and the results militate

---

311

against such a view. First, his results all take the form of ratios or proportions, giving upper and lower limits for the relative sizes and distances on the basis of the assumptions as set out; no absolute figures are presented.87 Then, the hypotheses include several that Aristarchus undoubtedly knew to be well wide of the mark. That appears to be the most likely explanation of the notorious sixth hypothesis, that the moon subtends an angle of 2° to the eye;88 where 1/2° was the usual ancient approximation and is indeed the figure we can attribute to Aristarchus on the basis of a report in Archimedes.89 Again, the fourth hypothesis simply assumes, with no attempt at justification, that the moon is at 87° to the sun when it appears to be halved.90 Again, the

---

312

fifth takes it that the breadth of the earth's shadow, viz., at the moon, is two moons.91 Moreover, the second hypothesis itself not only discounts lunar parallax but takes the moon to move in a simple circle with the earth as centre—and no serious Greek astronomer had thought that since before Eudoxus.

Such a set of hypotheses would, of course, be an unmitigated disaster in any attempt to arrive at concrete determinations of the actual sizes and distances of the moon and sun. What Aristarchus is doing, rather, is exploring the geometry of the problems. Given certain assumptions—and it will not matter, for the sake of the geometry, that some of the values are a little, and others wildly, inaccurate—what follows? The study is certainly relevant to astronomy, in particular because it shows how one could obtain actual solutions to the astronomical parameters, that is, it offers one set of answers to the question of the premises, or data, needed in order to arrive at such solutions. Yet it remains itself essentially a study of the geometry of the problems.92

The Aims and Assumptions of Greek Astronomers

As this last example shows, certain types of simplifying assumption involve not so much discounting a value that can—with greater or less justification—be deemed to be negligible, as a veritable mutation of the problem. Once certain of the known empirical data are suspended, the study becomes one of pure geometry and does not offer to solve, though it remains relevant to, the astronomical problems themselves. Now, it is just such a shift that Duhem and his followers saw as typical of the dominant strand in Greek astronomy: a lack of concern with the physics of the problems in favour of a preoccupation with the mathematics, the construction of models that are purely calculating devices with nothing to do with any underlying physical realities.93 It is

indeed undeniable that there are instances (Aristarchus' treatise is one) where the problems are treated, at least for the time, as problems of geometry. There is certainly a tradition of the investigation of the mathematics relevant and useful to astronomy that exists side by side with astronomy itself—a tradition that goes back to Autolycus' work On the Moving Sphere .94 But that cannot be said to vindicate the line of interpretation that Duhem advocated. What that line of interpretation itself discounts, or at least seriously underestimates, is an equally undeniable concern with more than just the mathematics of the problems in much—indeed, in my opinion, most—ancient Greek astronomy.

In what are admittedly complex issues,95 the chief objection to Duhem can most easily be illustrated in relation to Ptolemy himself.

First, the treatise known as the Planetary Hypotheses provides incontestable evidence that he aimed for a physical account of astronomical phenomena. There he discusses the nature and relations of the spheres on which the heavenly bodies move. The circles that govern the movements of the planets, sun, and moon are conceived as strips of spheres.96 He even engages with the problems of celestial dynamics, that is, with what makes the heavenly bodies move or the forces at work, when he suggests that we should suppose that each of the planets possesses its own vital force: they move because they are alive.97

But the case does not rest with that work. Within the Syntaxis itself, the very rejection of heliocentricity or, rather, the rejection of the ascription of any movement to the earth shows that, for all the concentration on the mathematics of the problems in that treatise, the whole discussion is set firmly in the framework of certain physical assumptions.98 There can be no question of the earth moving, in Ptolemy's view, primarily because of the (apparent) absence of the expected physical effects of its movement on the earth's surface. If the earth rotated, for instance, you would expect the violence of that motion to have visible effects around us. Clouds, or missiles travelling through the air, could, he says, never move eastwards, for they would always be anticipated by the motion of the earth itself.99

To return to the chief point with which we are concerned here, namely, the nature of and constraints on the idealisations that Greek astronomers allowed themselves. Ptolemy, at least, certainly does not permit himself any general escape clause. In every or almost every case where he introduces an idealisation or a simplification, he has to exercise his judgement concerning the magnitude and character of the discounting. So far as his primary assumptions go, he claimed, as we saw, that he adopts something "paradoxical" only when the consequences fall within the limits of negligible difference. Elsewhere he often justifies the approximations he makes on the grounds of the specific problems encountered in securing reliable data.100 Although we may often question his judgement and may sometimes even suspect his bona fides , he does not proceed as if he could allow himself any arbitrary adjustment he liked—that is, what he could cheerfully agree to be such—an adjustment that would have the effect of turning his discussion into a purely hypothetical, mathematical exercise. The constraints on that discussion come both from the physics of the situation (on the issue of the movement of the earth) and from the astronomical data as secured, as well as may be, by observation.

There is, however, one notable, indeed notorious, instance that looks, and to some extent is, an exception to what is still the general rule. This is the famous case of the discrepancy between what his theory predicts and what is observed on the question of the angular diameter of the moon. It follows from Ptolemy's lunar model that the maximum distance of the moon from the earth is nearly twice the

Figure 3
Ptolemy's model to explain the moon's second anomaly.
The moon's epicycle, centre C, moves round a centre (F)
which itself describes a circle round the earth (E). F moves
round E with the same angular velocity as, but in the contrary
sense to, the movement of C round E. At position (1) (syzygy)
 the model is equivalent to a simple epicycle model. At
position (3) (quadrature), when the moon is at apogee or perigree
on the epicycle (that is, at  a  or at c ) the model is again equivalent
to a simple epicycle model so far as the moon's angular
distance from the sun in concerned. But at position (3),
when the moon is at b  or d , midway between apogee and
perigee on the epicycle, the effect of the new model is to
increase the apparent diameter of the epicycle. 
Derived from G. E. R. Lloyd,  Greek Science after Aristotle , fig. 27.

minimum distance (see Figure 3).101 The angular diameter of the moon should, in turn, vary roughly by a similar amount, a factor of 2. Yet it patently does not. Nor does the evidence in the Syntaxis suggest that Ptolemy thought that it did. It is true that he gives specific values only for the maximum and minimum apparent diameter at syzygy (not for the maximum at quadrature),102 but those he offers are of the right

order of magnitude, a minimum of 31' 20" and a maximum at perigree at syzygy of 35' 20".103 Moreover, and to complicate matters further, the Planetary Hypotheses tackles the problem of how the spheres of the heavenly bodies nest into one another, where it is assumed that the maximum distance of one body corresponds to the minimum distance of the one above it, and there Ptolemy clearly accepts the geometrical consequences of his epicycle-eccentric model in the Syntaxis as correct.104 So far from being embarrassed by those consequences, he takes them as the basis of his calculations of the absolute distances of the moon and other bodies.

Here, then, we have a major discrepancy between the theory and the data of observation, and Ptolemy's lack of embarrassment just increases ours, since it looks as if he has simply discarded part of the phenomena quite arbitrarily. That he has discarded part of his data is clear. That it is quite arbitrary is more debatable. We have to recall that the theory worked extremely well as a theory of the longitudinal positions of the moon, where it represented a quite marked improvement on Hipparchus' lunar model, which itself gave tolerably serviceable results.105 As regards the lack of appreciable variation in the apparent size of the moon, how—without recourse to desperate expedients—Ptolemy thought he could get round the difficulty we do not know.106 But he may not have despaired—presumably he did not despair—of

some explanation being possible. In his view, we may assume, the difficulty presented by this phenomenon was not great enough to justify his abandoning the model as a whole.

As we have noted before, until such time as a superior model is available, any scientist would be justified in continuing to maintain, in the face of prima facie counter-evidence, a theory that had shown its ability to account for at least part of the phenomena, though every scientist should in principle, to be sure, be especially self-critical on the question of when the strength of the counter-evidence is such as to make a new model imperative.107 Yet the price Ptolemy has paid in this case is clear: the elision of part of the data is here no mere temporary

simplification for the sake of argument, but represents a limitation on the viability of the model itself.

Conclusions for the Exact Sciences

Our survey, to date, of some of the main types of simplification and idealisation in Greek science has been drastically selective, but some points have, I hope, emerged sufficiently clearly. The move to discount some of the phenomena in question is associated with some of the most notable successes of Greek science. On occasion, to one looking back with the benefits of hindsight, it seems as if the problem in ancient science is too little abstraction from the complexities of the phenomenal situation, rather than too much, though there was—there is—no way of telling in advance when this may be the case. Some attention, at least, is paid by Ptolemy, for one, to the conditions under which simplification is possible, though he provides no exact rules, only rough-and-ready practical guidelines, with his appeal to a vague, certainly unquantified, notion of "negligible difference." That already indicates some awareness of the problem of discounting parts of the phenomena to leave in play only what is readily explicable. While this was often a sensible policy, it could also prove all too facile a manoeuvre, when recalcitrant data that are central to a problem are simply ignored and when there is no question of their being reintroducible, in principle, at a later stage, with the theory remaining intact.

The Life Sciences:
Teleology

Thus far we have taken our examples from the exact sciences, but comparable moves can be documented also in other areas of ancient speculative thought with results that must provoke further reflection on the aims and methods of ancient investigators. Teleology offers a general rubric under which we can discuss some especially striking examples from various areas of the life sciences.108 From the time of

Plato, at least, the notion that the world as a whole is well-ordered, the product of divine design, is one of the most powerful motive forces in ancient science, though it remained a far from unanimous, indeed a much contested, view.109 The question we may raise in this regard is whether or how far teleological accounts were secured at a cost of discarding part of the phenomena in a way that is broadly comparable with the elisions we have studied from the exact sciences.

In the first developed statement of a teleological cosmology, in Plato's Timaeus —and often thereafter—it is explicity recognised that other factors besides the good have to be taken into account. Plato's Demiurge and the workings of reason are confronted with the factor of necessity, exemplified by the concomitance of material properties, as when the hardness of bone necessary to protect the head is inseparable from a heaviness that weighs it down and makes for insensitivity.110 The human race would have been longer-lived but less intelligent if the head had been covered by a thicker layer of bone: as it is, unable to secure both long life and intelligence, god sacrifices the former, lesser end to insure for humans, as far as possible, a noble and intelligent, if shorter, life. In Aristotle, too, the final cause is often contrasted with what he too calls necessity—that is, simple, not conditional, necessity111 —again associated with the material properties of things. Some

things are so because they have to be so, or happen to be—the colour of the eyes, for instance—not for the sake of some end.112

Since teleology does not apply without exception in Plato or Aristotle,113 there is no need for failures of the good to be denied —though both philosophers will insist that the Demiurge or nature has secured

the best possible results, within the constraints of necessity.114 Failures need not simply be elided, since they can be laid at the door of necessity or the recalcitrance of matter, even though for Plato, and to some extent for Aristotle, that risks amounting to a concession that they are, in that respect at least, beyond explanation, since a proper explanation, by definition, will be in terms of the good.115

Moreover, the normative role of the concept of nature in Aristotle, in the zoological treatises especially, deserves remarking. His official and explicit statement, many times repeated, is that nature corresponds to what happens always or for the most part.116 In practice, however, "natural" is sometimes reserved not for what happens usually, but for what is quite exceptional.117 This is the case, for instance, where we are told that in humans alone the natural parts are fully "according to nature": in humans alone the "upper" part is directed to

the "upper" part of the universe, and the right side is most rightsided.118 Here what Aristotle describes as "natural" is what he deems to be best, where he uses the human species as the norm by which the rest of the animal kingdom is to be judged. By that standard all other animals fall short. Yet the ideal they fall short of is still referred to as what is "according to nature" or "natural," despite the fact that this picks out not what happens always nor even for the most part, but what is true of humans alone.

Many of the parts and functions of the lower animals are thus evaluated from the point of view of those of higher species, especially of the supreme species, humans. The heuristic value of this idea is clear. It enables Aristotle to recognise, for example, that in the so-called bloodless animals there is an analogous fluid that performs the same functions as blood,119 or, again, that there are analogues to the heart, in his view the control centre of the vital functions.120 Yet, equally clearly, he is led to make some very dubious value judgements. He speaks repeatedly of the parts of certain animals, or of whole species, as deformed or maimed , using the very same terms,121 such as

the

Similar tendencies are particularly prominent in Galen. The whole of his treatise On the Use of Parts and many other extended passages in other works are devoted to establishing and illustrating the thesis that nature does nothing in vain, which he often, indeed generally, construes as not just a general but an exceptionless rule: every part has a purpose, and nature is perfect.126 But the tension this thesis sets up can be seen in his anatomy, his physiology, and his pathology.

Thus, developing a common Greek idea,127 Galen represents apes as caricatures of human beings.128 Yet, as is well known, he often uses apes—as others had done before him—as the basis of his anatomical descriptions of humans; his account of the muscles, for example, explicity derives from his dissections of apes.129 From the point of view of transferring conclusions to human anatomy, the ape had better be as close to us as possible.130 Yet so far from some of Galen's great admiration for humans extending to the ape, he calls the ape ridiculous: it has a ridiculous soul and so also a ridiculous body.131 Yet why, if nature does nothing in vain, it plays such jokes, is not explained—and similar points apply also, regrettably, to Galen's account of the human female.132

Elsewhere—in, for example, his account of the blood-vascular system—we can see the heuristic value of the principle that each part serves a purpose, yet his identification of purposes is selective. Thus he infers that blood is transferred from the right to the left side of the heart, in the adult, through pores in the septum separating the ventricles. He does not claim that these pores can be seen, though pits in the septum suggest their beginnings.133 But they are necessary to account for blood in the arterial system.134 However, he knows very well that in the embryo there is a direct route for the blood between the two atria, namely, through the foramen ovale, and he also knows that this closes after birth.135 Why it should close should be a problem, since if it had remained open nature would not have needed the interventricular pores. Yet Galen quite fails to discuss this, merely remarking how marvellous it is that the foramen closes after birth and asserting that it would be of no use in the adult.136 It is enormously to his credit that he realises that the communications in the embryo heart differ from those in the child once born, and it is to his credit too that

he does not fudge the function of the foramen ovale, of which he provides the first extant description.137 Thus there is no question of his attempting to deny that the foramen exists or that it acts as a foramen. Nevertheless, it is striking that his thinking is sufficiently compartmentalised for the difficulty I have mentioned not to have occurred to him.

Finally, a far more massive elision is involved in his treatment of diseases, where we may recall some of the problems raised in Chapter 1. How, we may ask, does an out-and-out teleologist account for diseases? Here, if anywhere, there is evidence of a failure of the good.138 One argument that was available, and that Galen duly uses, is that nature can only achieve as good results as the material she has to work with will allow.139 Left to herself, Galen says, nature would have made us immortal.140 He also argues that residues, for example, are formed as the necessary by-products of other physiological processes that are essential to secure some good, and, again, that potentially damaging bile is needed to counteract the potentially damaging phlegmatic residues:141 one thing leads to another. He asserts that when the animal is healthy, there is no danger, but adds that nature foresaw that it would be easy for excessive residues to be purged from the stomach by vomiting—a remedy long used by Greek doctors.142 Nature evidently needs a helping hand; but Galen still fails to confront the question of the break-down of the system in ill-health. What good does that do?

None, obviously; it is simply the necessary consequence of the materials we are made of. But the problem is that that factor had been appealed to before, to account for how we come to have residues in health. Why those potentially damaging residues should get out of control, why there is a disruption of the status quo in the body, is left unexplained, at least unexplained in teleological terms.

The thesis that nature always acts for the good can only be sustained by resolutely focusing on some parts of the phenomena to the exclusion of others that had also to be reckoned as part of common knowledge. The failure of the animal kingdom to be humans is not allowed to count as counter-evidence even to the weaker, qualified Aristotelian version of the thesis, for many animals, as degenerate or deformed, are not fully "natural." Nor are evident inconveniences in the anatomy or the physiological processes of humans allowed to tell against the stronger, Galenic position, and no more are diseases. It is not that teleology as such is mistaken in principle. On the contrary, in many areas and on many questions it proved itself in the ancient world—as it was also to do later—a marvellously powerful heuristic tool. Yet the negative features of its use, as a device for exclusion, for foreclosure, are manifest.

To try to understand this dominant—though, it should be repeated, far from universal—trend in ancient science, it may be helpful to recall our earlier discussions of the extent to which Greek scientists offered accounts that did not merely differ from but directly rivalled and aimed to supersede traditional mythical and religious beliefs and attitudes.143 While many ancient scientists had no intention of incorporating a moral message in their work, many others had and did. Even where that was not the primary motivation of their inquiry, it was sometimes an adjunct to it. Ptolemy not only draws personal comfort from the order revealed by astronomy, he claims (following Plato) that it improves men's characters,144 and that the same is true also of the

study of harmonics.145 But the revelation of order is not, of course, by itself bad science. The nub of the question is what kind of order, and how—with what scruples—secured. The double bind on the teleologists was that the greater the potential strength of the moral message concerning the beauty and goodness of nature, the more had to be set aside and either ignored completely or set down to necessity and to the recalcitrance of matter. The most striking examples of the difficulty arise in connection with claims made in the life sciences, but the exact sciences too exemplify the point,146 and even where the good is not at issue, there were hesitations and waverings on the limits of permissible, and those of necessary, idealisations.

The Value and Effect of Science in the Ancient World

These case-studies have raised a number of extremely general issues in the interpretation of ancient Greek science, and we may, in conclusion—and at the risk of still further sweeping generalisations—broach as a final topic the question of some of its values and effects. From the point of view of the ancient world it is worth asking what difference science made. The question relates to their point of view, since from ours parts of the answer, concerning what difference their science made, must be clear. From the Renaissance on, the myths and realities of Greek science have been enormously influential: myths, because the ancients' ideas have often been distorted when invoked on either side of later disputes, whether to be idealised or to be reviled; realities, because not everything that Greek science has been taken to stand for is mere fantasy, in particular not certain key methodological notions, including those of the value of empirical research, of the application of mathematics to the understanding of the physical world, and of an axiomatic deductive system. The repercussions both of those myths and of those realities have been immense, even though it goes without saying that not every idea influential in the rise of modern science has an ancient antecedent, real or mythical—in particular not our intense preoccupation with the possibility that science, by being applied, may provide the key to material progress and prosperity (an idea only modestly represented in the ancient world).147 Moreover, when translated into modern terms and given an institutional framework as a result partly of that preoccupation, what were mere aspirations towards understanding and control in the ancient world have certainly been transformed in the process of their very actualisation.

The blunter and in some ways harder question I proposed concerned the ancients themselves. There the inquiry into nature was generally an activity confined to a tiny elite and intelligible to not many more. Natural science, and even mathematics, established only very limited bridgeheads in what passed for moderately general education. Long after the correct explanation of eclipses was available, ordinary soldiers—and some of their generals—were still capable of being frightened by them, as the debacle of the Athenian retreat from Syracuse illustrates.148 Moreover, in that instance, those ordinary soldiers were nevertheless able, at least according to the story in Plutarch, to win their freedom, in some cases, by reciting passages from Euripides.149

Even among the literate elite themselves, the gap between those who were capable of independent research and those who merely knew something about it was very great, as the immensely learned, but at points quite uncritical and confused, Pliny illustrates.150 Introductory or elementary textbooks came to be produced in mathematics, astronomy, and medicine, but in late antiquity this increasingly had the negative effect of defining the outer limits of what there was to know, as much as the positive one of increasing the chance of what was within those limits being preserved.151 Medicine, to be sure, was al-

ways of exceptional general interest.152 The other main area that involves the inquiry concerning nature where knowledge and interest extended beyond a small minority was astrology, which must be granted an important positive role in keeping some scientific knowledge alive, since, as we remarked before, some of the same framework of theory underpinned it as underpinned the study of planetary motions in themselves.153

Much of the otherwise reasonably well-educated or well-read public remained very largely ignorant of advanced natural science. There were particular discoveries—such as that of the vast size of the universe in comparison with the earth—that might have had important repercussions on common assumptions, but they did not, or did not to any great extent, even when they were not totally ignored.154 The day when science could shake the whole foundation of the belief in the privileged place of man in the universe was not yet. The ancients themselves often maintained the belief in some form, and they tended rather to be fortified in it by their scientific studies.155

One general moral was, however, quite widely learned. Natural scientific explanations appeared to have enough success to justify the general claim that natural phenomena have naturalistic explanations. Yet even here bad examples (such as the quite speculative and largely imaginary theories of thunder and lightning) were cited as often as good ones (such as eclipses), and it is notable that those who used this argument in late antiquity were more often philosophers—such as the Epicureans156 —than those who actually engaged extensively in advanced scientific research. Meanwhile, more sinisterly, those successes of science, especially the demonstration of the orderliness of heavenly motions, were also appealed to, as early as Plato, in order to support a particular view of the moral governance of the cosmos, itself invoked—in Plato's case—as justification for drastic measures of social control directed against atheists and dissidents of every kind.157 More generally, whenever the order revealed in nature could be represented as hierarchical, this provided grist to authoritarian mills.158

As seen by the average theatre-goer, those who studied nature were figures of fun, in Aristophanes' day, in Plautus'—and in Molière's.159 Natural science was thus assimilated to any other kind of mumbo-jumbo or wonder-work, including to some more traditional modes of

special wisdom such as prophecy or divination. Furthermore, although some ancient natural scientists were keen to differentiate themselves from rivals, whether from divination, from philosophy, or from within science itself, others, as we have seen, sought, rather, to associate their activity to moral philosophy (astronomy is good for the soul) or even to religion,160 as when Galen talks about the study of the parts of animals in terms drawn from the mystery religions and speaks of his own book on that subject as a hymn to nature and, indeed, superior to ordinary hymns.161 In part this simply reflects the modalities of the expression of the theoretical motivation of scientific research (which was not the only possible motivation; there were other, practical ones as well, especially in medicine).162 But while to assimilate science to moral

philosophy, to the pious worship of nature, even to prophecy, might make it more prestigious, even more comprehensible to a certain audience, this also masked certain differences between science and other modes of wisdom. Anatomical research might be described by Galen as an initiation into the mysteries of nature, but in many respects it was unlike any other initiation: it was harder work, and the results obtained were subject to a different kind of scrutiny and verification. Ptolemy too might hope that studying examples of heavenly order might make you more orderly in everyday life. But, again, that heavenly order was to be revealed only by distinct and rather rigorous methods.

Much of the ancient inquiry concerning nature was formalised common knowledge, and much was fantastic speculation. But some of it was neither, as we can see from such examples as the proofs of the sphericity of the earth, or of Archimedes' principle, or of the role of the valves of the heart, or by such discoveries as that of the precession of the equinoxes, or the nervous system, or the diagnostic value of the pulse. To express an allegiance to the principles of engaging in research and of securing a comprehensive and reliable data base, to the need to put theories to the test, to expose and root out unexamined assumptions, to withhold judgement where the evidence was insufficient, to acknowledge your own mistakes and uncertainty—all this was often no more than a matter of paying lip-service to high-sounding ideals. But if this was to bluff (and as we have seen, it often was), it was a bluff that could be called, and we have also seen how, on occasion, it was called, and how the ideals were at least sometimes lived up to and the promises they implied fulfilled.

For all the more or less ill-informed, at the limit actually malicious, confusion of science with some other kinds of wisdom—a confusion to some extent fed by the scientists themselves—it was, as those very scientists were, to judge from their practice, well aware, a wisdom with a difference. It was a wisdom committed to different procedures of discovery and of the justification of belief—even if the full force of those differences was hardly generally appreciated, and even if the full demonstration of its potential had to wait until modern times. It was more vulnerable than other modes of wisdom, since in principle it incorporated within itself an invitation to challenge its results (it gave

hostages to its opponents); at the same time it was more secure, insofar as parts of those challenges could be withstood successfully. It played for higher stakes, and sometimes won, even if not as often as it claimed. The distinction between science and myth, between the new wisdom and the old, was often a fine one, and the failures of ancient science to practise what it preached are frequent; yet what it preached was different from myth, and not just more of the same, more myth. The rhetoric of rationality was powerful and cunning rhetoric, yet it was exceptional rhetoric, not so much in that it claimed not to be rhetoric at all (for any rhetoric may aim to conceal itself), as in supplying the wherewithal for its own unmasking—even if some of its exponents did not notice that the mask was still in place. If many of the new wise men were short on delivery, they were long on aspiration, and the aspirations were of a kind that were, in time, to produce extraordinary delivery.

Meanwhile, however, the fact that in its beginnings, science was often explicitly concerned, if sometimes rather naively, with the moral dimension of the activity of science itself reminds us, if we need reminding, that it originated in no merely intellectualist debate. Indeed, its offering an alternative world view, in the widest sense an alternative morality, was central to some of its confrontations with traditional wisdom, though the fact that science may and to some extent must incorporate such values was rather to be lost sight of in the aftermath of the scientific revolution and has only gradually come to be recognised once more in recent times. There is a moral for us today, too, in the point that, again from its very beginnings, we can detect some tension in disciplines that professed that they must give a public account of themselves but that, to a greater or lesser degree, were bound to remain specialised, if not exclusive, studies. We have had many occasions to point to the mystifications of the ancient inquiry into nature, but of course that is a feature that is still with us today, and one whose threat has increased immeasurably with the increasing remoteness and specialisations of science—as one might say of the massive superstructures that have been erected on or, rather, built over the foundations laid by some ancient visionaries.