The Nature and functions of Analogical Reasoning
Analogical reasoning has played an important role in the development of the sciences. As a means of explaining the unfamiliar in terms of the
familiar or of subsuming one field under the laws governing another, it has didactic and heuristic value; fertile analogical theories may enrich both the borrowing and the lending disciplines. The stimuli to reasoning from analogy may be both general and specific. In the seventeenth century, Galileo, Descartes, Newton, and others had predisposed savants to "a unitary conception of natural forces," and discoveries in many individual scientific disciplines were so impressive as to become paradigmatic for other fields as well. Thus botanists were beguiled in particular by advances in animal physiology to essay zoological methods and theories in their own domain.[2]
Two characteristics distinguish late seventeenth-century analogical reasoning about plants and animals from earlier comparative theories. First, unlike the traditional theories of sympathies and antipathies, the new analogies provoked further tests; insofar as the model itself was experimental, so was the analogical hypothesis. Second, savants spurned the technological models and mathematical standards that many had previously favored and chose instead models and standards from the life sciences themselves. That was possible principally because the Harveian theory explaining the motions of the heart and blood offered a seductive model. Consequently, much analogical reasoning in botany reveals a double trend: toward increased experimentalism in botany and zoology and toward greater self-reliance within the biological sciences.
The most ambitious and elusive of botanical analogical leaps in the seventeenth century was the hypothesis that sap circulates in plants as blood does in animals. First propounded in 1660 by Johann Daniel Major, only one generation after William Harvey published his De motu cordis, the idea caught on quickly in England, France, and Italy. Although Nehemiah Grew and Marcello Malpighi are probably the best known adherents of the theory, they were not alone in exploring it systematically. Members of the Academy were the first to push the analogy to its limits. Claude Perrault and Edme Mariotte defended the idea at meetings of the Academy during the summer of 1668, with Nicolas Marchant demonstrating Mariotte's experiments and Samuel Cottereau Duclos opposing the hypothesis. In 1679 and 1680, Mariotte, Perrault, and Duclos published revised statements on the subject, and later in the 1680s other academicians, especially La Hire, tried to repair the analogy.[3] Their efforts shed light on how the Academy fostered the biological sciences, on the dramatic changes in botanical research in the late seventeenth century, and on the merits of analogical reasoning.
Before examining the theory of the circulation of the sap as developed in
the Academy, a double foundation must be laid by establishing the nature of analogical reasoning and by describing the features of the Harveian model that inspired academicians. Only then can academicians' elaboration of the hypothesis be assessed.
Analogy is a means of comparing two things. By identifying similar traits in both objects, scientists infer the existence of a causal mechanism affecting both. Several types of analogy used by scientific savants have been identified by historian-philosophers of science. Claire Salomon-Bayet distinguishes "lazy-universal" from "experimental or observational" analogies; Georges Canguilhem differentiates mathematical analogies from explanation by reduction; and Mary Hesse compares formal and material analogies.
Salomon-Bayet's distinction is addressed specifically to the early modern period. Taking Paracelsianism as the exemplar, she defines lazy analogy as a mental habit of ancient origin that simply assumes untested the sympathy or antipathy of all parts of the universe. By contrast, experimental or observational analogy is open to verification and correction. Experimental analogy subsumes particular objects or phenomena under general theories either by applying the laws or theories of one discipline to another or by employing a model; the first method is more fertile than the latter, which has didactic but not explanatory power.[4]
Canguilhem focuses on analogical reasoning in biology, contrasting deduction (or the use of mathematical models) and explanation by reduction (or the use of mechanical analogies or analogical models). The former is less naive but also less useful than the latter for biology, which is not always susceptible to expression in mathematical language.[5] Canguilhem's discussion also clarifies Salomon-Bayet's distinction between analogy from theories and analogy from models. Two examples suggest the two kinds — structural and functional — of analogy: the stirrup and anvil after which the bones in the ear are named, and the ancient irrigation system which inspired the Greek concept of the motion of blood. Unlike Salomon-Bayet, who insists that a fertile analogy must prompt experiment or observation, Canguilhem allows that in biology analogy from models can be an alternative to experiment, because models permit "the comparison of entities which resist analysis.[6] Both Canguilhem and Salomon-Bayet agree that models may aid the quest for laws.
Mary Hesse is interested in both the physical and the biological sciences and, unlike Canguilhem and Salomon-Bayet, systematically analyzes analogical reasoning as a logical tool appropriate in all sciences. Hesse distinguishes between material analogy and formal analogy. Material analogy
is both substantive and predictive, whereas formal analogy is neither, since it is simply a one-to-one correspondence between different interpretations of the same formal theory. Thus Hesse's analysis of material analogy is relevant to seventeenth-century botany.
Material analogy is a means of comparing different organisms or phenomena by pairing and comparing their individual traits. The model is the organism or phenomenon that is already understood; the explicandum is the organism or phenomenon that needs to be explained. A systematic comparison of their traits will determine whether the explicandum can be understood in terms of the model. Thus, if the traits in the model resemble those in the explicandum, and if the traits in the model constitute a causal mechanism, then the same causal mechanism may be inferred in the explicandum.
Hesse provides a schema for such comparisons, listing the paired traits in two columns, one for the model and one for the explicandum. Paired traits are subject to "horizontal" comparison, while the theory linking a set of traits as the causal mechanism in the model provides a "vertical" connection. The closer and more numerous the horizontal similarities between pairs, the more likely that the vertical causal chain of the model may be inferred to exist in the explicandum.[7]
Material analogies may have explanatory power if three conditions are met. First, the model and explicandum must have something in common beyond the analogy in question, that is, there must be "pretheoretic" similarities between them. Second, their horizontal similarities must be substantial. Third, there must be a causal connection among the traits in the model.[8]
Hesse's analysis clarifies Canguilhem's and Salomon-Bayet's distinctions. Thus the most fruitful dichotomy is not between models and the application of one discipline to another, as Salomon-Bayet argues, nor between mathematical models and explanation by reduction, as Canguilhem would have it. Rather, there are empty and productive analogies, and the latter may be either mathematical or material; but only material analogies with pretheoretic similarities may have predictive power.
Analogical reasoning has various advantages and shortcomings. As a form of induction, it is prey to all the shortcomings of the inductive method. But analogical argument enjoys a special role when observation or experiment are inadequate.[9] In such a case, however, it is inconclusive not only for all the usual inductive reasons but also because it rests on an incomplete identification of similarities. Nevertheless, analogy offers a means of selecting
a hypothesis, because it draws attention to comparable properties that may betray causal similarities.[10]
As differentiated from experiment, analogy permits comparisons between traits or phenomena that cannot be analyzed.[11] Just as an experimenter uses theory to suggest predictions that do not proceed from tests and observations, so the savant uses analogy to suggest hitherto unsuspected causes or theoretical entities.[12]
Analogy resembles theory, because it offers a way of subsuming a pattern of behavior under a set of laws, and because it holds out the promise of generating explanations and predictions. Canguilhem explains how analogies differ from experiment and are like theories:
What validates a theory is the possibility of extrapolation and prediction which it permits in directions which the experiment, keeping to its own level, would not have indicated. Similarly, models are judged and tested one against another by the completeness of the accounts they give of the properties to which they direct attention, in the object of study, and also by their aptitude for revealing properties hitherto unnoticed. The model, one could say, predicts.[13]
In explaining this similarity of analogical reasoning to theory, Max Black's study of metaphor is useful. A metaphor is a comparison whose thrust is indefinite. So long as the scientist does not know "how far the comparison extends" and tries to push the analogy to its extreme, unexpected theoretical implications may emerge, for "it is precisely in its extension that the fruitfulness of the model may lie."[14]
Good analogies, therefore, supplement and encourage experiments and, like theories, suggest what, unobserved, might have remained unsuspected. It sometimes happens that an analogy, like a metaphor, changes the way both the model and the thing being explained are viewed. This may be due to the impoverishment of the model,[15] or to changes in the meanings of the concepts associated with the model and explicandum; sometimes "the two systems are seen as more like each other."[16]
Analogical thought has influenced biological thought in both positive and negative ways, depending on how the model is selected. For example, when models are more appropriate than experiments, analogy can stimulate alternative observations or anticipate evidence that is inaccessible given experimental capabilities. But overreliance on mechanical and technological models has injured biological analysis, by emphasizing structure at the expense of function. Thus, Greek and Latin anatomical nomenclature suggests the appearance but not the function or causal mechanism of the anatomical part. Such analogies cannot "show the identity of the
general laws of the two fields of phenomena which are brought together" and thus are causally insignificant.[17]
The risks and rewards entailed in the choice of model are illustrated in two theories of the motion of the blood. Both Harvey and the ancients explained the motion of the blood analogically. The ancients compared it to the unidirectional supply of water to irrigation channels and hence argued that blood was absorbed by the body and had to be continually replenished; their theory was conceptual, not experimental. Harvey replaced the notion of irrigation with the idea of circulation within a closed circuit, an idea that was compatible with his experimental findings.[18] Models chosen from technology on the basis of structural resemblance are likely to lead to an explanatory cul-de-sac when applied to the biological sciences. But in the seventeenth and eighteenth centuries savants began to use biological models more often, with positive results for the life sciences and especially for plant and animal physiology.
Analogical reasoning can serve as the prelude to comparative method. This is particularly important in analogies between plants and animals, which often resemble one another functionally, but have different structures. Either similarities or differences may be emphasized, but pretheoretic resemblances determine whether the comparisons are valuable.[19] The important point for comparative method is to test, not assume, any similarities. As will be seen in the following chapter, some academicians used analogy in precisely this fashion; starting with a comparison between plants and animals, they tested the analogy experimentally, admitting structural dissimilarities between plants and animals and investigating how plants accomplished equivalent functions in the absence of equivalent organs. In such cases, analogy identifies crucial dissimilarities and becomes a preliminary step to understanding causal differences.
Analogies are full of pitfalls for the unwary. Even scientists who rigorously examine the traits of two organisms for dissimilarities need to guard against claiming too much for an analogy. In the eighteenth century, Albrecht von Haller complained that analogy had become a substitute for experiment. This was the flaw that had weakened medicine, he believed, because "the great source of error in physics" was due to "physicians, at least a great part of them, making few or no experiments, and substituting analogy instead of them."[20] Analogies should inspire experiment, and although they may extend it, they should not be a substitute for it. The overenthusiastic savant runs the risk of conferring "a representational value on a model" and of letting the model become axiomatic instead of being
only the lender of a mechanism.[21] Analogies are frail inductive tools. When the identification of similarities or dissimilarities is incomplete, then the analogy is inconclusive.
In summary, analogies have more than a didactic value to scientists. They offer a means of selecting hypotheses. As a weak form of induction, they can be useful when only a few instances are known or when only sparse observational data exist. They should inspire, may supplement, and will sometimes replace experiments. They resemble theories in suggesting new experiments, subsuming the behavior of an object under a general rule, predicting, and explaining. They are fertile because, like metaphors, their extension is indefinite; when scientists push analogies to their extremes, they may discover what would otherwise have eluded them. The best analogies pay compound interest on what they have borrowed, by changing the way both the borrowing and the lending disciplines are perceived. Finally, failed analogies have a particular use: by drawing attention to crucial dissimilarities in the things being compared, they stimulate a search for the causal mechanism. Failed analogies, therefore, are the beginning of comparative method and show where further research will be necessary.
Improved analogical reasoning helped advance the biological sciences. The choice of model was important. What was needed was a broadly conceived, well developed theory, one with adequate observational and experimental supports to win adherents, and sufficient specificity to avoid sectarian splits. Chemistry was appealing, and was regarded by Paracelsus, Helmont, Boyle, and others as a source of knowledge about the basic and unchanging components of the universe, but it was beset by doctrinal divisions.
In the absence of an approved general explanatory theory, savants had recourse to smaller-scale theories with a more limited explanatory range. William Harvey's writings on the movements of the heart and blood offered just such a theory, and as his hypothesis became acceptable scientists in other fields borrowed it. In the Academy and elsewhere, botanists formulated the hypothesis that sap circulates in plants. Their analogical leap is an important case study for several reasons. It is an example of borrowing from within the biological sciences and illumines the relative importance of structural and functional analogies in botany. It indicates whether savants tested analogy experimentally and how they responded to its limitations. Finally, it reveals that when the model failed, academicians used analogy as a stimulus to comparative method and thus came to ask an important botanical question.