In its Theoretical use 325

■ p ' , process by which the science of mathematics is built up. It is true that he calls attention to the fact that

mathematics has not to do with substances, but only with special aspects of them which are abstracted from i ■

their other aspects. And he also points out that

» * 1 m there are many such aspects of substances, e.g. their

motion, which may be made the subjects of special sciences. Still he seems to contemplate it as the ideal of a science, that it should be based upon the definition of a substance-^a definition which expresses the form realised in such a substance—and that its demonstrations should result in the exhibition of all the ^propm which are analytically deducible from that definition.1

• . ■ « * might be taken to the above statements, if they were intended as a complete account of Aristotle's views upon logical method. They correspond to the ideal of science which is expressed in the Metaphym, Book 7. In the Posterior A nalytic we find two other views which are not easily reconcilable either with it or with each other. In the first book nothing is said of substances, as such i but the general conception of demonstration is still that it is deduction of propria from a definition. And it is implied, I think, that this definition must express the formal cause of the subject—say, a triangle^-of which the science treats. Aristotle seems mainly to be thinking of mathematics, though, as stated above, he does not apprehend the synthetic character of mathematical reasoning. In the second book, however, demonstration is taken as the proof of the existence of an attribute, or the occurrence of an event, through its own definition : and this definition may be given through thé efficient, as weU; as the formal and final causés. Further the cause in question is always the proximate cause, and nothing is said as to the mode in which this cause is to be connected with the definition of the subject, which in the first book


Now it is hardly necessary to say that Aristotle's actual efforts at scientific construction do not conform to this type. He is not content, in practice, to seek for some abstract principle or definition of the object in question, and then to derive everything analytically from it. What he usually does is, first, to establish by induction and dialectical reasoning some very general view of the subject of investigation, and then to distinguish different elements within it, and to endeavour, by further inductions and inferences, to determine their relations as parts of a whole which is one with itself through all its differences. He thus proceeds not from the concrete to the abstract, but from the abstract to the concrete, not by analysis and m was spoken of as supplying the middle term in scientific demonstration. Another view is suggested in the Metaphysk (Book 7, oh. 11 seq.) by the fact that Aristotle has great difficulty in determining that the definition of a substance should express only its form and #

not its matter. There and more definitely in his works upon the science of nature (especially Phys., II, 8, and the Pari, An., I, 1) it is recognised that there are two lines of scientific enquiry; one, which deals with the final cause (which is shown to bo one with the formal cause) and the properties deduoible therefrom; and another, whioh deals with the necessary conditions of its realisation, and, therefore, with material and efficient causes. Matter, of course, is here taken not as the indeterminate basis of all exist« ence of which he speaks in Met., 1029a, 24, but as equivalent to the material constituents (in our sense) of the plants or animals. This corresponds to the view of Plato spoken of above (pp. 130» 241). I shall have to say more of it in the next chapter. Zn reference to these differences, I can only suggest that Aristotle forgets or modifies his general statements, when he has to deal with particular branches of science.

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