ONE: His [Aristotles] theory of syllogism is simply an explicit statement of the fact that all knowledge, all thought, rests on universal truths or general propositionsthat all knowledge, whether deductive or inductive, is arrived at by the aid, the indispensable aid, of general propositions. We in England have been almost charmed into the belief that reasoning is perpetually from particular to particular, and a village matron and her Lucy have been used to express the truth for us in the concrete form adapted to our weaker comprehension (Mills Logic, bk. ii. ch. 3). We shall next be told, forsooth, that oxygen and hydrogen do not enter into the composition of water, because our village matron perpetually drinks it without passing through either element, and the analysis of the chemist will be proved as great a fiction as the analysis of the logician. Aristotle has supplied the links which at once upset all such superficial389 analysis. He has shown that even in analogy or example, which apparently proceeds in this way from one particular instance to another particular instance, we are only justified in so proceeding in so far as we have transformed the particular instance into a general proposition.284A milling tool with twenty edges should represent as much wearing capacity as a like number of separate tools, and may be said to equal twenty duplicate tools; hence, in cutting grooves, notches, or similar work, a milling tool is equivalent to a large number of duplicate single tools, which cannot be made or set with the same truth; so that milling secures accuracy and duplication, objects which are in many cases more important than speed.
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