Aristotle on Demonstration. What makes knowledge “scientific” (epistemonikos) according to Aristotle is that it should constitute strict demonstration (apodeixis). And by demonstration /5/ he means an inference from premisses which are true, primary, immediate, more knowable (gnorimos) than, and prior to the conclusion, and further that the premisses furnish an explanation of the conclusion.1 It is not enough that the inference be a deductively valid syllogism; logical validity does not suffice to render a piece of reasoning scientific. It is not even enough that the inference be a valid one from true premisses. The premisses must be of a quite definite kind, and they must specify in a unique way the cause of the effect or property of which scientific knowledge is desired.

How are the premisses of the requisite sort to be obtained? Not by further demonstration, for that would lead to regress. The premisses must be primary and immediate; that is, they must carry conviction in their own right once they are properly understood. (The English term “self-evident,” with its overtone of “obvious,” can be misleading in this context.) But how is such an understanding to be attained? Aristotle knew perfectly well that on an answer to this question his entire account of science would stand or fall. But he is famously laconic in his response.2

Experience (empeiria) is, it appears, crucial to the discovery of the necessary premisses, the starting points of demonstration in natural science: /6/

It pertains to experience to provide the principles of any subject. In astronomy, for example, astronomical experience supplied the principles of the science; it was only when the phenomena were adequately grasped that the demonstrations proper to astronomy were discovered. Similarly with any other art or science.3

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Through perception we register particulars, but these particulars themselves are not objects of scientific knowledge, which is directed to universals.4 The process leading from the perception of particular things to the grasp of universals Aristotle calls epagoge, which is often translated as “induction.” Is there, then, a second sort of inference, a form of systematic generalization, that provides the starting point for demonstration? Ought we say that Aristotle proposes not one but two forms of inference, demonstration and induction, together leading to science (episteme)? Epagoge is, indeed, sometimes described as though it proceeded by enumeration, or depended on a systematic comparison of instances.5

But any resemblance to what Bacon will later call induction is misleading. In Aristotle’s view, it seems, rather, to be a process of recognizing the universal in a few particulars, of grasping the phenomena as instances of a specific universal. It does not depend on sample size.6 There is first the /7/ ability to perceive (which humans share with animals); the perceptions persist and constitute memory. And “out of frequently repeated memories of the same thing develops experience.”7 In this way the universal is, as it were, “stabilized” in the soul, bringing about a state of mind called nous (insight, intuition, comprehension). Nous is a direct grasp of the universals already implicit in perception, and is brought about by epagoge.8 It is more basic than demonstration; it is, Aristotle assures us, the originative source of science since it anchors the premisses from which demonstration begins.9

Underlying this analysis, of course, is Aristotle’s doctrine of the mind’s ability to receive the form of an object. “The thinking part of the soul must therefore be, while impassible, capable of receiving the form of an object; that is, it must be potentially identical in character with its object without being the object.”10 So that “mind is what it is in virtue of becoming all things.”11 The veridical character of episteme depends on this ability of mind to grasp form, as presented in perceived appearance. The form conveys the essential nature of the thing perceived, and so the basic premisses of demonstration can be required not only to be true but to be necessarily true, displaying causal relationships that are “more knowable” in themselves than the fact to be demonstrated. /8/

Here in brief and familiar outline is how Aristotle proposes that science should be acquired. There are obviously many difficulties and obscurities in the account. How, for example, is one to deal with the obvious problem of sense-error? Aristotle himself points it out: “We must maintain that not everything which appears is true; firstly, because even if sensation . . . is not false, still appearance is not the same as sensation.”12 Only “reliable” (aei kurios) phenomena can serve as a basis for natural science, he reminds his reader.13 But how is one to know, in an absolutely assured way, which of the phenomena can be counted as reliable?

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More fundamentally, what justifies us in supposing that the forms given us in perception really do convey the essence of the thing perceived? Aristotle recognizes in passing that there may be a “failure” in perception when we are unable to perceive the inner structures of a substance on which a property, like the ability of a burning-glass to set objects on fire, may depend.14 If we were to be able to see pores in the glass and the light passing through these pores, then “the reason of the kindling would be clear to us.” But as it is, such microstructures lie permanently outside the range of our senses. “Light shines through a lantern because that which consists of relatively small particles necessarily passes through pores /9/ larger than those particles.”15 Aristotle is clearly aware of the challenge this sort of explanation poses for his phenomenalist account of the natural sciences, but he nowhere deals with this directly.16 Instead, he restricts himself to observed correlations in the examples on which he relies (as in his celebrated explanation of the lack of incisors in the upper jaws of horned animals in terms of the nutriment needed for their horns17), or to simple causal analyses, as in his frequent references to eclipses.

In a significant passage, he draws a distinction between knowledge “of the fact” (oti, quia) and knowledge “of the reasoned fact” (dioti, propter quid ). Since he is trying in this passage to explain how demonstration works, the examples he chooses are of special interest. They are drawn from astronomy, an odd choice it might seem. Our perceptual knowledge of the heavenly bodies is obviously very limited; they are, he notes elsewhere:

excellent beyond compare and divine, but less accessible to knowledge. The evidence that might throw light on them, and on the problems we long to solve respecting them, is furnished but scantily by sensation. Whereas respecting perishable plants and animals we have abundant information, living as we do in their midst. Both domains, /10/ however, have their special charm. The scanty conceptions to which we can attain of celestial things give us, from their excellence, more pleasure then all our knowledge of the world in which we live . . . . On the other hand, in certitude and completeness our knowledge of terrestrial things has the advantage. Moreover, their greater nearness and affinity to us balances somewhat the loftier interest of the heavenly things . . . .18

Where the presumptive pores in glass that allow light to pass are imperceptible to us because of their minute size, the difficulty with the heavenly bodies is one both of distance and of nature. Not only does their great distance prevent us from observing their properties in any other than a perfunctory way, but (in Aristotle’s view, at least) we have reason to believe that these bodies are fundamentally different in nature to the bodies of earth by means of which our perceptual expectations have been molded. So our explorations of the skies must be regarded as conjectural. Why, then, choose examples drawn from astronomy to illustrate a thesis about strict demonstration in natural science? Was it just because of his general fondness for astronomical illustrations (“a half-glimpse of persons

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that we love is more delightful than a more leisurely look at others”19), or was it /11/ because these examples were in some special way apposite?

The Nontwinkling Planets. The distinction he draws between two grades of knowledge was intended in part to help overcome the difficulty of discovering a unique causal explanation when one has to work backward from perceived effect to less familiar cause. To see this will require a detailed analysis of the key passage in the Posterior Analytics (I, 13). He gives two examples of the sort of problem that, despite appearances, lends itself to demonstration. The most striking property of the planets (other than the “wandering” motion that gave them their original Greek name) is that they do not twinkle. Alone among the heavenly bodies they shine with a steady light. How are we to explain this? How are we to “demonstrate” the property of nontwinkling they possess? Only by finding the more basic property of planets responsible for the fact that they do not twinkle. Aristotle proposes nearness as a plausible candidate. But are the planets nearer than the other heavenly bodies? A confident assertion follows: “That which does not twinkle is near: we must take this truth as having been reached by induction or sense-perception.”20 /12/

This gives him an apparent proof of nearness:

S1 A That which does not twinkle is near B The planets do not twinkle

Therefore the planets are near

This he calls a demonstration of the fact (oti). It is an improper demonstration because it is not causally explanatory: nontwinkling does not explain the nearness. The major premiss is merely an observed correlation between two properties of shining bodies: if they do not twinkle, then they are observed to be near. This is sufficient, however, to prove the truth of the conclusion. And now this conclusion can become the minor premiss of a new syllogism:

S2 A Nearby (shining) objects do not twinkle B Planets are near

Therefore planets do not twinkle

This is (Aristotle says) a demonstration of the reasoned fact, a proper demonstration, because it gives the cause of (or reason for) the fact. The middle term joining the extremes functions to explain the link between them: nearness is the reason why planets do not twinkle. What gives this demonstration force as demonstration for Aristotle is not merely its syllogistic validity but its explanatory force. /13/

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But is S2 a proper demonstration? It would appear not, and for two separate reasons. Neither premiss seems to qualify as the sort of necessary truth that a demonstration requires as starting point. How would one establish the necessity of S2A, the claim that nearby shining objects do not twinkle? It is not enough that it just happens to be true (if indeed it is true). “True in every instance,” Aristotle himself reminds us, does not suffice; the attribute (nontwinkling, in this case) must be “commensurately universal,” that is, it must belong to every instance (of nearby shining object) essentially.21 It must be shown to “inhere necessarily in the subject.” Induction-as-generalization will not do; at best, all it can show is factual correlation of attribute and subject. Epagoge cannot (as Aristotle knows) reduce to induction, in the sense of generalization.

It is worth noting, indeed emphasizing, that exactly the same issue arose for the logical positivists when they tried to define the notion of “law” that was so basic to their account of explanation. It is not enough for an inductive generalization to be factually true (“everyone in this room is over five feet tall”) for it to serve as the starting point of a scientific explanation. An “accidental” universal will not sustain the sort of counterfactual conditional (“if x had been in this room . . . ”) that is taken to be diagnostic of “genu- /14/ ine” (what Aristotle would call “essential”) lawlikeness. We shall return to this later. Suffice for the moment to say that any account of science that rests (as Aristotle’s does) on attributes given in perception is bound to have trouble in separating “essential” from accidental linkages, in construing causality as anything more than invariable correlation.

How is epagoge supposed to lead us to the insight that nearness is the cause of nontwinkling in the planets? Is some kind of immediate grasp of the universals, nearness and nontwinkling (in the case of planets), sufficient? It is clearly not enough for epagoge to bring us to recognize the two universals in their particular instances; they have also to be seen as causally (necessarily) related. In On the Heavens, Aristotle does give a hint as to what the causal relationship might be. Noting that the sun appears to twinkle at sunrise and sunset, he goes on:

This appearance is due not to the sun itself but to the distance from which we observe it. The visual ray being excessively prolonged becomes weak and wavering. The same reason probably accounts for the apparent twinkling of the fixed stars and the absence of twinkling in the planets. The planets are near, so that the visual ray reaches them in full vigor, but when it /15/ comes to the fixed stars it is quivering because of the distance and its excessive extension; and its tremor produces an appearance of motion in the star.22

Here is a theoretical account of why twinkling occurs, and how it may be due to distance. It relies on the notion of a “visual ray” that goes out from the eye, and is attenuated by distance. This is obviously not something that could be derived directly by epagoge from perception of particulars. It is a tentative conjecture about an underlying process that might account

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for the twinkling of the distant stars. Its explanatory force comes from its ampliative character: it does not just associate twinkling with great distance, but suggests why this association might betoken a causal connection. The necessity is of a weak hypothetical sort: if there are visual rays and if visual rays tend to attenuate with distance (more theory needed here), then the stars will (necessarily) twinkle. What allows one to transcend mere factual correlation in this case is not nous as direct insight into essence, into causal relations themselves not given in perception, but plausible theoretical reconstruction in terms of postulated underlying structures.

In his “official” account of the nature of demonstration in natural science in the Posterior Analytics, Aristotle nowhere explicitly admits the /16/ mediating role played by theory in the establishing of causal connections. He leaves the reader to believe that there is a power of mind which can somehow, subsequent to perception, attain to the essence of natural things immediately. It is not hard to see why he does this. It is crucial, in his mind, that the premisses from which science begins be “primary,” that is, not themselves in need of further evidential support. They must be definitively true. Unless this be granted, there is no hope of attaining the “eternal and necessary knowledge” that he holds out as the aim of his inquiry into nature. But once one admits that either premiss is “theoretical” in the sense sketched above, one has implicitly given up on this aim. For theory (e.g., about visual rays) is clearly not primary; it is in need of further corroboration, of systematic testing. Nor is it definitive; Aristotle himself allows that his suggestion that visual rays attenuate in vigor the further they travel is at best only probable.

His attempt to supplement the phenomenalism of his starting point with an optimistic rationalist account of what epagoge can accomplish, brings out the main weakness in his account of demonstration. This can be seen in another way if we shift attention to the minor premiss, S2B. How are we to know that this premiss is true? Perception alone does not allow us to claim that the /17/ planets are near. Their nearness is not perceived; it has to be inferred. How, then, can the minor premiss be regarded as primary? Aristotle introduces a distinction between something “more knowable in itself’ and something “more knowable to us.”23 The fact that planets do not twinkle is more knowable to us; the fact that they are near is more knowable in itself because it serves as a causal principle. But how do we get from the former to the latter?

S1 makes use of that which we know (that the planets do not twinkle) to arrive at a new truth: that the planets are near. The order of exposition followed by Aristotle suggests that the “demonstration of the fact” provides the needed minor premiss (S2B) for the demonstration proper displayed in S2. Does this work? Everything depends on the major premiss S1A: That which does not twinkle is near. This is where the choice of the nontwinkling planets turns out to be a brilliant one. For one can plausibly

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point the causal arrow in either direction. Distance causes twinkling (which yields S1A, if one allows the negation of the rather vague term “distant” to be equivalent to “near”). Perhaps this is why Aristotle says so confidently of S1A: “We must take this truth as having been reached by epagoge or by perception.”24 (As we have already seen, however, something more than generalization is required here, something /18/ like the attenuation theory of On the Heavens.) If one grants that (great) distance “causes” twinkling, then the (relative) nearness of the planets is established. But Aristotle clearly takes the causal arrow to operate in the other direction also: nearness causes (explains) nontwinkling (S2A). This is much more problematic. Distance is, so far as one can see, not the only possible cause of the twinkle in starlight. So nearness alone does not demonstratively explain why the planets do not twinkle. This latter is not a deductive causal relationship, though Aristotle’s choice of negative characteristics (nondistant, nontwinkling) that can be thought of in a positive way (nearness, emitting steady light) conceals this. The causal arrow does not really point in both directions here, though it would be easy to miss this.

Aristotle was too good a logician not to realize what was going on here. He recognizes that a condition is necessary in order for his analysis of proper and improper demonstration to hold. The two attributes (nontwinkling and nearness in the case of the planets) have to be reciprocally predicable, or to put this in another way, the major premiss has to be convertible. Whatever does not twinkle is near, and whatever is near does not twinkle. This is equivalent to requiring that the cause postulated be the only possible cause, so that one can infer in either direction. /19/ Now, of course, if this can be taken for granted, the problem of constructing a demonstration is greatly eased. There is still the question of how epagoge is to lead us to the grasp of causal relationships. But at least we do not have the further problem of dealing with alternative possible causes, each of them sufficient to explain the effect. The normally hypothetical character of inference from effect back to efficient cause (what we shall later call retroductive inference) has been tacitly suppressed.

A glance at Aristotle’s other illustration of the two kinds of demonstration bears this out:

S3 A Whatever waxes thus is spherical B The moon waxes thus

Therefore the moon is spherical

This is demonstration of the fact that the moon is spherical, relying on the knowledge that the moon goes through certain phases in relation to the sun’s position, and, second, that waxing in this way implies a spherical shape.

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S4 A Whatever is spherical waxes thus B The moon is spherical

Therefore the moon waxes thus

This is demonstration proper because the spherical shape is the cause of the waxing, and the truth of the minor premiss (S4B) is certified in advance /20/ by S3. Aristotle remarks that a “quick wit” (agkinoia) is needed in order to grasp that the lunar phases are due to a reflection of sunlight.25 But this is a case where the perceived phenomenal correlation leads particularly easily to a postulation of the causal connection. The wit does not have to be especially quick!

More important, the major premiss once again looks more or less convertible: spherical shape causes waxing thus, and waxing thus (more or less) implies a spherical shape. It is true that other possible causes of the waxing could not have been entirely ruled out in Aristotle’s day, but it would have seemed overwhelmingly likely that sunlight falling on a spherical moon was the cause. Geometrical optics lends itself nicely to necessary-seeming claims and to simple inductive evidence. Thus, not only do we have a cause but it can plausibly be represented as the only possible cause. And this is needed for Aristotle’s account of demonstration to work. Such cases are obviously not typical of the broad range of contexts in natural science where demonstration/explanation is sought. And even these special cases do not really enable necessity to be claimed for the premisses. The transition from “better known to us” to “more knowable in itself ” must remain tentative except in the most favorable of cases. Talk about the “pores” that allow light to pass /21/ through glass, of “visual rays” and the way they are attenuated over distance, of the manner in which nutrients that would otherwise have been channeled to the incisors of the upper jaw are diverted to the production of horns in horned animals, cannot be fitted into the straitjacket of demonstration. Strict demonstration in cases such as the astronomical ones above will work only when a causal relationship between A and B can be “seen” to hold with necessity, and when B also requires A, i.e., when A can be “seen” to be the only possible cause of B.

The Living World. This latter condition would be particularly difficult to satisfy in the domain of living things, the domain to which Aristotle devoted such an extraordinary effort. It has often been noted that in his voluminous writings on animals there are few, if any, instances of the demonstrative form laid down in the Posterior Analytics. This has, indeed, furnished a major topic of scholarly research in recent years.26 In his review of more than five hundred animal species, he lists for each species numerous properties that could serve as differentiae. Scholars have tried hard to extract a natural classification from this profusion, but it is clear that none is there: Further, it seems doubtful that one was intended, since the divisions given

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are frequently criss-cross, as Aristotle himself notes.27 He does suggest pos- /22/ sible causal connections between properties: the lungs temper the heat of the body in warm-blooded animals;28 the kidneys carry more fat than do other internal organs because the kidneys require a greater supply of heat, being closer to the surface and having much “concoction” to perform, and fat is a cause of heat.29

From our point of view, these would seem to be no more than causal speculations, prompted by some fairly casual correlations and some very general theories about the role of such causal agencies as heat and fat in the animal body. How could they ever be made demonstrative? What would the “primary premisses” in the study of living things look like?30

Functional explanations of the sort Aristotle relied on offer a particular challenge in that regard: “The function of the lungs is to cool the blood and hence the body.” Even if one could show that respiration is needed to cool the body and that it does cool the body, how would one show that it does not also have another function? This is the equivalent of the problem about the convertibility of the major premiss in the case of the astronomical examples earlier. What he needs, according to his theory of demonstration, is definitions in which the essences of the various natural kinds are expressed. But if these definitions are complex, containing a list of differentiae (as he appears to envisage), and if /23/ many of the terms used are equivocal, “said in many ways,” as he admits they are, how could one ever trace a unique causal line with necessity from the genus or from one or a cluster of the differentiae to the property to be explained? The case to which later Aristotelians would always return was that of man, with a conveniently simple single differentia. But this, as Aristotle himself recognized, was altogether untypical of the inquiry into animal natures generally. “If demonstration still remained an ideal in zoology, as in mathematics, it was an ideal that had to recede the more Aristotle’s zoological researches progressed.”31 To what extent was Aristotle himself aware of the limited applicability of his teaching on demonstration?

Introducing an ingenious but highly speculative account of comets, shooting stars, and the “fuel” that sustains them, he says: “We consider a satisfactory explanation of phenomena inaccessible to observation to have been given when our account of them is free of impossibilities.”32

A weak criterion, indeed, in comparison with the exacting demands of demonstration! In On the Heavens, he frequently laments how far short of demonstration his account falls: “When anyone shall succeed in finding proofs of greater precision, gratitude will be due to him for the discovery, but at present we must be content with what /24/ seems to be the case.”33

He obviously thought that proofs “of greater precision” were, in principle, constructible; the significance to his doctrine of epagoge of “phenomena inaccessible to observation” had not, to all appearances, sunk in. Our later story will be devoted to the reweaving of these threads that he

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for the first time separated off. The patterns of inference/explanation in contemporary science are strikingly different from those proposed in the Posterior Analytics. But the quest for a causal explanation of natural phenomena that should be as epistemically secure as possible still remains.

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