A science, then, may be analysed into three constituents. These are: (1) a determinate class of objects which form the subject-matter of its inquiries. In an orderly exhibition of the contents of the science, these appear, as in Euclid, as the initial data about which the science reasons; (2) a number of principles, postulates, and axioms, from which our demonstrations must start. Some of these will be principles employed in all scientific reasoning. Others will be specific to the subject-matter with which a particular science is concerned; (3) certain characteristics of the objects under study which can be shown by means of our axioms and postulates to follow from our initial definitions, the accidentia per se of the objects defined. It is these last which are expressed by the conclusions of scientific demonstration. We are said to know scientifically that B is true of A when we show that this follows, in virtue of the principles of some science, from the initial definition of A. Thus if we convinced ourselves that the sum of the angles of a plane triangle is equal to two right angles by measurement, we could not be said to have scientific knowledge of the proposition. But if we show that the same proposition follows from the definition of a plane triangle by repeated applications of admitted axioms or postulates of geometry, our knowledge is genuinely scientific. We now know that it is so, and we see why it is so; we see the connection of this truth with the simple initial truths of geometry.
This leads us to the consideration of the most characteristic point of Aristotle's whole theory. Science is demonstrated knowledge, that is, it is the knowledge that certain truths follow from still simpler truths. Hence the simplest of all the truths of any science cannot themselves be capable of being known by inference. You cannot infer that the axioms of geometry are true because its conclusions are true, since the truth of the conclusions is itself a consequence of the truth of the axioms. Nor yet must you ask for demonstration of the axioms as consequences of still simpler premisses, because if all truths can be proved, they ought to be proved, and you would therefore require an infinity of successive demonstrations to prove anything whatever. But under such conditions all knowledge of demonstrated truth would be impossible. The first principles of any science must therefore be indemonstrable. They must be known, as facts of sense-perception are known, immediately and not mediately. How then do we come by our knowledge of them? Aristotle's answer to this question appears at first sight curiously contradictory. He seems to say that these simplest truths are apprehended intuitively, or on inspection, as self-evident by Intelligence or Mind. On the other hand, he also says that they are known to us as a result of induction from sense-experience. Thus he seems to be either a Platonist or an empiricist, according as you choose to remember one set of his utterances or another, and this apparent inconsistency has led to his authority being claimed in their favour by thinkers of the most widely different types. But more careful study will show that the seeming confusion is due to the fact that he tries to combine in one statement his answers to two quite different questions, (1) how we come to reflect on the axioms, (2) what evidence there is for their truth. To the first question he replies, "by induction from experience," and so far he might seem to be a precursor of John Stuart Mill. Successive repetitions of the same sense-perceptions give rise to a single experience, and it is by reflection on experience that we become aware of the most ultimate simple and universal principles. We might illustrate his point by considering how the thought that two and two are four may be brought before a child's mind. We might first take two apples, and two other apples and set the child to count them. By repeating the process with different apples we may teach the child to dissociate the result of the counting from the particular apples employed, and to advance to the thought, "any two apples and any two other apples make four apples." Then we might substitute pears or cherries for the apples, so as to suggest the thought, "two fruits and two fruits make four fruits." And by similar methods we should in the end evoke the thought, "any two objects whatever and any other two objects whatever make four objects." This exactly illustrates Aristotle's conception of the function of induction, or comparison of instances, in fixing attention on a universal principle of which one had not been conscious before the comparison was made.
Now comes in the point where Aristotle differs wholly from all empiricists, later and earlier. Mill regards the instances produced in the induction as having a double function; they not merely fix the attention on the principle, they also are the evidence of its truth. This gives rise to the greatest difficulty in his whole logical theory. Induction by imperfect enumeration is pronounced to be (as it clearly is) fallacious, yet the principle of the uniformity of Nature which Mill regards as the ultimate premiss of all science, is itself supposed to be proved by this radically fallacious method. Aristotle avoids a similar inconsistency by holding that the sole function of the induction is to fix our attention on a principle which it does not prove. He holds that ultimate principles neither permit of nor require proof. When the induction has done its work in calling attention to the principle, you have to see for yourself that the principle is true. You see that it is true by immediate inspection just as in sense-perception you have to see that the colour before your eyes is red or blue. This is why Aristotle holds that the knowledge of the principles of science is not itself science (demonstrated knowledge), but what he calls intelligence, and we may call intellectual intuition. Thus his doctrine is sharply distinguished not only from empiricism (the doctrine that universal principles are proved by particular facts), but also from all theories of the Hegelian type which regard the principles and the facts as somehow reciprocally proving each other, and from the doctrine of some eminent modern logicians who hold that "self-evidence" is not required in the ultimate principles of science, as we are only concerned in logic with the question what consequences follow from our initial assumptions, and not with the truth or falsehood of the assumptions themselves.
The result is that Aristotle does little more than repeat the Platonic view of the nature of science. Science consists of deductions from universal principles which sensible experience "suggests," but into which, as they are apprehended by a purely intellectual inspection, no sense-data enter as constituents. The apparent rejection of "transcendental moonshine" has, after all, led to nothing. The only difference between Plato and his scholar lies in the clearness of intellectual vision which Plato shows when he expressly maintains in plain words that the universals of exact science are not "in" our sense-perceptions and therefore to be extracted from them by a process of abstraction, but are "apart from" or "over" them, and form an ideal system of interconnected concepts which the experiences of sense merely "imitate" or make approximation to.
One more point remains to be considered to complete our outline of the Aristotelian theory of knowledge. The sciences have "principles" which are discerned to be true by immediate inspection. But what if one man professes to see the self-evident truth of such an alleged principle, while another is doubtful of its truth, or even denies it? There can be no question of silencing the objector by a demonstration, since no genuine simple principle admits of demonstration. All that can be done, e.g. if a man doubts whether things equal to the same thing are equal to one another, or whether the law of contradiction is true, is to examine the consequences of a denial of the axiom and to show that they include some which are false, or which your antagonist at least considers false. In this way, by showing the falsity of consequences which follow from the denial of a given "principle," you indirectly establish its truth. Now reasoning of this kind differs from "science" precisely in the point that you take as your major premiss, not what you regard as true, but the opposite thesis of your antagonist, which you regard as false. Your object is not to prove a true conclusion but to show your opponent that his premisses lead to false conclusions. This is "dialectical" reasoning in Aristotle's sense of the word, i.e. reasoning not from your own but from some one else's premisses. Hence the chief philosophical importance which Aristotle ascribes to "dialectic" is that it provides a method of defending the undemonstrable axioms against objections. Dialectic of this kind became highly important in the mediæval 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 Theologiæ of Thomas is regularly constituted by arguments based on the premisses of actual or possible antagonists, and is strictly dialectical. (To be quite accurate Aristotle should, of course, have observed that this dialectical method of defending a principle becomes useless in the case of a logical axiom which is presupposed by all deduction. For this reason Aristotle falls into fallacy when he tries to defend the law of contradiction by dialectic. It is true that if the law be denied, then any and every predicate may be indifferently ascribed to any subject. But until the law of contradiction has been admitted, you have no right to regard it as absurd to ascribe all predicates indiscriminately to all subjects. Thus, it is only assumed laws which are not ultimate laws of logic that admit of dialectical justification. If a truth is so ultimate that it has either to be recognised by direct inspection or not at all, there can be no arguing at all with one who cannot or will not see it.)
CHAPTER III
FIRST PHILOSOPHY
First Philosophy is defined by Aristotle as a "science which considers What Is simply in its character of Being, and the properties which it has as such." That there is, or ought to be, such a science is urged on the ground that every "special" science deals only with some restricted department of what is, and thus considers its subject-matter not universally in its character of being, or being real, but as determined by some more special condition. Thus, First Philosophy, the science which attempts to discover the most ultimate reasons of, or grounds for, the character of things in general cannot be identified with any of the "departmental" sciences. The same consideration explains why it is "First Philosophy" which has to disentangle the "principles" of the various sciences, and defend them by dialectic against those who impugn them. It is no part of the duty of a geometer or a physicist to deal with objections to such universal principles of reasoning as the law of contradiction. They may safely assume such principles; if they are attacked, it is not by specifically geometrical or physical considerations that they can be defended. Even the "principles of the special sciences" have not to be examined and defended by the special sciences. They are the starting-points of the sciences which employ them; these sciences are therefore justified in requiring that they shall be admitted as a condition of geometrical, or physical, or biological demonstrations. If they are called in question, the defence of them is the business of logic.
First Philosophy, then, is the study of "What Is simply as such," the universal principles of structure without which there could be no ordered system of knowable objects. But the word "is" has more than one sense. There are as many modes of being as there are types of predication. "Substances," men, horses, and the like, have their own specific mode of being--they are things; qualities, such as green or sweet, have a different mode of being--they are not things, but "affections" or "attributes" of things. Actions, again, such as building, killing, are neither things nor yet "affections" of things; their mode of being is that they are processes which produce or destroy things. First Philosophy is concerned with the general character of all these modes of being, but it is specially concerned with that mode of being which belongs to substances. For this is the most primary of all modes of being. We had to introduce a reference to it in our attempt to say what the mode of being of qualities and actions is, and it would have been the same had our illustrations been drawn from any other "categories." Hence the central and special problem of First Philosophy is to analyse the notion of substance and to show the causes of the existence of substances.
Next, we have to note that the word "substance" itself has two senses. When we spoke of substance as one of the categories we were using it in a secondary sense. We meant by substances "horse," "man," and the rest of the "real kinds" which we find in Nature, and try to reproduce in a scientific classification. In this sense of the word "substances" are a special class of predicates, as when we affirm of Plato that he is a man, or of Bucephalus that he is a horse. But in the primary sense a substance means an absolutely individual thing, "this man," or "this horse." We may therefore define primary substances from the logician's point of view by saying that they can be only subjects of predication, never predicates. Or again, it is peculiar to substances, that while remaining numerically one a substance admits of incompatible determinations, as Socrates, remaining one and the same Socrates, is successively young and old. This is not true of "qualities," "actions," and the rest. The same colour cannot be first white and then black; the same act cannot be first bad and then good. Thus we may say that individual substances are the fixed and permanent factors in the world of mutability, the invariants of existence. Processes go on in them, they run the gamut of changes from birth to decay, processes take place among them, they act on and are acted on by one another, they fluctuate in their qualities and their magnitude, but so long as a substance exists it remains numerically one and the same throughout all these changes. Their existence is the first and most fundamental condition of the existence of the universe, since they are the bearers of all qualities, the terms of all relations, and the agents and patients in all interaction.