Philosophy, as understood by Aristotle, may be said to be the organized whole of disinterested knowledge, that is, knowledge which we seek for the satisfaction which it carries with itself, and not as a mere means to utilitarian ends. The impulse which receives this satisfaction is curiosity or wonder, which Aristotle regards as innate in man, though it does not get full play until civilization has advanced far enough to make secure provision for the immediate material needs of life. Human curiosity was naturally directed first to the outstanding “marvelous works” of the physical world, the planets, the periodicity of their movements, the return of the seasons, winds, thunder and lightning, and the like. Hence the earliest Greek speculation was concerned with problems of astronomy and meteorology. Then, as reflection developed, men speculated about geometrical figure and number, the possibility of having assured knowledge at all, the character of the common principles assumed in all branches of study or of the special principles assumed in some one branch, and thus philosophy has finally become the disinterested study of every department of Being or Reality. Since Aristotle, like Hegel, thought that his own doctrine was, in essentials, last word of speculation, the complete expression of the principles by which his predecessors had been unconsciously guided, he believes himself in a position to make a final classification of the branches of science, showing how they are related and how they are discriminated from one another. This classification we have now to consider.

Classification of the Sciences

To begin with, we have to discriminate Philosophy from two rivals with which it might be confounded on a superficial view, Dialectic and Sophistry. Dialectic is the art of reasoning accurately from given premises, true or false. This art has its proper uses, and of one of these we shall have to speak. But in itself it is indifferent to the truth of its premises. You may reason dialectically from premises which you believe to be false, for the express purpose of showing the absurd conclusions to which they lead. Or you may reason from premises which you assume tentatively to see what conclusions you are committed to if you adopt them. In either case your object is not directly to secure truth, but only to secure consistency. Science or Philosophy aims directly at truth, and hence requires to start with true and certain premises. Thus the distinction between Science and Dialectic is that Science reasons from true premises, Dialectic only from “probable” or “plausible” premises.¹ Sophistry differs from Science in virtue of its moral character. It is the profession of making a living by the abuse of reasoning, the trick of employing logical skill for the apparent demonstration of scientific or ethical falsehoods. “The sophist is one who earns a living from an apparent but unreal wisdom.” (The emphasis thus falls on the notion of making an “unreal wisdom” into a trade. The sophist’s real concern is to get his fee.) Science or Philosophy is thus the disinterested employment of the understanding in the discovery of truth.

A Third

We may now distinguish the different branches of science as defined. The first and most important division to be made is that between Speculative or Theoretical Science and Practical Science. The broad distinction is that which we should now draw between the Sciences and the Arts (i.e. the industrial and technical, not the “fine” arts). Speculative or Theoretical Philosophy differs from Practical Philosophy in its purpose, and, in consequence, in its subject-matter, and its formal logical character. The purpose of the former is the disinterested contemplation of truths which are what they are independently of our own volition; its end is to know and only to know. The object of “practical” Science is to know, but not only to know but also to turn our knowledge to account in devising ways of successful interference with the course of events. (The real importance of the distinction comes out in Aristotle’s treatment of the problems of moral and social science. Since we require knowledge of the moral and social nature of men not merely to satisfy an intellectual interest, but as a basis for a sound system of education and government. Politics, the theory of government, and Ethics, the theory of goodness of conduct, which for Aristotle is only a subordinate branch of Politics, belong to Practical, not to Theoretical Philosophy, a view which is attended by important consequences.)

It follows that there is a corresponding difference in the objects investigated by the two branches of Philosophy. Speculative or Theoretical Philosophy is concerned with “that which cannot possibly be other than it is,” truths and relations independent of human volition for their subsistence, and calling simply for recognition on our part. Practical Philosophy has to do with relations which human volition can modify, “things which may be other than they are,” the contingent. (Thus e.g. not only politics, but medicine and economics will belong to Practical Science.)

Hence again arises a logical difference between the conclusions of Theoretical and those of Practical Philosophy. Those of the former are universal truths deducible with logical necessity from self-evident² principles. Those of the latter, because they relate to what “can be otherwise,” are never rigidly universal; they are general rules which hold good “in the majority of cases.” but are liable to occasional exceptions owing to the contingent character of the facts with which they deal. It is a proof of a philosopher’s lack of grounding in logic that he looks to the results of a practical science (e.g. to the detailed precepts of medicine or ethics) for a higher degree of certainty and validity than the nature of the subject matter allows. Thus for Aristotle the distinction between the necessary and the contingent is real and not merely apparent, and “probability is the guide” in studies which have to do with the direction of life.

We proceed to the question how many subdivisions there are within “theoretical” Philosophy itself. Plato had held that there are none. All the sciences are deductions from a single set of ultimate principles which it is the business of that supreme science to which Plato had given the name of Dialectic to establish. This is not Aristotle’s view. According to him, “theoretical” Philosophy falls into a number of distinct though not coordinate branches, each with its own special subjects of investigation and its own special axiomatic principles. Of these branches there are three, First Philosophy, Mathematics, and Physics. First Philosophy–afterwards to be known to the Middle Ages as Metaphysics³–treats, to use Aristotle’s own expression, of “Being qua Being.” This means that it is concerned with the universal characteristics which belong to the system of knowable reality as such, and the principles of its organization in their full universality. First Philosophy alone investigates the character of those causative factors in the system which are without body or shape and exempt from all mutability. Since in Aristotle’s system God is the supreme Cause of this kind, First Philosophy culminates in the knowledge of God, and is hence frequently called Theology. It thus includes an element which would today be assigned to the theory of knowledge, as well as one which we should ascribe to metaphysics, since it deals at once with the ultimate postulates of knowledge and the ultimate causes of the order of real existence.

Mathematics is of narrower scope. What it studies is no longer “real being as such,” but only real being in so far as it exhibits number and geometrical form. Since Aristotle holds the view that number and figure only exist as determinations of objects given in perception (though by a convenient fiction the mathematician treats of them in abstraction from the perceived objects which they qualify), he marks the difference between Mathematics and First Philosophy by saying that “whereas the objects of First Philosophy are separate from matter and devoid of motion, those of Mathematics, though incapable of motion, have no separable existence but are inherent in matter.” Physics is concerned with the study of objects which are both material and capable of motion. Thus the principle of the distinction is the presence or absence of initial restrictions of the range of the different branches of Science. First Philosophy has the widest range, since its contemplation covers the whole ground of the real and knowable; Physics the narrowest, because it is confined to a “universe of discourse” restricted by the double qualification that its members are all material and capable of displacement. Mathematics holds an intermediate position, since in it one of these qualifications is removed, but the other still remains, for the geometer’s figures are boundaries and limits of sensible bodies, and the arithmetician’s numbers properties of collections of concrete objects. It follows also that the initial axioms or postulates of Mathematics form a less simple system than those of First Philosophy, and those of Physics than those of Mathematics. Mathematics requires as initial assumptions not only those which hold good for all thought, but certain other special axioms which are only valid and significant for the realm of figure and number; Physics requires yet further axioms which are only applicable to “what is in motion.” This is why, though the three disciplines are treated as distinct, they are not strictly coordinate, and “First Philosophy,” though “first,” is only prima inter pares.

We thus get the following diagrammatic scheme of the classification of sciences:–

Practical Philosophy is not subjected by Aristotle to any similar subdivision. Later students were accustomed to recognize a threefold division into Ethics (the theory of individual conduct), Economics (the theory of the management of the household), Politics (the theory of the management of the State). Aristotle himself does not make these distinctions. His general name for the theory of conduct is Politics, the doctrine of individual conduct being for him inseparable from that of the right ordering of society. Though he composed a separate course of lectures on individual conduct (the Ethics), he takes care to open the course by stating that the science of which it treats is Politics, and offers an apology for dealing with the education of individual character apart from the more general doctrine of the organization of society. No special recognition is given in Aristotle’s own classification to the Philosophy of Art. Modern students of Aristotle have tried to fill in the omission by adding artistic creation to contemplation and practice as a third fundamental form of mental activity, and thus making a threefold division of Philosophy into Theoretical, Practical, and Productive. The object of this is to find a place in the classification for Aristotle’s famous Poetics and his work on Rhetoric, the art of effective speech and writing. But the admission of the third division of Science has no warrant in the text of Aristotle, nor are the Rhetoric and Poetics, properly speaking, a contribution to Philosophy. They are intended as collections of practical rules for the composition of a pamphlet or a tragedy, not as a critical examination of the canons of literary taste. This was correctly seen by the dramatic theorists of the seventeenth century. They exaggerated the value of Aristotle’s directions and entirely misunderstood the meaning of some of them, but they were right in their view that the Poetics was meant to be a collection of rules by obeying which the craftsman might make sure of turning out a successful play. So far as Aristotle has a Philosophy of Fine Art at all, it forms part of his more general theory of education and must be looked for in the general discussion of the aims of education contained in his Politics.

The Methods of Science

No place has been assigned in the scheme to what we call logic and Aristotle called Analytics, the theory of scientific method, or of proof and the estimation of evidence. The reason is that since the fundamental character of proof is the same in all science, Aristotle looks upon logic as a study of the methods common to all science. At a later date it became a hotly debated question whether logic should be regarded in this way as a study of the methods instrumental to proof in all sciences, or as itself a special constituent division of philosophy. The Aristotelian view was concisely indicated by the name which became attached to the collection of Aristotle’s logical works. They were called the Organon, that is, the “instrument,” or the body of rules of method employed by Science. The thought implied is thus that logic furnishes the tools with which every science has to work in establishing its results. Our space will only permit of a brief statement as to the points in which the Aristotelian formal logic appears to be really original, and the main peculiarities of Aristotle’s theory of knowledge.

Formal Logic

In compass the Aristotelian logic corresponds roughly with the contents of modem elementary treatises on the same subject, with the omission of the sections which deal with the so-called Conditional Syllogism. The inclusion of arguments of this type in medieval and modern expositions of formal logic is principally due to the Stoics, who preferred to throw their reasoning into these forms and subjected them to minute scrutiny. In his treatment of the doctrine of Terms, Aristotle avoids the mistake of treating the isolated name as though it had significance apart from the enunciations in which it occurs. He is quite clear on the all-important point that the unit of thought is the proposition in which something is affirmed or denied, the one thought-form which can be properly called “true” or “false.” Such an assertion he analyses into two factors, that about which something is affirmed or denied (the Subject), and that which is affirmed or denied of it (the Predicate). Consequently his doctrine of the classification of Terms is based on a classification of Predicates, or of Propositions according to the special kind of connection between the Subject and Predicate which they affirm or deny. Two such classifications, which cannot be made to fit into one another, meet us in Aristotle’s logical writings, the scheme of the ten “Categories” or “Predicaments,” and that which was afterwards known in the Middle Ages as the list of “Predicables,” or again as the “Five Words.” The list of “Categories” reveals itself as an attempt to answer the question in how many different senses the words “is a” or “are” are employed when we assert that “x is y” or “x is a y” or “xs are ys.” Such a statement may tell us 1) what x is, as if I say “x is a lion”; the predicate is then said to fall under the category of Substance; 2) what x is like, as when I say “x is white, or x is wise,”—-the category of Quality; 3) how much or how many x is, as when I say ” there are five xs ” or ” x is five feet long,”—the category of Quantity; 4) how x is related to something else, as when I say ” x is to the right of y” ” x is the father of y,”—the category of Relation, These are the four chief “categories” discussed by Aristotle. The remainder are 5) Place, 6) Time, 7) and 8) Condition or State, as when I say “x is sitting down ” or “x has his armor on,”—-(the only distinction between the two cases seems to be that 7) denotes a more permanent state of x than 8)); 9) Action or Activity, as when I say “x is cutting,” or generally “x is doing something to y”; 10) Passivity, as when I say “x is being cut,” or more generally, “so-and-so is being done to x.” No attempt is made to show that this list of “figures of predication” is complete, or to point out any principle which has been followed in its construction. It also happens that much the same enumeration is incidentally made in one or two passages of Plato. Hence it is not unlikely that the list was taken over by Aristotle as one which would be familiar to pupils who had read their Plato, and therefore convenient for practical purposes. The fivefold classification does depend on a principle pointed out by Aristotle which guarantees its completeness, and is therefore likely to have been thought out by him for himself, and to be the genuine Aristotelian scheme. Consider an ordinary universal affirmative proposition of the form “all xs are ys.” Now if this statement is true it may also be true that “all xs are ys” or it may not. On the first supposition we have two possible cases, 1) the predicate may state precisely what the subject defined is; then y is the Definition of x, as when I say that “men are mortal animals, capable of discourse.” Here it is also true to say that “mortal animals capable of discourse are men,” and Aristotle regards the predicate “mortal animal capable of discourse” as expressing the inmost nature of man. 2) The predicate may not express the inmost nature of the subject, and yet may belong only to the class denoted by the subject and to every member of that class. The predicate is then called a Proprium or property, an exclusive attribute of the class in question. Thus it was held that “all men are capable of laughter” and “all beings capable of laughter are men,” but that the capacity for laughter is no part of the inmost nature or “real essence” of humanity. It is therefore reckoned as a Proprium.

Again in the case where it is true that ” all xs are ys” but not true that all “ys are xs,” y may be part of the definition of x or it may not. If it is part of the definition of x it will be either 3) a Genus or wider class of which x forms a subdivision, as when I say, “All men are animals,” or 4) a Difference, that is, one of the distinctive marks by which the xs are distinguished from other sub-classes or species of the same genus, as when I say, “All men are capable of discourse.” Or finally 5) y may be no part of the definition of x, but a characteristic which belongs both to the xs and some things other than xs. The predicate is then called an Accident. We have now exhausted all the possible cases, and may say that the predicate of a universal affirmative proposition is always either a definition, a proprium, a genus, a difference, or an accident. This classification reached the Middle Ages not in the precise form in which it is given by Aristotle, but with modifications mainly due to the Neo-Platonic philosopher Porphyry. In its modified form it is regarded as a classification of terms generally. Definition disappears from the list, as the definition is regarded as a complex made up of the genus, or next highest class to which the class to be defined belongs, and the differences which mark off this particular species or sub-class. The species itself which figures as the subject-term in a definition is added, and thus the ” Five Words ” of medieval logic are enumerated as genus, species, difference, proprium, accident.

The one point of philosophical interest about this doctrine appears alike in the scheme of the “Categories” in the presence of a category of “substance,” and in the list of “Predicables” in the sharp distinction drawn between “definition” and “proprium.” From a logical point of view it does not appear why any proprium, any character belonging to all the members of a class and to them alone, should not be taken as defining the class. Why should it be assumed that there is only one predicate, viz. man, which precisely answers the question, “What is Socrates?” Why should it not be equally correct to answer, “a Greek,” or “a philosopher”? The explanation is that Aristotle takes it for granted that not all the distinctions we can make between “kinds” of things are arbitrary and subjective. Nature herself has made certain hard and fast divisions between kinds which it is the business of our thought to recognize and follow. Thus according to Aristotle there is a real gulf, a genuine difference in kind, between the horse and the ass, and this is illustrated by the fact that the mule, the offspring of a horse and an ass, is not capable of propagating. It is thus a sort of imperfect being, a kind of “monster” existing contra naturam. Such differences as we find when we compare e.g. Egyptians with Greeks do not amount to a difference in “kind.” To say that Socrates is a man tells me what Socrates is, because the statement places Socrates in the real kind to which he actually belongs; to say that he is wise, or old, or a philosopher merely tells me some of his attributes. It follows from this belief in “real” or “natural” kinds that the problem of definition acquires an enormous importance for science. We, who are accustomed to regard the whole business of classification as a matter of making a grouping of our materials such as is most pertinent to the special question we have in hand, tend to look upon any predicate which belongs universally and exclusively to the members of a group, as a sufficient basis for a possible definition of the group. Hence we are prone to take the “nominalist” view of definition, i.e. to look upon a definition as no more than a declaration of the sense which we intend henceforward to put on a word or other symbol.⁴ And consequently we readily admit that there may be as many definitions of a class as it has different propria. But in a philosophy like that of Aristotle, in which it is held that a true classification must not only be formally satisfactory, but must also conform to the actual lines of cleavage which Nature has established between kind and kind, the task of classificatory science becomes much more difficult. Science is called on to supply not merely a definition but the definition of the classes it considers, the definition which faithfully reflects the “lines of cleavage” in Nature. This is why the Aristotelian view is that a true definition should always be per genus et differentias. It should “place” a given class by mentioning the wider class next above it in the objective hierarchy, and then enumerating the most deep-seated distinctions by which Nature herself marks off this class from others belonging to the same wider class. Modern evolutionary thought may possibly bring us back to this Aristotelian standpoint. Modern evolutionary science differs from Aristotelianism on one point of the first importance. It regards the difference between kinds, not as a primary fact of Nature, but as produced by a long process of accumulation of slight differences. But a world in which the process has progressed far enough will exhibit much the same character as the Nature of Aristotle. As the intermediate links between “species” drop out because they are less thoroughly adapted to maintain themselves than the extremes between which they form links, the world produced approximates more and more to a system of species between which there are unbridgeable chasms; evolution tends more and more to the final establishment of “real kinds,” marked by the fact that there is no permanent possibility of cross-breeding between them. This makes it once more possible to distinguish between a “nominal” definition and a “real” definition. From an evolutionary point of view, a “real” definition would be one which specifies not merely enough characters to mark off the group defined from others, but selects also for the purpose those characters which indicate the line of historical development by which the group has successively separated itself from other groups descended from the same ancestors. We shall learn yet more of the significance of this conception of a “real kind” as we go on to make acquaintance with the outlines of First Philosophy. Over the rest of the formal logic of Aristotle we must be content to pass more rapidly. In connection with the doctrine of Propositions, Aristotle lays down the familiar distinction between the four types of proposition according to their quantity (as universal or particular) and quality (as affirmative or negative), and treats of their contrary and contradictory opposition in a way which still forms the basis of the handling of the subject in elementary works on formal logic. He also considers at great length a subject nowadays commonly excluded from the elementary books—-the modal distinction between the Problematic proposition (x may be y), the Assertory (x is y) and the Necessary (x must be y), and the way in which all these forms may be contradicted. For him, modality is a formal distinction like quantity or quality, because he believes that contingency and necessity are not merely relative to the state of our knowledge, but represent real and objective features of the order of Nature.

In connection with the doctrine of Inference, it is worth while to give his definition of Syllogism or Inference (literally “computation”) in his own words. “Syllogism is a discourse wherein certain things (viz. the premises) being admitted, something else, different from what has been admitted, follows of necessity because the admissions are what they are.” The last clause shows that Aristotle is aware that the all-important thing in an inference is not that the conclusion should be novel but that it should be proved. We may have known the conclusion as a fact before; what the inference does for us is connect it with the rest of our knowledge, and thus to show why it is true. He also formulates the axiom upon which syllogistic inference rests, that “if A is predicated universally of B and B of C, A is necessarily predicated universally of C.” Stated the language of class-inclusion, and adapted to include the case where B is denied of C, this become the formula, “whatever is asserted universally, whether positively or negatively, of a class B asserted in like manner of any class C which is wholly contained in B,” the axiom de omni et nullo medieval logic. The syllogism of the “first figure,” to which this principle immediately applies, is accordingly regarded by Aristotle as the natural and perfect form of inference. Syllogisms of the second and third figures can only be shown to fall under the dictum by a process of “reduction” or transformation into corresponding arguments in the first “figure,” and are therefore called “imperfect” or “incomplete,” because they do not exhibit the conclusive force of the reasoning with equal clearness, and also because no universal affirmative conclusion can be proved in them, and the aim of science is always to establish such affirmatives. The list of “moods” of the three figures, and the doctrine of the methods by which each mood of the imperfect figures can be replaced by an equivalent mood of the first, is worked out substantially as in our current text-books. The so-called “fourth” figure is not recognized, its moods being regarded merely as unnatural and distorted statements of those of the first figure.

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 premises 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 elicit 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 neighbors are bad things.” Hence he calls such appeals to example “rhetorical” reasoning, because the politician⁵ 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 colors, 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 cognized 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, unrealized 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 behavior 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 premises. 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 premises 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,”⁶ 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.

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 proof. “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 questions 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 catalog 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 premises 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 premises, 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 analyzed 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 premises, 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 favor 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 premise 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 color 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 modem 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 premise, 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 premises 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 premises. 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 medieval 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 premises 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 recognized by direct inspection or not at all, there can be no arguing at all with one who cannot or will not see it.)