Part 2

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 _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 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:--

Science | +-----------+------------+ | | Theoretical Practical | +---+---------+-----------+ | | | First Philosophy Mathe- Physics or matics Theology

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 mediaeval 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 "_x_s are _y_s." 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 _x_s are _y_s." Now if this statement is true it may also be true that "all _y_s are _x_s," 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 _x_s are _y_s," but not true that all "_y_s are _x_s," _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 _x_s 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 _x_s and some things other than _x_s. 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 mediaeval 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 mediaeval 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.