Part 3

*Induction*.--Of the use of "induction" in Aristotle's philosophy we shall speak under the head of "Theory of Knowledge." Formally it is called "the way of proceeding from particular facts to universals," and Aristotle insists that the conclusion is only proved if _all_ the particulars have been examined. Thus he gives as an example the following argument, "_x_, _y_, _z_ are long-lived species of animals; _x_, _y_, _z_ are the only species which have no gall; _ergo_ all animals which have no gall are long-lived." This is the "induction by simple enumeration" denounced by Francis Bacon on the ground that it may always be discredited by the production of a single "contrary instance," _e.g._ a single instance of an animal which has no gall and yet is not long-lived. Aristotle is quite aware that his "induction" does not establish its conclusion unless all the cases have been included in the examination. In fact, as his own example shows, an induction which gives certainty does not start with "particular facts" at all. It is a method of arguing that what has been proved true of each sub-class of a wider class will be true of the wider class as a whole. The premisses are strictly universal throughout. In general, Aristotle does not regard "induction" as _proof_ at all. Historically "induction" is held by Aristotle to have been first made prominent in philosophy by Socrates, who constantly employed the method in his attempts to establish universal results in moral science. Thus he gives, as a characteristic argument for the famous Socratic doctrine that knowledge is the one thing needful, the "induction," "he who understands the theory of navigation is the best navigator, he who understands the theory of chariot-driving the best driver; from these examples we see that universally he who understands the theory of a thing is the best practitioner," where it is evident that _all_ the relevant cases have _not_ been examined, and consequently that the reasoning does not amount to proof. Mill's so-called reasoning from particulars to particulars finds a place in Aristotle's theory under the name of "arguing from an example." He gives as an illustration, "A war between Athens and Thebes will be a bad thing, for we see that the war between Thebes and Phocis was so." He is careful to point out that the whole force of the argument depends on the _implied_ assumption of a universal proposition which covers both cases, such as "wars between _neighbours_ are bad things." Hence he calls such appeals to example "rhetorical" reasoning, because the politician is accustomed to leave his hearers to supply the relevant universal consideration for themselves.

*Theory of Knowledge*.--Here, as everywhere in Aristotle's philosophy, we are confronted by an initial and insuperable difficulty. Aristotle is always anxious to insist on the difference between his own doctrines and those of Plato, and his bias in this direction regularly leads him to speak as though he held a thorough-going naturalistic and empirical theory with no "transcendental moonshine" about it. Yet his final conclusions on all points of importance are hardly distinguishable from those of Plato except by the fact that, as they are so much at variance with the naturalistic side of his philosophy, they have the appearance of being sudden lapses into an alogical mysticism. We shall find the presence of this "fault" more pronouncedly in his metaphysics, psychology, and ethics than in his theory of knowledge, but it is not absent from any part of his philosophy. He is everywhere a Platonist _malgre lui_, and it is just the Platonic element in his thought to which it owes its hold over men's minds.

Plato's doctrine on the subject may be stated with enough accuracy for our purpose as follows. There is a radical distinction between sense-perception and scientific knowledge. A scientific truth is exact and definite, it is also true once and for all, and never becomes truer or falser with the lapse of time. This is the character of the propositions of the science which Plato regarded as the type of what true science ought to be, pure mathematics. It is very different with the judgments which we try to base on our sense-perceptions of the visible and tangible world. The colours, tastes, shapes of sensible things seem different to different percipients, and moreover they are constantly changing in incalculable ways. We can never be certain that two lines which seem to our senses to be equal are really so; it may be that the inequality is merely too slight to be perceptible to our senses. No figure which we can draw and see actually has the exact properties ascribed by the mathematician to a circle or a square. Hence Plato concludes that if the word science be taken in its fullest sense, there can be no science about the world which our senses reveal. We can have only an approximate knowledge, a knowledge which is after all, at best, probable opinion. The objects of which the mathematician has certain, exact, and final knowledge cannot be anything which the senses reveal. They are objects of _thought_, and the function of visible models and diagrams in mathematics is not to present _examples_ of them to us, but only to show us imperfect _approximations_ to them and so to "remind" the soul of objects and relations between them which she has never cognised with the bodily senses. Thus mathematical straightness is never actually beheld, but when we see lines of less and more approximate straightness we are "put in mind" of that absolute straightness to which sense-perception only approximates. So in the moral sciences, the various "virtues" are not presented in their perfection by the course of daily life. We do not meet with men who are perfectly brave or just, but the experience that one man is braver or juster than another "calls into our mind" the thought of the absolute standard of courage or justice implied in the conviction that one man comes nearer to it than another, and it is these absolute standards which are the real objects of our attention when we try to define the terms by which we describe the moral life. This is the "epistemological" side of the famous doctrine of the "Ideas." The main points are two, (1) that strict science deals throughout with objects and relations between objects which are of a purely intellectual or conceptual order, no sense-data entering into their constitution; (2) since the objects of science are of this character, it follows that the "Idea" or "concept" or "universal" is not arrived at by any process of "abstracting" from our experience of sensible things the features common to them all. As the particular fact never actually exhibits the "universal" except approximately, the "universal" cannot be simply disentangled from particulars by abstraction. As Plato puts it, it is "apart from" particulars, or, as we might reword his thought, the pure concepts of science represent "upper limits" to which the comparative series which we can form out of sensible data continually approximate but do not reach them.

In his theory of knowledge Aristotle begins by brushing aside the Platonic view. Science requires no such "Ideas," transcending sense-experience, as Plato had spoken of; they are, in fact, no more than "poetic metaphors." What is required for science is not that there should be a "one over and above the many" (that is, such pure concepts, unrealised in the world of actual perception, as Plato had spoken of), but only that it should be possible to predicate one term universally of many others. This, by itself, means that the "universal" is looked on as a mere residue of the characteristics found in each member of a group, got by abstraction, _i.e._ by leaving out of view the characteristics which are peculiar to some of the group and retaining only those which are common to all. If Aristotle had held consistently to this point of view, his theory of knowledge would have been a purely empirical one. He would have had to say that, since all the objects of knowledge are particular facts given in sense-perception, the universal laws of science are a mere convenient way of describing the observed uniformities in the behaviour of sensible things. But, since it is obvious that in pure mathematics we are not concerned with the actual relations between sensible data or the actual ways in which they behave, but with so-called "pure cases" or ideals to which the perceived world only approximately conforms, he would also have had to say that the propositions of mathematics are not strictly true. In modern times consistent empiricists have said this, but it is not a position possible to one who had passed twenty years in association with the mathematicians of the Academy, and Aristotle's theory only begins in naturalism to end in Platonism. We may condense its most striking positions into the following statement. By science we mean _proved_ knowledge. And proved knowledge is always "mediated"; it is the knowledge of _conclusions_ from premisses. A truth that is scientifically known does not stand alone. The "proof" is simply the pointing out of the connection between the truth we call the conclusion, and other truths which we call the premisses of our demonstration. Science points out the _reason why_ of things, and this is what is meant by the Aristotelian principle that to have science is to know things through their _causes_ or _reasons why_. In an ordered digest of scientific truths, the proper arrangement is to begin with the simplest and most widely extended principles and to reason down, through successive inferences, to the most complex propositions, the _reason why_ of which can only be exhibited by long chains of deductions. This is the order of logical dependence, and is described by Aristotle as reasoning _from_ what is "more knowable in its own nature,"[#] the simple, to what is usually "more familiar to _us_," because less removed from the infinite wealth of sense-perception, the complex. In _discovery_ we have usually to reverse the process and argue from "the familiar to us," highly complex facts, to "the more knowable in its own nature," the simpler principles implied in the facts.

[#] This simple expression acquires a mysterious appearance in mediaeval philosophy from the standing mistranslation _notiora naturae_, "better known to nature."

It follows that Aristotle, after all, admits the disparateness of sense-perception and scientific knowledge. Sense-perception of itself never gives us scientific truth, because it can only assure us that a fact is so; it cannot _explain_ the fact by showing its connection with the rest of the system of facts, "it does not give the _reason_ for the fact." Knowledge of perception is always "immediate," and for that very reason is never scientific. If we stood on the moon and saw the earth, interposing between us and the sun, we should still not have scientific knowledge about the eclipse, because "we should still have to ask for the _reason why_." (In fact, we should not know the reason _why_ without a theory of light including the proposition that light-waves are propagated in straight lines and several others.) Similarly Aristotle insists that Induction does not yield scientific truth. "He who makes an induction points out something, but does not demonstrate anything."

For instance, if we know that _each_ species of animal which is without a gall is long-lived, we may make the induction that _all_ animals without a gall are long-lived, but in doing so we have got no nearer to seeing _why_ or _how_ the absence of a gall makes for longevity. The question which we may raise in science may all be reduced to four heads, (1) Does this thing exist? (2) Does this event occur? (3) If the thing exists, precisely what is it? and (4) If the event occurs, _why_ does it occur? and science has not completed its task unless it can advance from the solution of the first two questions to that of the latter two. Science is no mere catalogue of things and events, it consists of inquiries into the "real essences" and characteristics of things and the laws of connection between events.

Looking at scientific reasoning, then, from the point of view of its formal character, we may say that all science consists in the search for "middle terms" of syllogisms, by which to connect the truth which appears as a conclusion with the less complex truths which appear as the premisses from which it is drawn. When we ask, "does such a thing exist?" or "does such an event happen?" we are asking, "is there a middle term which can connect the thing or event in question with the rest of known reality?" Since it is a rule of the syllogism that the middle term must be taken universally, at least once in the premisses, the search for middle terms may also be described as the search for universals, and we may speak of science as knowledge of the universal interconnections between facts and events.

A science, then, may be analysed into three constituents. These are: (1) a determinate class of objects which form the subject-matter of its inquiries. In an orderly exhibition of the contents of the science, these appear, as in Euclid, as the initial data about which the science reasons; (2) a number of principles, postulates, and axioms, from which our demonstrations must start. Some of these will be principles employed in all scientific reasoning. Others will be specific to the subject-matter with which a particular science is concerned; (3) certain characteristics of the objects under study which can be shown by means of our axioms and postulates to follow from our initial definitions, the _accidentia per se_ of the objects defined. It is these last which are expressed by the conclusions of scientific demonstration. We are said to know scientifically that B is true of A when we show that this follows, in virtue of the principles of some science, from the initial definition of A. Thus if we convinced ourselves that the sum of the angles of a plane triangle is equal to two right angles by measurement, we could not be said to have scientific knowledge of the proposition. But if we show that the same proposition follows from the definition of a plane triangle by repeated applications of admitted axioms or postulates of geometry, our knowledge is genuinely scientific. We now know that it is so, and we see _why_ it is so; we see the connection of this truth with the simple initial truths of geometry.

This leads us to the consideration of the most characteristic point of Aristotle's whole theory. Science is demonstrated knowledge, that is, it is the knowledge that certain truths follow from still simpler truths. Hence the simplest of all the truths of any science cannot themselves be capable of being known by inference. You cannot infer that the axioms of geometry are true because its conclusions are true, since the truth of the conclusions is itself a consequence of the truth of the axioms. Nor yet must you ask for demonstration of the axioms as consequences of still simpler premisses, because if all truths can be proved, they ought to be proved, and you would therefore require an infinity of successive demonstrations to prove anything whatever. But under such conditions all knowledge of demonstrated truth would be impossible. The first principles of any science must therefore be indemonstrable. They must be known, as facts of sense-perception are known, immediately and not mediately. How then do we come by our knowledge of them? Aristotle's answer to this question appears at first sight curiously contradictory. He seems to say that these simplest truths are apprehended intuitively, or on inspection, as self-evident by Intelligence or Mind. On the other hand, he also says that they are known _to us_ as a result of induction from sense-experience. Thus he _seems_ to be either a Platonist or an empiricist, according as you choose to remember one set of his utterances or another, and this apparent inconsistency has led to his authority being claimed in their favour by thinkers of the most widely different types. But more careful study will show that the seeming confusion is due to the fact that he tries to combine in one statement his answers to two quite different questions, (1) how we come to reflect on the axioms, (2) what evidence there is for their truth. To the first question he replies, "by induction from experience," and so far he might seem to be a precursor of John Stuart Mill. Successive repetitions of the same sense-perceptions give rise to a single experience, and it is by reflection on experience that we become aware of the most ultimate simple and universal principles. We might illustrate his point by considering how the thought that two and two are four may be brought before a child's mind. We might first take two apples, and two other apples and set the child to count them. By repeating the process with different apples we may teach the child to dissociate the result of the counting from the particular apples employed, and to advance to the thought, "any two apples and any two other apples make four apples." Then we might substitute pears or cherries for the apples, so as to suggest the thought, "two fruits and two fruits make four fruits." And by similar methods we should in the end evoke the thought, "any two objects whatever and any other two objects whatever make four objects." This exactly illustrates Aristotle's conception of the function of induction, or comparison of instances, in fixing attention on a universal principle of which one had not been conscious before the comparison was made.

Now comes in the point where Aristotle differs wholly from all empiricists, later and earlier. Mill regards the instances produced in the induction as having a double function; they not merely fix the attention on the principle, they also are the evidence of its truth. This gives rise to the greatest difficulty in his whole logical theory. Induction by imperfect enumeration is pronounced to be (as it clearly is) fallacious, yet the principle of the uniformity of Nature which Mill regards as the ultimate premiss of all science, is itself supposed to be proved by this radically fallacious method. Aristotle avoids a similar inconsistency by holding that the sole function of the induction is to fix our attention on a principle which it does not prove. He holds that ultimate principles neither permit of nor require proof. When the induction has done its work in calling attention to the principle, you have to see for yourself that the principle is true. You see that it is true by immediate inspection just as in sense-perception you have to see that the colour before your eyes is red or blue. This is why Aristotle holds that the knowledge of the principles of science is not itself science (demonstrated knowledge), but what he calls intelligence, and we may call intellectual intuition. Thus his doctrine is sharply distinguished not only from empiricism (the doctrine that universal principles are proved by particular facts), but also from all theories of the Hegelian type which regard the principles and the facts as somehow reciprocally proving each other, and from the doctrine of some eminent modern logicians who hold that "self-evidence" is not required in the ultimate principles of science, as we are only concerned in logic with the question what consequences follow from our initial assumptions, and not with the truth or falsehood of the assumptions themselves.

The result is that Aristotle does little more than repeat the Platonic view of the nature of science. Science consists of deductions from universal principles which sensible experience "suggests," but into which, as they are apprehended by a purely intellectual inspection, no sense-data enter as constituents. The apparent rejection of "transcendental moonshine" has, after all, led to nothing. The only difference between Plato and his scholar lies in the clearness of intellectual vision which Plato shows when he expressly maintains in plain words that the universals of exact science are not "in" our sense-perceptions and therefore to be extracted from them by a process of abstraction, but are "apart from" or "over" them, and form an ideal system of interconnected concepts which the experiences of sense merely "imitate" or make approximation to.

One more point remains to be considered to complete our outline of the Aristotelian theory of knowledge. The sciences have "principles" which are discerned to be true by immediate inspection. But what if one man professes to see the self-evident truth of such an alleged principle, while another is doubtful of its truth, or even denies it? There can be no question of silencing the objector by a demonstration, since no genuine simple principle admits of demonstration. All that can be done, _e.g._ if a man doubts whether things equal to the same thing are equal to one another, or whether the law of contradiction is true, is to examine the consequences of a denial of the axiom and to show that they include some which are false, or which your antagonist at least considers false. In this way, by showing the falsity of consequences which follow from the denial of a given "principle," you indirectly establish its truth. Now reasoning of this kind differs from "science" precisely in the point that you take as your major premiss, not what you regard as true, but the opposite thesis of your antagonist, which you regard as false. Your object is not to prove a true conclusion but to show your opponent that _his_ premisses lead to false conclusions. This is "dialectical" reasoning in Aristotle's sense of the word, _i.e._ reasoning not from your own but from some one else's premisses. Hence the chief philosophical importance which Aristotle ascribes to "dialectic" is that it provides a method of defending the undemonstrable axioms against objections. Dialectic of this kind became highly important in the mediaeval Aristotelianism of the schoolmen, with whom it became a regular method, as may be seen _e.g._ in the _Summa_ of St. Thomas, to begin their consideration of a doctrine by a preliminary rehearsal of all the arguments they could find or devise against the conclusion they meant to adopt. Thus the first division of any article in the _Summa Theologiae_ of Thomas is regularly constituted by arguments based on the premisses of actual or possible antagonists, and is strictly dialectical. (To be quite accurate Aristotle should, of course, have observed that this dialectical method of defending a principle becomes useless in the case of a logical axiom which is presupposed by all deduction. For this reason Aristotle falls into fallacy when he tries to defend the law of contradiction by dialectic. It is true that if the law be denied, then any and every predicate may be indifferently ascribed to any subject. But until the law of contradiction has been admitted, you have no right to regard it as absurd to ascribe all predicates indiscriminately to all subjects. Thus, it is only assumed laws which are _not_ ultimate laws of logic that admit of dialectical justification. If a truth is so ultimate that it has either to be recognised by direct inspection or not at all, there can be no arguing at all with one who cannot or will not see it.)

*CHAPTER III*

*FIRST PHILOSOPHY*