Eliminating Indefiniteness or Variation

As I said earlier, one cannot assume that because some accounts or descriptions of a certain domain are inexact, inexactness cannot be eliminated from them, or different accounts cannot be given that are exact or at least that are more exact than the original ones. Can the inexactness under consideration here be eliminated from the accounts of matters of conduct

or can it at least be reduced? The last possibility is of importance given Aristotle's claim that nature or natural phenomena are, as matters of conduct presumably are, characterized by the same kinds of inexactness. If accounts of other domains that are subject to the same kinds of inexactness can achieve a reasonable level of exactness, why not those about the domain consisting of matters of conduct? Can the techniques that are helpful in reducing the inexactness of accounts of biological phenomena, for example, be useful for reducing inexactness in the case of ethical accounts?

I gave some evidence above that Aristotle takes the features of variation and indefiniteness to characterize some natural phenomena—for example, he thinks that the periods of generation and gestation in many animals exhibit much variation and cannot be accurately fixed. These examples are not isolated instances, however. The extent of these kinds of inexact-ness in the order of nature is, according to Aristotle, considerable:

8.16

The Ascidians differ very little in their nature from plants, but they are more akin to animals than the Sponges are, which are completely plants. Nature passes in a continuous gradation [ ] from lifeless things to animals, and on the way there are living things which are not actually animals, with the result that one class is so close to the next that the difference seems infinitesimal. Now a sponge, as I said just now, is in all respects like a plant: it lives only while it is growing on to something, and when it is pulled off it dies. What are called Holothuria and the Sea-lungs and other similar sea-animals differ only slightly from the sponges in being unattached. They have no power of sensation, but they live just as if they were plants unattached to soil. . . . Sometimes it is doubtful whether these Ascidians and any other such group of creatures ought to be classed as plants or as animals: In so far as they live only by growing on to some other object they approach the status of a plant; but yet they have some fleshy substances and therefore probably are capable of sensation of a kind. (P.A.681al2)

Nature, according to Aristotle, has no sharp or clear boundaries: "It passes in a continuous gradation from lifeless things to animals." It is difficult or even impossible to determine exactly where plants end and animals begin or whether the sponge and the Ascidians are plants or animals. Concerning the sponge, Aristotle, despite his claim above that it is in all respects like a plant, cannot determine to his satisfaction whether it is a plant or an animal. In H.A. (548b10) he reports the common disputes as to whether sponges have sensation, but he goes on to argue that they do have sensation and therefore are animals (549a8, 487b10). There are many groups of animals that, according to Aristotle, "dualize"; they straddle the divisions of plants and animals by "inclining towards the plants on one side and the animals on the other" (P.A. 681b3). Among these Aristotle includes the knides, sea-anemones, starfish, and testacea (P.A. 681b10).

Other animals "dualize" with respect to different divisions: for example, the hermit-crab between the crustacea and testacea (H.A. 529624), the pig between solid-hoofed and cloven-hoofed (H.A. 499b12, b21), the ape between man and quadrupeds (H.A. 502a16) or between biped and quadruped (P.A. 689632), the ostrich between bird and quadruped (P.A. 697b14).

I should add to the above list the phenomena Aristotle lists in the passage from the Top. quoted above (8.14), for example, night, shadow, earthquake, cloud, and wind. For these are, again, things that lack definite or clear boundaries. The same is true with the phenomena of eclipse, thunder, or deciduousness that Aristotle discusses in the Post. Anal. (93a20, 98b). Again, throughout the biological treatises Aristotle speaks of the extensive variation that exists in most animal characteristics. Thus, there is considerable variation in the parts of animals—for example, there are many differences in the lung (P.A. 669a25), ears vary considerably from one species to the other (H.A. 492a25), so does hair (517b10), the head and the neck (497b15), the reproductive organs (500620), the teeth (501a8), the mouth (502a6), the tongue in birds (504a35), and in general all internal parts (509a27).

The above examples of natural phenomena that presumably exhibit variation or indefiniteness show the extent to which nature is, according to Aristotle, inexact. Recognizing this is important for the purpose of comparing how he deals with the supposed inexactness of the domain of nature and that of matters of conduct. Consider, for instance, Aristotle's treatment of the phenomena of eclipse, thunder, and deciduousness in the Post. Anal. He first proposes in that treatise the following definitions of them: "Thunder is a noise in the clouds," "Eclipse is a privation of light," and "Deciduousness is leaf-shedding" (93a20, 98b). These quasi-conceptual or verbal definitions reflect most clearly the vagueness or in-definiteness we tend to associate with these phenomena. For what quality or quantity of noise, privation of light, or leaf-shedding constitutes these phenomena? Not every noise in the sky is thunder, or every privation of light an eclipse, and there is difficulty in fixing, as Aristotle would say, the exact differentiae of these phenomena. Even deciduousness, which has often been taken as being reasonably well defined, is problematic. Not all types or quantities of leaf-shedding are cases of deciduousness. Is a tree that sheds its leaves in the spring—for example, Erythrina caffra —deciduous? Or is one that sheds its leaves but replaces them simultaneously or almost simultaneously? The differentiae these sorts of definitions use cannot be fixed precisely.

The vagueness of these verbal definitions can perhaps be reduced or eliminated by replacing them with definitions that state the causes of the

relevant phenomena. Such a move is quite familiar to Aristotle. He offers the following causal definitions of these same phenomena: "Eclipse [of the moon] is the obstruction by the earth of the moon's light," "Thunder is an extinction of fire in a cloud," "Deciduousness is the coagulation of the sap at the junction of the leaf-stalk" (93b5-10, 99a29). The advantage of such causal definitions is that they succeed to some extent in moving away from terms or concepts that seem to be inherently loose, vague, or indefinite. Thus, by defining thunder as the extinction of fire in a cloud, one avoids the looseness or vagueness of the term "noise," but problems still remain. For even this definition uses the term "cloud," which is, like "wind" or "night" or "shadow," vague or indefinite. The same is perhaps true with the other causal definitions Aristotle gives, and probably is true with any causal definition. Aristotle is, of course, ready to admit that no object of perception can be defined exactly or that those disciplines dealing with things as inhering in matter are less exact than those that deal with things as not inhering in matter.^[20] Yet the causal definitions Aristotle gives are less inexact than the verbal ones.

Again, in dealing with the considerable variation of the domain of nature, Aristotle's strategy is to offer definitions that aim at leaving behind such variation or differences. In defining the parts of animals, for example, he opts always for a functional definition of a part. Thus, despite the differences or variation in the lungs of animals—they can be small, large, spongy, dry, full of blood, bloodless, and so forth—the lung is simply the organ of breathing (P.A. 669a15) or it is that whose function is always breathing (669b8). Aristotle succeeds in this way in bypassing, so to speak, the variations which natural phenomena exhibit; he succeeds in moving to a level of generality or abstraction that is almost free of the problems he attributes to the phenomena.

Naturally, the question arises why Aristotle's strategies for dealing with vagueness or variation in the domain of nature cannot be applied to matters of conduct. One may concede to Aristotle that the accounts of matters of conduct cannot be as exact as those of mathematical objects, but go on to argue that if our accounts of matters of conduct could be made as exact as those of the disciplines studying the order of nature, it will be sufficient. Why do the problems of vagueness or variation not concern Aristotle as much in relation to the study of the order of nature as they do in relation to the study of matters of conduct? Are there reasons for thinking that our accounts of the domain of ethics must be more inexact than those of the domain of the disciplines studying nature?

One may, for example, argue that matters of conduct exhibit these types of inexactness to a much greater degree than natural phenomena do. Although this is by no means obvious, there may be reasons for taking it seriously. For a considerable component of the domain of conduct consists

of the various virtues and vices, which, according to Aristotle, are dispositions or states of character, or something akin to these. But dispositions have always been considered to be paradigms of indefiniteness or vagueness. If this assumption is correct, it is not surprising that Aristotle's efforts to give adequate definitions of gentleness, liberality, irascibility, ambitiousness, and so forth produce little in terms of exact definitions. It is also not surprising that he comes to the conclusion that such elements of conduct cannot be defined exactly. However, not all elements of conduct are dispositions. Aristotle claims that happiness, the good, and pleasure are not. Also, nature itself includes many dispositions, and one must not forget phenomena such as wind, night, shadow, heaps, and so forth.

Even if matters of conduct were to be inexact to a greater degree than natural phenomena are, it is not clear why the inexactness in the accounts given of the former cannot be reduced in the way it can in the accounts given of the latter. It is not obvious, that is, that there is a problem in applying, for example, Aristotle's strategy of replacing verbal definitions with causal-explanatory ones in the case of matters of conduct. One may, for instance, succeed in reducing the inexactness of our account of gentleness by moving from a verbal definition of it to a causal one as Aristotle does in the case of thunder. Thus, Aristotle gives a causal-explanatory definition of fear: "Fear is a process of cooling produced through scantiness of blood and insufficiency of heat" (P.A. 692a23). This definition can be used, in turn, to give a causal-explanatory account of cowardice that may avoid some of the indefiniteness of a verbal definition of it: "Those [animals], however, that have excessively watery blood are somewhat cowardly. This is because water is congealed by cold; and coldness also accompanies fear; therefore in those creatures whose heart contains a predominantly watery blend, the way is already prepared for a cowardly disposition" (P.A. 650b27). Elsewhere Aristotle associates fear, cowardice, and courage in an animal with the size of its heart, but again the causal or explanatory mechanism is that of heat: "Those [animals] with a large heart are cowardly, those with small or moderate-sized ones, courageous (this is because in the former class the affection which is normally produced by fear is present to begin with, as their heat is not proportionate to the size of the heart, but is small and therefore hardly noticeable in the enormous space that it occupies; so that their blood is comparatively cold)" (667a15).^[21]

I do not mean to suggest that all causal-explanatory accounts have to be like the ones Aristotle gives of fear, cowardice, or courage—that is, physicalistic. Aristotle's strategy of replacing verbal definitions with causal-explanatory ones does not specify that definitions of the latter type must be in physicalistic terms, although many of Aristotle's own definitions are physicalistic. Also, it is not certain that such definitions are always an improvement over verbal ones with regard to indefiniteness. Definitions

or explanations that use such terms as "cold," "heat," "watery blend," "large," or "small" are likely to face their share of indefiniteness or vagueness. But it is clear that Aristotle's strategy of replacing verbal definitions by causal-explanatory ones need not be excluded from application in the case of matters of conduct, and Aristotle does not say that it is excluded.

One cannot assume that causal-explanatory definitions are possible in the case of every matter of conduct or that the indefiniteness of any account is due to its not being a causal-explanatory one. What kind of causal account, for example, is one likely to give of the city that is of any relevance to the issue of indefiniteness or vagueness?^[22] Similarly, the problem of indefiniteness in the case of heaps or baldness has not much to do with the causes of these things or phenomena. Whatever the causes of baldness, the problem is one of drawing the boundaries or limits of the phenomena or the relevant concept.

If, indeed, the problem is in most cases that of drawing boundaries or limits, one can see why matters of conduct may pose greater problems than natural phenomena. Drawing boundaries of indefinite phenomena or concepts is not, as I said above and as Aristotle recognizes, easy in any domain. Yet where one draws the boundary in the case of baldness, wind, or shadow is perhaps not very important; not much may depend on it. With such phenomena we may decide to have recourse to Aristotle's special ordinance and draw the boundary at some point. But in matters of conduct much depends on where one draws the line. It may mean the difference between virtue and vice, good and bad, noble and base, blameworthy and praiseworthy, and so on. The reason Aristotle finds it difficult to simply decide on the limits of gentleness is that the line between it and irascibility is the boundary between virtue and vice and hence the boundary between an agent's being praiseworthy and blameworthy. Yet it is not certain that the difference between drawing boundaries in the world of nature and matters of conduct is as large as it at first appears. The scientist who wishes to know where life begins cannot just draw the boundary anywhere, and of course where we draw the line in the case of concepts such as animal, life, fear, and so forth may be of great importance to ethics. Our moral positions on abortion, euthanasia, or cowardice may partly rest on where such boundaries are drawn.

One might also argue that it would be difficult to deal with the problem of variation in matters of conduct in the way Aristotle deals with it in the case of natural phenomena—that is, by disregarding such variations and by moving to a higher plane of generality or abstraction. Thus, what matters in the case of the lung is its function and not the many differences among lungs. It is much harder to disregard the differences or variation in matters of conduct, for they seem to be essential: Differences in the circumstances, time, emotion, persons, merit of persons, nobility, neces-

sity, and so forth, are relevant in giving an account of choice, obligations to our parents, the nature of gentleness, friendship. They are certainly of great relevance in the context of action—in making a choice, in deciding whether to obey our parents, or to be someone's friend.

Perhaps in some cases the variation in the order of nature may be easy to disregard, although this cannot be generalized. But one may be willing to concede that variation in matters of conduct cannot be disregarded. Although one may be willing to recognize the above considerations as providing some reasons for thinking that the inexactness under discussion here poses more problems for matters of conduct than it does for natural phenomena, this may not be the end of the matter. Not all natural phenomena are, after all, alike. Although being an animal is, as Aristotle points out, to some extent inexact, being bald or being a heap is clearly much more so. Some things or phenomena are less indefinite than others, or at least some are definite enough that acceptable definitions or accounts can be given of them.

It might be possible, then, to distinguish within the domain of conduct matters which exhibit the inexactness Aristotle cites to a much higher degree than others, and of the latter class of things adequate definitions or accounts can perhaps be given. Aristotle however tends at times, and without further argument, to view all matters of conduct as being equally inexact and more inexact than the objects mathematics and the scientific disciplines investigate. This tendency is due to the emphasis he places on the more particular or practical concerns of the discipline of ethics in contrast to the general or abstract concerns that are the focus of other disciplines.

Aristotle takes ethics to be a practical discipline, to have practice or action as its ultimate goals. He also insists that these practical goals of the discipline require that it reaches the particulars, that its primary concerns are with the particular or specific rather than with the general or abstract aspects of conduct. Unlike theoretical disciplines that supposedly stay at the level of the general or abstract, practical disciplines need to reach the level of the particular or specific, but some features of exactness/inexactness may be more prevalent or pervasive at one level than they are at the other. In addition, some of these features may pose greater (or lesser) problems when present at one level than when present at the other. At the level of the particulars, for example, matters of conduct may exhibit considerable variation and such variation may be of great importance in making decisions, choosing a course of action, determining whether blame or praise is due, and so forth. But this does not rule out the possibility that other matters or at least aspects of them do not exhibit such variation or that they do so to a far lesser extent, for, perhaps, the moral virtues are subject to variation but the intellectual ones are not, or while the cases

of courage, liberality, or gentleness may exhibit considerable variation, virtue itself may not. Thus virtue, both moral and intellectual, may be defined as that which makes something good and causes it to perform its function well (N.E. 1106a15). Such a definition appears to succeed, as the functional definitions of the parts of animals do, in bypassing variation and giving a more general or abstract account.

Aristotle gives a number of definitions which, by being highly general or abstract, seem to deal successfully with the feature of variation he attributes to matters of conduct. So he defines magnanimity as intolerance of dishonor or being unaffected by good and bad fortune (Post. Anal. 97b20). In similar fashion he defines most of the virtues and vices in E.E (II.iii). The same can be said of the account of happiness as that which can be only an end in itself and of the good of F in terms of the function of F. These accounts may be lacking in detail, but this is clearly another matter.

One cannot, in other words, rule out the possibility that some elements or aspects of matters of conduct can be treated at a level of generality or abstractness that is sufficient for avoiding or at least minimizing the problems of inexactness that concern Aristotle. Grant may, therefore, have been correct in suggesting that Aristotle tends to overstate the scope and degree of inexactness under consideration here in relation to matters of conduct, an overstatement that appears to have been accepted by the ancient commentators.^[23] Once one distinguishes somewhat more sharply than Aristotle is willing to do between the theoretical concerns of philosophical ethics and those of practice that he often stresses, one sees that some elements of conduct and some accounts of them (the most abstract and general ones) may be less subject to the inexactness that concerns Aristotle.

Thus, Aristotle himself recognizes in 8.2 that accounts dealing with particulars are likely to be more lacking in exactness than the general ones. Aristotle is correct on this point. It is quite possible that the individual virtues exhibit greater variation or indefiniteness than virtue itself does. It may therefore be more difficult to define what gentleness or irascibility is than what virtue is. Aristotle's own discussion bears this out. Similarly, it appears that the concept art is less problematic with respect to the types of inexactness under consideration here than the concept tragedy . The latter concept has resisted any and every attempt to articulate a reasonably precise definition of it.^[24]

Yet Aristotle may have had some reasons for insisting that matters of conduct or our accounts of them pose greater problems than natural phenomena and our accounts of them, and these reasons may ultimately have something to do with the specific accounts he himself gives of the basic elements of conduct and with his own conception of ethical theory.

For if the basic elements of the subject matter of ethics and its principles or axioms exhibit the kind of inexactness Aristotle claims that they do, then all the other things that are derived, proved, or demonstrated from them will most likely also be affected by these same features. If, for instance, the good or virtue and our accounts of them were to exhibit these features of inexactness, then the rest of our accounts in ethics would probably also be inexact. But why is the case of ethics different from that of the investigation of, for example, the biological phenomena? After all, Aristotle defines animal as that which is capable of sensation (P.A. 653b23, 666a35), and clearly sensation is not free of indefiniteness or vagueness. As seen earlier, some living things occupy the fuzzy area between animal and plant; they, as Aristotle says, "dualize."

Although one can accept, as Aristotle does, that nature exhibits indefiniteness, the problems matters of conduct pose may nonetheless be far greater than those natural phenomena pose. Consider, for example, the problems Aristotle encounters with giving an account of virtue. There is, as I said above, some account of virtue that seems, on the surface at least, not to be affected by variation or indefiniteness—namely, that virtue is that which makes something good and causes it to perform its function well. Yet the definition of virtue that Aristotle relies upon in order to explain or define the nature of the individual virtues, the definition that does most of the work in the N.E. , is a classic example of an account suffering from inexactness for which there seems to be no obvious remedy. The definition, of course, is none other than the one Aristotle gives at N.E. in terms of a notion that is a paradigm of inexactness—namely, the notion of the mean. Indeed, not only does Aristotle insist that the differentia of virtue is the mean, he argues that the mean relevant to virtue is not some exact quantity that can be determined mathematically by a mathematical operation on some other mathematical quantity or quantities, but something that is relative to the agent and the practical circumstances. But this nonmathematical way of explicating the mean introduces so many indefinite or indeterminate factors that the differentia of virtue remains, for all practical purposes, intractable.

Virtue is, however, one of the basic elements of Aristotle's ethical theory. It has a role to play in the explication of other components of his theory. The definition of virtue Aristotle gives is to be used in explicating the nature of the individual virtues as well as vices—for example, the nature of courage, temperance, gentleness, irascibility. All of them are either instances of virtue or vice; they are either instances of the mean or of deviation from it. Thus, the problems with Aristotle's account of virtue or vice that result from the inexactness of the notion of the mean will be encountered again in our explication of the particular virtues or vices in terms of this same notion.

Consider, for instance, some of the accounts of the virtues or vices Aristotle gives in the E.E. In trying to define irascibility or the irascible person, Aristotle writes, "The man that gets more angry and more quickly and with more people than he ought is irascible" (1221a15). This account, which Aristotle takes to exemplify the use of the mean in explaining the virtues or vices, is, like the accounts of all the other virtues and vices he gives in this context (see in particular those of cowardice, insensitivity, and jealousy), as indefinite as one is likely to meet. For what exactly is asserted by claiming that the irascible person gets "more angry and more quickly"? Aristotle, of course, recognizes the vagueness of such accounts and concludes his discussion of the virtues by remarking, "Let us then accept these simple definitions, and let us make them more precise when we are speaking about the opposite dispositions" (1221b8). When, however, Aristotle returns to an examination of the virtues that is supposed to produce accounts of them that are more exact, things are not any different. Let me give as an example part of what he says about gentleness in his more exact account of it:

I do not wish to insist here that for definitions to work they must be exact, as Aristotle himself often says in the logical treatises; that they must specify the quantity and quality of the differentiae, that such specifications must be numerical, or even that numerical specifications are possible.^[25] What I wish to point out, or what is important to recognize, is that if the basic elements of matters of conduct exemplify the above kind of vagueness or if the highest definiteness our accounts can attain is that exemplified by Aristotle's discussion of gentleness, then there is more reason to be concerned about the inexactness of ethics than about that of the disciplines investigating natural phenomena, for although animal may not be altogether definite, it is not as indefinite as virtue seems to be. The indefiniteness of animal appears to affect not every animal, but only a few at the fringes—for example, the sponges, sea-anemones. But the inexactness of virtue affects every virtue and vice—all of them are almost equally problematic. The inexactness of virtue, a basic element in Aristotle's ethical

theory, filters down, so to speak, to every one of the particular virtues and vices.

Suppose, in addition, that the Good itself, the good of an F, or a good F are to be explicated ultimately in a way that involves the notion of virtue. This is clearly the case in Aristotle's ethical theory. The notion of a good F is, according to Aristotle, to be understood in terms of the virtue of F. Similarly, what the good of an F consists of is to be explained in terms of the function and virtue of F.^[26] If this is so, then the inexactness of virtue will most likely filter down to every important aspect of Aristotle's theory.

The problems of inexactness Aristotle encounters in his own theory and the way the inexactness of the basic elements affects other components of his theory are likely to be found in any theory that relies on these same elements. Thus Rawls offers a definition of a good F that is not very different with respect to definiteness from some of Aristotle's accounts:

A is a good X if and only if A has the properties (to a higher degree than the average or standard X) which is rational to want in an X, given what X's are used for or are expected to do, and the like (whatever rider is appropriate).^[27]

An account that faces similar problems is the one given by Ross, although he seems to be aware of the difficulties:

And "good of its kind" is relative in a further sense, viz. that it is comparative. We have in mind what we suppose to be a rough average of the excellence of the members of the kind, and we call anything better than this good anything worse than it bad, not implying that there any fixed neutral point at which what is good ends and what is bad begins. "Good" in this usage means "better than average" or perhaps "considerably better than the average," "bad "worse than average" or perhaps "considerably worse than the average."^[28]

These accounts of "good of its kind" are, with regard to their definiteness, as problematic as Aristotle's own account of virtue or of being a good F. The notions of "average," "standard," "rational to want," and so forth are notorious for their lack of any clear or definite boundaries. Ross recognizes this and he does not wish to be taken as "implying that there is any fixed neutral point at which what is good ends and what is bad begins."

It is quite possible, then, that Aristotle's reasons for taking matters of conduct and our accounts of them to be more problematic with respect to their inexactness than natural phenomena and our accounts of them stem in part from his conception of ethical theory and the particular accounts he gives of some of the basic elements of conduct in his own theory. A different theory that assigns a lesser, or no role at all, to virtue may perhaps fare better as far as exactness is concerned than Aristotle's own theory' does. Even an ethical theory that takes virtue as a basic element

but nonetheless succeeds in treating it not as a disposition will have made another step toward reducing the kinds of inexactness that concern Aristotle. But most importantly, a theory that succeeds in explicating virtue without reference to the mean or at least without reference to the kind of mean Aristotle's theory relies upon will have made the most significant step toward reducing inexactness. Given the kind of ethical theory he puts forth, these options are not open to Aristotle.