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:--