CONTENTS

CHAP.

I. LIFE AND WORKS

II. THE CLASSIFICATION OF THE SCIENCES: SCIENTIFIC METHOD

III. FIRST PHILOSOPHY

IV. PHYSICS

V. PRACTICAL PHILOSOPHY

BIBLIOGRAPHY

ARISTOTLE

CHAPTER I

LIFE AND WORKS

It has not commonly been the lot of philosophers, as it is of great poets, that their names should become household words. We should hardly call an Englishman well read if he had not heard the name of Sophocles or MoliÈre. An educated man is expected to know at least who these great writers were, and to understand an allusion to the Antigone or Le Misanthrope. But we call a man well read if his mind is stored with the verse of poets and the prose of historians, even though he were ignorant of the name of Descartes or Kant. Yet there are a few philosophers whose influence on thought and language has been so extensive that no one who reads can be ignorant of their names, and that every man who speaks the language of educated Europeans is constantly using their vocabulary. Among this few Aristotle holds not the lowest place. We have all heard of him, as we have all heard of Homer. He has left his impress so firmly on theology that many of the formulae of the Churches are unintelligible without acquaintance with his conception of the universe. If we are interested in the growth of modern science we shall readily discover for ourselves that some knowledge of Aristotelianism is necessary for the understanding of Bacon and Galileo and the other great anti-Aristotelians who created the "modern scientific" view of Nature. If we turn to the imaginative literature of the modern languages, Dante is a sealed book, and many a passage of Chaucer and Shakespeare and Milton is half unmeaning to us unless we are at home in the outlines of Aristotle's philosophy. And if we turn to ordinary language, we find that many of the familiar turns of modern speech cannot be fully understood without a knowledge of the doctrines they were first forged to express. An Englishman who speaks of the "golden mean" or of "liberal education," or contrasts the "matter" of a work of literature with its "form," or the "essential" features of a situation or a scheme of policy with its "accidents," or "theory" with "practice," is using words which derive their significance from the part they play in the vocabulary of Aristotle. The unambitious object of this little book is, then, to help the English reader to a better understanding of such familiar language and a fuller comprehension of much that he will find in Dante and Shakespeare and Bacon.

Life of Aristotle.--The main facts of Aristotle's life may be briefly told. He was born in 385-4 B.C. at Stagirus, a little city of the Chalcidic peninsula, still called, almost by its ancient name, Chalcis, and died at the age of sixty-two at Chalcis in Euboea. Thus he is a contemporary of Demosthenes, his manhood witnessed the struggle which ended in the establishment of the Macedonian monarchy as the dominant power in Hellas, and his later years the campaigns in which his pupil Alexander the Great overthrew the Persian Empire and carried Greek civilisation to the banks of the Jumna. In studying the constitutional theories of Aristotle, it is necessary to bear these facts in mind. They help to explain certain limitations of outlook which might otherwise appear strange in so great a man. It throws a great deal of light on the philosopher's intense conviction of the natural inferiority of the "barbarian" intellect and character to remember that he grew up in an outlying region where the "barbarian" was seen to disadvantage in the ordinary course of life. Hence the distinction between Greek and "barbarian" came to mean for him much what the "colour-line" does to an American brought up in a Southern State. So, again, when we are struck by his "provincialism," his apparent satisfaction with the ideal of a small self-contained city-state with a decently oligarchical government, a good system of public education, and no "social problems," but devoid alike of great traditions and far-reaching ambitions, we must remember that the philosopher himself belonged to just such a tiny community without a past and without a future. The Chalcidic cities had been first founded, as the name of the peninsula implies, as colonies from the town of Chalcis in Euboea; Corinth had also been prominent in establishing settlements in the same region. At the height of Athenian Imperial prosperity in the age of Pericles the district had fallen politically under Athenian control, but had been detached again from Athens, in the last years of the Archidamian war, by the genius of the great Spartan soldier and diplomat Brasidas. Early in the fourth century the Chalcidic cities had attempted to form themselves into an independent federation, but the movement had been put down by Sparta, and the cities had fallen under the control of the rising Macedonian monarchy, when Aristotle was a baby. A generation later, a double intrigue of the cities with Philip of Macedon and Athens failed of its effect, and the peninsula was finally incorporated with the Macedonian kingdom. It is also important to note that the philosopher belonged by birth to a guild, the Asclepiadae, in which the medical profession was hereditary. His father Nicomachus was court physician to Amyntas II., the king for whose benefit the Spartans had put down the Chalcidic league. This early connection with medicine and with the Macedonian court explains largely both the predominantly biological cast of Aristotle's philosophical thought and the intense dislike of "princes" and courts to which he more than once gives expression. At the age of eighteen, in 367-6, Aristotle was sent to Athens for "higher" education in philosophy and science, and entered the famous Platonic Academy, where he remained as a member of the scientific group gathered round the master for twenty years, until Plato's death in 347-6. For the three years immediately following Aristotle was in Asia Minor with his friend and fellow-student Hermeias, who had become by force of sheer capacity monarch of the city of Atarneus in the Troad, and was maintaining himself with much energy against the Persian king. Pythias, the niece of Hermeias, became the philosopher's wife, and it seems that the marriage was happy. Examination of Aristotle's contributions to marine biology has shown that his knowledge of the subject is specially good for the Aeolic coast and the shores of the adjacent islands. This throws light on his occupations during his residence with Hermeias, and suggests that Plato had discerned the bent of his distinguished pupil's mind, and that his special share in the researches of the Academy had, like that of Speusippus, Plato's nephew and successor in the headship of the school, been largely of a biological kind. We also know that, presumably shortly after Plato's death, Aristotle had been one of the group of disciples who edited their teacher's unpublished lectures. In 343 Hermeias was assassinated at the instigation of Persia; Aristotle honoured his memory by a hymn setting forth the godlikeness of virtue as illustrated by the life of his friend. Aristotle now removed to the Macedonian court, where he received the position of tutor to the Crown Prince, afterwards Alexander the Great, at this time (343 B.C.) a boy of thirteen. The association of the great philosopher and the great king as tutor and pupil has naturally struck the imagination of later ages; even in Plutarch's Life of Alexander we meet already with the full-blown legend of the influence of Aristotle's philosophical speculations on Alexander. It is, however, improbable that Aristotle's influence counted for much in forming the character of Alexander. Aristotle's dislike of monarchies and their accessories is written large on many a page of his Ethics and Politics; the small self-contained city-state with no political ambitions for which he reserves his admiration would have seemed a mere relic of antiquity to Philip and Alexander. The only piece of contemporary evidence as to the relations between the master and the pupil is a sentence in a letter to the young Alexander from the Athenian publicist Isocrates who maliciously congratulates the prince on his preference for "rhetoric," the art of efficient public speech, and his indifference to "logic-choppers." How little sympathy Aristotle can have had with his pupil's ambitions is shown by the fact that though his political theories must have been worked out during the very years in which Alexander was revolutionising Hellenism by the foundation of his world-empire, they contain no allusion to so momentous a change in the social order. For all that Aristotle tells us, Alexander might never have existed, and the small city-state might have been the last word of Hellenic political development. Hence it is probable that the selection of Aristotle, who had not yet appeared before the world as an independent thinker, to take part in the education of the Crown Prince was due less to personal reputation than to the connection of his family with the court, taken together with his own position as a pupil of Plato, whose intervention in the public affairs of Sicily had caused the Academy to be regarded as the special home of scientific interest in politics and jurisprudence. It may be true that Alexander found time in the midst of his conquests to supply his old tutor with zoological specimens; it is as certain as such a thing can be that the ideals and characters of the two men were too different to allow of any intimate influence of either on the other.

When Alexander was suddenly called to the Macedonian throne by the murder of his father in 336 B.C., Aristotle's services were no longer needed; he returned to Athens and gave himself to purely scientific work. Just at this juncture the presidency of the Academy was vacant by the death of Speusippus, Aristotle's old associate in biological research. Possibly Aristotle thought himself injured when the school passed him over and elected Xenocrates of Chalcedon as its new president. At any rate, though he appears never to have wholly severed his connection with the Academy, in 335 he opened a rival institution in the Lyceum, or gymnasium attached to the temple of Apollo Lyceus, to which he was followed by some of the most distinguished members of the Academy. From the fact that his instruction was given in the peripatos or covered portico of the gymnasium the school has derived its name of Peripatetic. For the next twelve years he was occupied in the organisation of the school as an abode for the prosecution of speculation and research in every department of inquiry, and in the composition of numerous courses of lectures on scientific and philosophical questions. The chief difference in general character between the new school and the Academy is that while the scientific interests of the Platonists centred in mathematics, the main contributions of the Lyceum to science lay in the departments of biology and history.

Towards the end of Alexander's life his attention was unfavourably directed on his old teacher. A relative of Aristotle named Callisthenes had attended Alexander in his campaigns as historiographer, and had provoked disfavour by his censure of the King's attempts to invest his semi-constitutional position towards his Hellenic subjects with the pomp of an Oriental despotism. The historian's independence proved fatal. He was accused of instigating an assassination plot among Alexander's pages, and hanged, or, as some said, thrown into a prison where he died before trial. Alexander is reported to have held Aristotle responsible for his relative's treason, and to have meditated revenge. If this is so, he was fortunately diverted from the commission of a crime by preoccupation with the invasion of India.

On the death of Alexander in 323 a brief but vigorous anti-Macedonian agitation broke out at Athens. Aristotle, from his Macedonian connections, naturally fell a victim, in spite of his want of sympathy with the ideals of Philip and Alexander. Like Socrates, he was indicted on the capital charge of "impiety," the pretext being that his poem on the death of Hermeias, written twenty years before, was a virtual deification of his friend. This was, however, only a pretext; the real offence was political, and lay in his connection with the Macedonian leader Antipater. As condemnation was certain, the philosopher anticipated it by withdrawing with his disciples to Chalcis, the mother city of his native Stagirus. Here he died in the following year, at the age of sixty-two or sixty-three.

The features of Aristotle, familiar to us from busts and intaglios, are handsome, but indicate refinement and acuteness rather than originality, an impression in keeping with what we should expect from a study of his writings. The anecdotes related of him reveal a kindly, affectionate character, and show little trace of the self-importance which appears in his work. His will, which has been preserved, exhibits the same traits in its references to his happy family life and its solicitous care for the future of his children and servants. He was twice married, first to Pythias, and secondly to a certain Herpyllis, by whom he left a son Nicomachus and a daughter. The "goodness" of Herpyllis to her husband is specially mentioned in the clauses of the will which make provision for her, while the warmth of the writer's feelings for Pythias is shown by the direction that her remains are to be placed in the same tomb with his own. The list of servants remembered and the bequests enumerated show the philosopher to have been in easier circumstances than Plato.

The Works of Aristotle.--The so-called works of Aristotle present us with a curious problem. When we turn from Plato to his pupil we seem to have passed into a different atmosphere. The Discourses of Socrates exhibit a prose style which is perhaps the most marvellous of all literary achievements. Nowhere else do we meet with quite the same combination of eloquence, imaginative splendour, incisive logic, and irresistible wit and humour. The manner of Aristotle is dry and formal. His language bristles with technicalities, makes little appeal to the emotions, disdains graces of style, and frequently defies the simplest rules of composition. Our surprise is all the greater that we find later writers of antiquity, such as Cicero, commending Aristotle for his copious and golden eloquence, a characteristic which is conspicuously wanting in the Aristotelian writings we possess. The explanation of the puzzle is, however, simple. Plato and Aristotle were at once what we should call professors and men of letters; both wrote works for general circulation, and both delivered courses of lectures to special students. But while Plato's lectures have perished, his books have come down to us. Aristotle's books have almost wholly been lost, but we possess many of his lectures. The "works" of Aristotle praised by Cicero for their eloquence were philosophical dialogues, and formed the model for Cicero's own compositions in this kind. None of them have survived, though some passages have been preserved in quotations by later writers. That the "works" are actually the MSS. of a lecturer posthumously edited by his pupils seems clear from external as well as from internal evidence. In one instance we have the advantage of a double recension. Aristotle's Ethics or Discourses on Conduct have come down to us in two forms--the so-called Nicomachean Ethics, a redaction by the philosopher's son, Nicomachus, preserving all the characteristics of an oral course of lectures; and a freer and more readable recast by a pupil, the mathematician Eudemus, known as the Eudemian Ethics. In recent years we have also recovered from the sands of Egypt what appears to be our one specimen of a "work" of Aristotle, intended to be read by the public at large, the essay on the Constitution of Athens. The style of this essay is easy, flowing, and popular, and shows that Aristotle could write well and gracefully when he thought fit.

CHAPTER II

THE CLASSIFICATION OF THE SCIENCES: SCIENTIFIC METHOD

Philosophy, as understood by Aristotle, may be said to be the organised 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 civilisation has advanced far enough to make secure provision for the immediate material needs of life. Human curiosity was naturally directed first to the outstanding "marvellous 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, the 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 premisses, 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 premisses. You may reason dialectically from premisses which you believe to be false, for the express purpose of showing the absurd conclusions to which they lead. Or you may reason from premisses 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 premisses. Thus the distinction between Science and Dialectic is that Science reasons from true premisses, Dialectic only from "probable" or "plausible" premisses. 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.

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-evident[#] 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.

[#] Self-evident, that is, in a purely logical sense. When you apprehend the principles in question, you see at once that they are true, and do not require to have them proved. It is not meant that any and every man does, in point of fact, always apprehend the principles, or that they can be apprehended without preliminary mental discipline.

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 co-ordinate 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 Metaphysics[#]--treats, to use Aristotle's own expression, of "Being quÀ 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 organisation 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 to-day 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.

[#] The origin of this name seems to be that Aristotle's lectures on First Philosophy came to be studied as a continuation of his course on Physics. Hence the lectures got the name Metaphysica because they came after (meta) those on Physics. Finally the name was transferred (as in the case of Ethics) from the lectures to the subject of which they treat.

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 co-ordinate, 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 recognise 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 organisation 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.

(a) Formal Logic.--In compass the Aristotelian logic corresponds roughly with the contents of modern 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 mediÆval 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," and that which was afterwards known in the Middle Ages as the list of "Predicaments" or "Heads of Predicates," 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 "x is tall" 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 armour 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 ys are xs," 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 mediÆval 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 "Predicaments" 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 recognise 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 reproduction. 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. 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 premisses) 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 to 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 in the language of class-inclusion, and adapted to include the case where B is denied of C this becomes the formula, "whatever is asserted universally, whether positively or negatively, of a class B is asserted in like manner of any class C which is wholly contained in B," the axiom de omni et nullo of mediÆval 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 recognised, 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 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 malgrÉ 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.