Updated: May 6
Watson, John. “Aristotle's Posterior Analytics: II. Induction.” The Philosophical Review 13, no. 2 (1904): 143. https://doi.org/10.2307/2176446
IN a former article the general character and presuppositions of demonstration, as conceived by Aristotle, were pointed out. It is the aim of science in all cases to discover the 'cause' for the existence of a certain property in an individual thing, or, what is the same thing, to show 'why' the thing cannot but have this property. For science, in the strict sense of the term, consists entirely in the comprehension of the reason why the individual possesses certain properties in common with all the other individuals of the same species. Demonstration is therefore the method by which the particular property found to belong to a thing is proved to be essential to it, in virtue of the possession by the thing of characteristics, which determine that it, in common with other things, must have that property. Aristotle's view of science thus implies that every demonstration proper presupposes that actual things have in them something permanent and unchangeable. It is true that things are found to have properties, the ' cause ' of which cannot be determined; but such properties do not fall within the sphere of science.
Demonstration, however, is only one side of the total process of knowledge. It is not self-sufficient but presupposes that we already in a certain sense have knowledge. For no proof of 'cause' can be given, unless the common and peculiar principles assumed in demonstration are absolutely true. The question therefore arises, how we obtain the principles from which the special sciences start, and which indeed as ultimate cannot be demonstrated by any science. This leads us to the special subject of the present article, the nature of induction, and its relations to other processes of knowledge.
Starting from immediate and indemonstrable principles, demonstration seeks to deduce all the properties which belong to individual things of a certain genus. But these things and properties must be actually known to exist, or there can be no 'cause' or 'ground' of their existence. There are, therefore, as Aristotle points out, four questions that have to be answered before the special problem of science can be solved: The 'fact' the 'cause' whether a subject is 'what ' it is. The first two questions are concerned with things and their properties, the second two with the primary principles from which these properties are to be derived or shown to be essential to the things in question. Strictly speaking, therefore, is concerned only with the ' fact ' and the 'cause'; for only these are capable of demonstration. We may even say that science proper has to do only with the 'cause’ since knowledge of the 'fact,' though it is indispensable to the demonstration of the 'cause’ does not yield a strictly scientific judgment.
Now, demonstration of the 'fact' consists in showing that a certain property belongs to a thing in common with all the individuals of the species to which it belongs. Thus, we may demonstrate that vines are broad-leaved because they belong to the class of deciduous trees, all of which are broad-leaved. This is only proof of a 'fact'; we have not demonstrated the 'cause’ for trees are not broad-leaved because they are deciduous. We do not assign the 'cause' when we show that one property is the invariable concomitant of another, but only when we show that one property is the necessary ground of another. In demonstrating the 'fact' we have to find a middle term. But there are cases in which it is not necessary to demonstrate the fact, and when, therefore, science can immediately go on to demonstrate the 'cause' This takes place when the concomitance of two properties is obtainable by induction, without recourse being had to demonstration. "It is only when perception fails us," says Aristotle, "that we have to ask the question whether a thing is so or not. If we were on the surface of the moon, we should not have to ask whether eclipses occur, or why they occur; both fact and cause would be simultaneously apparent. The universal law would arise to our knowledge from the visible phenomena. The present interference of the earth is visible to us; the simultaneous failure of light is also apparent; the universal principle would then be seized." At first sight this passage seems to assert that 'both fact and cause' are discovered by perception. But this is not Aristotle's meaning; what he wishes to show is merely that induction obtains from perception the data for the conclusion that there is a concomitance of two facts, failure of light in the moon and the interposition of the earth. For induction cannot establish a 'cause' and still less can perception do so. That this is Aristotle's meaning is plain from another passage, in which he uses precisely the same illustration: "Even if we stood upon the moon and saw the earth obstructing it, we should not know the cause of the eclipse; we should only perceive the phenomenon of the eclipse; the cause of it we should not know in its universality; for what we perceived was not the universal principle. Of course, if we frequently contemplated the occurrence of the fact, we should get on the track of the universal principle and should be able to demonstrate it; for in several particular occurrences the universal becomes manifest." Aristotle's view, then, is that while we can by induction obtain a knowledge of the concomitance of two facts, we cannot in this way dispense with demonstration; for only by demonstration can we convert a mere concomitance into a causal connection. There are cases, however, as he indicates, in which induction enables us to dispense with a demonstration of the ' fact.' How we obtain a knowledge of the 'fact' is not the important thing; it may be through induction from observed facts, or it may be by syllogistic inference from facts; but in all cases we must be sure of the fact before we have any ground for valid demonstration of the cause, and we cannot even demonstrate a fact except from knowledge supplied by induction. The problem of science is to determine the essential properties of things, i. e., to show why things must have certain properties, and this problem cannot be solved unless we know that things actually have those properties. Induction must therefore precede demonstration.
The precise relation of induction to demonstration is, however, not free from difficulty. An induction is complete when, by an examination of various particulars, we are enabled to reach a proposition which is true without exception. On the other hand, Aristotle distinctly states that induction can never lead to the establishment of a proposition truly 'universal' i. e., one which is true of all the members of a class, true essentially, and true of the class as such. How, then, is the transition to be made from the inductive result, which only establishes the 'fact’ and the demonstrative conclusion, which reveals the cause? To answer this question, we must consider the relation of cause and effect. Does the existence of an effect necessarily imply the existence of one, and only one cause? Thus, if there is an eclipse of the moon, must there also be interposition of the earth? If trees are deciduous, must coagulation of their sap take place? Aristotle's answer is that wherever we have discovered the real or essential ground, the cause and the effect are necessarily reciprocal; in other words, there is only one cause and one effect. Thus, we do not demonstrate the cause of eclipse, unless we show that it takes place only when there is interposition.
But, while every demonstration of cause is based upon the necessary connection of the cause assigned with the given effect, we usually begin by discovering an invariable concomitance of two attributes. In this case we may not have reached the 'cause'; for though the invariable concomitance of two phenomena may usually be taken to indicate a causal connection, this is not always the case, nor can we ever conclude from invariable concomitance to necessary connection. Thus, we may discover by induction that those trees which are deciduous are also broad-leaved; but we cannot conclude that the 'cause' of their being deciduous is that they are broad-leaved; the 'cause' is in fact the coagulation of the sap in winter in this class of trees. Wherever, therefore, we do not discover a single cause of a given effect, we have not discovered the real cause, but only an invariable concomitant. A plurality of 'causes,' when the term 'cause' is taken in its proper sense as that without which the effect cannot be, is a contradiction in terms. 1 It follows that induction can never of itself prove the cause. An inductive syllogism is defined by Aristotle as one in which we "conclude by means of the minor term that the major term is predicable of the middle"; in other words, it is the process by which we conclude from observed facts that an attribute found in all of these is invariably conjoined with some other attribute found in all of them. We find, e.g., that man, horse, mule, etc., are long-lived; we also learn by induction that they are gallless; and we conclude that all gall-less animals are long-lived. Since man, horse, mule, etc., constitute the whole of the species 'gall-less,' the minor premise may be converted simply. Thus, we obtain the syllogism:
Man, horse, mule, etc., are long-lived,
The gall -less animals are man, horse, mule, etc.,
Therefore, the gall-less animals are long-lived.
But, though in this way we establish the concomitance of the attributes 'gall-less' and 'long-lived,' we do not thereby prove that 'gall-lessness' is the 'cause' of 'long-life.' The inductive syllogism only enables us to assert that 'gall-less' and 'long lived' are attributes invariably found in certain animals, not to connect the attributes as cause and effect. Induction can never establish causal connection. Even if we could learn from inductive observation that isosceles, scalene, and equilateral triangles contain two right angles, we should only establish the 'fact,' not the 'cause'
Now, if induction never takes us beyond the fact of concomitance, how is the universal principle obtained? Is it obtained, Aristotle answers, by the direct grasp of the mind which detects in the concomitance of attributes the cause or ground. Having obtained in this way our universal principle, we are able to demonstrate the cause in regular syllogistic form. The test of our having really obtained the principle seems to be that it, and only it, explains the fact, though it can hardly be said that Aristotle makes this clear. In any case, Aristotle's doctrine is that induction prepares the way for demonstration by revealing concomitant phenomena, the transition to demonstration being made by the direct intuition of the principle involved in the various particulars. Though it can hardly be denied that the transition from invariable concomitance to absolute invariability is hard to justify, it must be said, in defence of Aristotle, that his doctrine is based upon the principle that nature is not a sphere in which pure contingency prevails, but is on the whole subject to law. This, indeed, is a presupposition for which Aristotle can supply no adequate justification; but, granting its truth, it is natural to suppose that when by induction we have discovered certain invariable conjunctions, the mind is able to seize upon the universal principle which these conjunctions suggest. All that Aristotle, however, can say in justification of the transition from the general to the universal, from 'fact' to 'cause,' is that when we are unable to find another middle term without going beyond the class in which our inquiries are carried on, we must accept the last middle term reached as expressing the cause. Having reached this stage, we demonstrate that the subject under consideration must have the property which we already know it to possess by connecting that property with the middle term or 'cause.'
Since the 'cause,' or at least the ' formal cause,' is identical with the definition of the property, it may be said that the object of demonstration is to enable us to define what the property in question is. We have therefore to ask what the general relation of demonstration to definition is. In seeking to answer this question, Aristotle begins with a 'dialectical' treatment, i. e., he starts from the ordinary view of definition as a finished product, which is independent of demonstration. From this point of view not only does definition seem to have no relation to demonstration, but it is hard to see how it can be justified at all. A definition presupposes the existence of that which is defined, and though we can understand how the existence of objects corresponding to the elementary conceptions of a science may be postulated, we cannot postulate the existence of a cause, which is only known as the result of a demonstration, as is the case in all demonstrations which establish a cause extraneous to the subject. If we could define 'eclipse' prior to demonstration, why should any demonstration be needed? Moreover, definition is in a peculiar sense a unity, containing no distinction of subject and predicate, whereas demonstration has to show that a certain predicate belongs to a subject, not in itself, but in its relation to something else.
After this dialectical treatment, Aristotle proceeds to give his own solution. Definition only seems to have no connection with demonstration, because the essence of the thing defined is viewed in separation from the concrete nature of the thing. But, in truth, the essence is the reason of the fact, from which it cannot be separated; and therefore, it can only be discovered after a distinction has been made between the fact and the reason of the fact. Hence, while the essence or cause cannot be demonstrated, since a demonstration of it would mean that it could be brought under a higher conception, it is only when demonstration has shown the necessary connection of a given property with its cause that we are able to define that property. The definition of the property is therefore subsequent to the demonstration of its cause, and, indeed, only differs verbally from the demonstration. The definition is in this case just the succinct statement of the demonstration; eclipse, e. g., is withdrawal of light by interposition of an opaque body. There are definitions, however, which are prior to demonstration, and indeed cannot be reached by demonstration, viz., the definition of the primary elements of a genus, as we find them, e. g., in geometry. Merely verbal definitions, again, are preparatory to these two classes of definition. It is thus evident that real definition, like demonstration, is based upon the essential or rational ground of a thing.
Now, the essence of a thing is that which determines the characteristics by which individual things are assigned to a certain class; and it is, therefore, important to determine the sum of attributes which constitute the conception of the thing. To discover the definition of a thing, we must find the primary genus and the attributes belonging as a whole to all the individuals of a species, but to no other individuals. This constitutes the definition of the thing. The definition, therefore, contains the genus and the specific attribute or attributes. Thus, the definition of the 'triad' is a 'number, odd, prime,' a sum of marks which is found in every 'triad’ but in no other species of the genus 'number.' Since the specific difference is the main thing to be attended to in definition, we should divide the genus into species in accordance with these three rules: (1) The divisions should be based upon oppositions actually found in nature; (2) we should descend in regular order from the less to the more specific; (3) we should carry on the division until we reach the characteristic or characteristics which constitute the lowest species. Division by dichotomy is, therefore, rather barren in results, for nothing is learned from mere negatives; the true method of division is to follow the natural divisions of things themselves. Nor is there any real force in the objection of Speusippus, that a complete definition demands an exhaustive knowledge of all the individuals falling under a genus. For, in the first place, we do not need to know accidental attributes, which do not affect the essence of a thing; and, in the second place, we are entitled, in accordance with the law of contradiction, to exclude the sum of attributes belonging to the excluded species, and thus we reach the attributes found as a whole only in the species defined.
We have seen that the middle term of a demonstrative syllogism may be (1) the 'essence' or 'formal cause.' But besides the formal cause the middle term may be (2) the material cause, (3) the efficient cause, (4) the final cause. In illustration of (2), the 'material cause,' Aristotle cites the demonstration that the angle in a semicircle is a right angle. The ' matter ' here spoken of is space, which is capable of being analyzed into its elements. Such an analysis is performed, when it is ideally divided, by drawing a perpendicular upon a straight line, the space being thus divided into two right angles. The demonstration in Euclid, III, 31, assumes as middle term "the half of two right angles," and thus we get the major premise, "the half of two right angles is a right angle." This being a primary proposition, it cannot be demonstrated, but is obtained by the direct intuition of the figure. It is then proved that the angle in a semicircle is equal to the half of two right angles; and thus, we obtain the conclusion that it is a right angle. The middle term, again, may be (3) the efficient cause. As an illustration Aristotle gives the syllogism:
All aggressors are naturally subject to attack from those they
The Athenians were the aggressors in assailing the Persians.
Therefore, the Athenians were subject to attack from the Persians.
Lastly, the middle term may be (4) the l final cause.' Aristotle at once illustrates the final cause and shows its contrast to the efficient cause. In the syllogism of efficient cause, we begin with the action and go on to the result, in the syllogism of final cause, we begin with the 'end,' and go back through the means for its accomplishment. Thus, we have the two syllogisms:
(1) Good digestion promotes health.
Walking after dinner promotes good digestion.
Therefore, walking after dinner promotes health.
(2) Healthy men have good digestions.
Walking after dinner makes men healthy.
Therefore, walking after dinner promotes good digestion.
We have already seen how induction is related to demonstration in those cases in which the cause is extraneous to the subject under consideration. Here induction prepares the material for demonstration by proving the invariable concomitance of two phenomena, thus enabling the mind by an intuitive act to seize upon the universal principle necessary for a demonstration of the cause. But induction performs a still more important service in the interest of deduction: it is by means of it that the special principles from which a given science reasons are discovered, though the discovery is not made by induction, but by the intelligence itself. Now, these principles, as we know, themselves presuppose certain common principles or axioms, and we have therefore to enquire whether these also are obtained through the instrumentality of induction, and, if not, how they are established.
Can we justify the assumption tacitly made by every special science that the common principles or axioms are absolutely true? What, for example, to take a typical instance, is the rational ground for the assumption of the principle of contradiction? No doubt this principle is seldom or never explicitly appealed to, but it is always tacitly assumed. No principle has the same degree of importance; for by its removal the whole edifice of knowledge must fall in ruins. Can we then show ground for our assumption of its absolute truth? The axiom states that if a thing exists or has a certain attribute, it cannot at the same time not exist, or not have that attribute. On this law of things Aristotle bases the correspondent law of thought, that, if a thing is affirmed to exist or to have a certain attribute, it cannot be denied to exist or to have that attribute. As Aristotle's general doctrine is that the truth of a judgment is determined by its correspondence with that which is, obviously the law of contradiction is primarily a law of being. His view is not that things must conform to the law of contradiction, because thought cannot at once affirm and deny; but that thought cannot at once affirm and deny, because to do so is inconsistent with the nature of things. For, if a thinking subject may at once affirm and deny the same thing, it follows that the same thing (the thinking subject) may at the same time have two contradictory attributes, which is a violation of the law of contradiction. Now, the truth of this law may be proved in a certain sense by showing the untenability of the opposite doctrine, and especially by a presentation of the absurd consequences of that doctrine; but it cannot, properly speaking, be demonstrated. Nor can it be reached by a process of induction; for, unless its truth is presupposed, there can be no induction. This does not mean that it is possessed by the mind prior to all experience, but only that its truth is directly grasped by the intelligence as involved in even the simplest knowledge of real things.
When Aristotle comes to consider the basis of the special principles presupposed in the several sciences, he finds it more difficult to give a satisfactory answer. The problem may be put in this way: If each science presupposes the existence and definition of its principles, how is this assumption to be justified? Or, since our problem rather is how the existence and definition of all the conceptions, primary and subordinate, can be legitimately assumed in demonstration, we have to ask by what right the truth of those conceptions is so assumed. For, though we can demonstrate that a given subject can only have a certain property, because that property is involved in the essence of the species to which it belongs, or is inseparably connected with an essential property of the class to which it belongs, we cannot demonstrate the essence of the species, or the definition of the property. This is the question with which Aristotle is occupied in the last chapter of the Posterior Analytics.
Now, we know that science is impossible unless the first principles from which demonstration starts are absolutely true. How, then, are those principles known to be true? Have we an innate knowledge of them, though it exists at first in an unconscious form? In other words, is the mind unconsciously in possession of such conceptions as 'line,' 'triangle’ 'circle,' and does it obtain a definition of them by mere analysis? This view can hardly be accepted, involving as it does the absurdity that we are unconscious of conceptions without which demonstration is impossible, and the knowledge of which is, therefore, the presupposition of all demonstration. Aristotle, with his doctrine that truth consists in a knowledge of the actual nature of things, could not possibly accept a view which derives the principles of all knowledge from ideas that cannot be shown to have any relation to actual things. On the other hand, if we admit that knowledge of these principles is acquired, how has this knowledge been obtained? It is no doubt true that science assumes their truth; but science is knowledge which exists in a reflective form; and all reflective knowledge, as we know, is derived from knowledge that we already have. How then does science come to have this prior knowledge? It cannot suddenly come into existence out of absolute ignorance; as in other cases, there must be a process by which an advance is made from implicit to explicit knowledge.
It is thus obvious that we must possess a peculiar faculty by which we are brought into direct contact with things, and this faculty is perception, which is 'an inborn faculty of discriminating' the sensible properties of things. Perception, however, is not yet the knowledge of the principles of science; for it does not tell us what are the essential as distinguished from the accidental properties of things. It is only through induction that from the confused knowledge of perception there emerges a knowledge of the essential determinations of things. But without perception no induction would be possible. It is indeed obvious that the lack of a sense would shut us out from a special kind of knowledge. If we were devoid of the sense of sight, how could, we have a science of optics? If we had no sense of hearing, how could there be a science of harmonics? Induction, therefore, presupposes perception; given perception, and we can understand how by a process of induction the conceptions postulated by demonstrative science may be obtained; but without induction there can be no demonstration. Even the abstract elements with which mathematics deals presuppose the inductive process by which they are obtained. If this is true of mathematics, it is still more obvious in the case of those sciences which deal with concrete things and events. No doubt Aristotle, in a passage already referred to, speaks as if perception may in some cases do the work, not only of induction, but even of demonstration. But perception can never of itself reveal the 'cause' of a fact. Even if we could see the pores in glass and observe light passing through them, we should not get beyond the fact that the light of the lantern perceived is in this case due to the porous nature of glass; to obtain the general principle we must have repeated perceptions, and the activity of thought by which the law is seized. Induction is thus in all cases necessary in the discovery of a principle. To perceive that which is in the strict sense universal is inconsistent with the nature of perception, which is limited to the apprehension of particular phenomena in a particular place and at a particular time. Nor can induction from repeated perception be completed without the intuitive grasp by thought of the universal principle.
Aristotle tells us the steps by which the transition is made from sensible perception to the grasp of principles. There is in man, and indeed in all animals, an 'inborn faculty of discrimination' which we call sensible perception. This faculty, however, only supplies the material for a higher stage of knowledge, when, as in man, some trace of what is given in sense is retained in the soul by memory. Experience, again, is memory working in accordance with mechanical laws of association, and many successive pictures of memory are required to make a single experience. In experience the mind simply works with a rule, as when the empirical physician, finding that a certain remedy cured Callias Socrates, and others of a particular disease, prescribes it in the case of a new patient. From experience, again, art and science arise when the law implied in the empirical rule is definitely grasped by thought and is thus seen to be applicable to all the individuals which have certain features in common. Thus, at the stage of art, the physician prescribes for a particular disease in accordance with the law which applies to all individuals suffering from it. We thus learn, on the one hand, that there is no innate knowledge of principles, and, on the other hand, that the knowledge of principles is not derived from some higher form of knowledge, but is evolved from perception by the activity of the mind in grasping the principle presupposed in perception. We may compare the process by which a principle becomes known to us to the way in which order is restored in a battle after a rout. First one man stops in his flight, then another, then one more, until there is a nucleus for real work. Similarly, the flow of fugitive impressions stops at one point; a similar impression comes along, is arrested by the first, and reinforces it; thus, after a time, there is formed a single experience. This supplies the starting point for the conscious process by which a system of conceptions is formed.
The formation of conceptions may be further explained as follows: The object of perception is always a sensible thing as here and now, in which accidental and essential qualities are not as yet discriminated. Nevertheless, the repetition of perceptions naturally leaves in the soul the conception of what is common to a number of individuals. In this way, after a number of individual men have been observed, there remains fixed in consciousness the general idea of ' man’ the special characteristics of Callias, Socrates, and others having dropped out of view. When a number of such universals are formed, higher and higher universals arise, until a universal which falls under no higher conception is obtained. We begin, for example, with this or that species of animal, advance to animal in general, and so to living being. This is the natural process of abstraction in the formation of conceptions; and induction, as Aristotle himself tells us, is just the conscious imitation of this natural process. Hence the principles obtained by induction must be derived from perception, though the intuitive grasp of thought is always implied.
We may sum up Aristotle's view of induction somewhat as follows: (I) Induction comes to the aid of demonstration either by supplying the materials necessary for the demonstration of a 'fact’ or by itself establishing the concomitance in a class of things of certain attributes. (2) No definition of an essential property, as distinguished from the essence of a thing, can be gained by induction; this can be effected only by the aid of demonstration, which brings to light, though it does not prove, the cause of the property. (3) Induction, however, is closely related to the real definition of the primary conceptions, which form the basis of all demonstration. Definition in this case is a statement of the essential content of things. Now, our knowledge of this content is derived in the first instance from the natural process of abstraction. From the perception of individuals there gradually emerges, in the way already explained, the conceptions which ordinary language indicates by class-names, e. g. 'man' ‘animal' ‘living being.’ With this process of abstraction induction cannot be identified; but the two processes differ mainly in the fact that abstraction is prior to reflective thought, whereas induction is essentially reflective and proceeds by a definite method. In many cases, therefore, induction starts from the conceptions already formed, and marked by a name, and employs these as a guide in its movement upward to universals. Even when it does so, however, the meaning of the conceptions formed by abstraction must not only be made clear and distinct by analysis, but they have in many cases to be rectified, so that induction is in a sense a re-formation of conceptions. The complete process of induction, indeed, always presupposes that the ground already traversed by abstraction should be gone over again, and thus induction is the virtual establishment of a new hierarchy of conceptions. Besides, there are cases in which we have not even a name by which to designate an important conception; and induction has therefore to form the conception for the first time, as, e. g. when it constitutes the new conception of ruminants. (4) What constitutes the distinctive character of induction is that it is the process towards the first principles of science. For, in all its operations, it is guided by the end towards which it is directed, the discovery of the ultimate grounds or causes of things; and, though this is a goal that it can never of itself attain, it is the indispensable pathway which must be traversed before thought can come into direct contact with its proper object, the intelligible and ultimate grounds of things. When this last point has been reached, the data for demonstration are ready, and the descent from the universal to the particular is affected. Aristotle, then, finds that in the construction of the sciences induction and demonstration each contributes its share. What, however, gives unity to the whole process of knowledge is the continual presence at every stage of the activity of thought which is ever seeking to grasp the universal nature of things. Even sensible perception, in so far as it apprehends properties which are indeed found in the sensible thing as here and now, but yet are not peculiar to this thing, implies the exercise of thought. So, when induction discovers in various objects of perception the invariable concomitance of attributes, rises from this concomitance to the universal principle. And, finally, when induction is the means of discovering the ultimate principles from which a given science starts, the discovery is possible only because grasps them directly and immediately. As these principles are the pre-condition of all demonstration, is the principle or starting point of science. There are, therefore, two aspects in which we can view: on the one hand, it is the source of the whole body of science, and, therefore, reveals to us the essential nature of things, and, on the other hand, it is the source of the first principles on which the whole edifice of science is based. Aristotle, therefore, holds that is able to grasp the essential nature of things, so far as these are reducible to rational system. It cannot, however, be said that he conceives of nature as rational through and through. From this conclusion he is deterred by his conviction that there always is in things an accidental or irrational element, which reason cannot comprehend. On the whole, law prevails in nature, and so far as this is the case science is possible; but there remains a large margin of contingency, which cannot be won for the orderly realm of science.