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DEDUCTION. Deduction is reasoning from a general principle to other less general truths which are dependent upon this prin .

ciple. It consists in showing that the general law or principle assumed as the starting point is applicable to a particular subject matter, and in drawing the necessary consequences of its application. The form of this mode of infer ence is therefore given by the syllogism (q.v,), where the major premise (all M is P) states the general law, the minor premise (S is M) the application to a particular case, from which the conclusion (S is P) follows as a necessary consequence. The principle of this method of reasoning is commonly described as subsumption: the conclusion is shown to fall under or be included in the more funda mental propositions which are assumed as the starting point. These latter propositions can similarly be derived from others of still greater generality, until at last we reach the ultimate principles which form the foundation of all science. As to the foundation on which the ulti mate principles themselves rest, various theortei have been held. Until comparatively recent times the prevailing view (though by no means universally adopted) has maintained that these propositions neither require nor admit of any demonstration. They are necessary intui tions of the mind whose certainty is direct and immediate, and of a higher type than demon strations can yield. They thus constitute the basis of all science, since they are the funda mental first truths to which all science appeals as to an unquestioned authority. In the 17th and 18th centuries particularly, mathematics was regarded as the ideal science, and the position of the indemonstrable first principles of all science was often paralleled with that of the axioms of mathematics. It was as sumed before the time of Kant that mathe matics was wholly a deductive science which derived its results through an analysis of its initial concepts. In like manner it was hoped to put all knowledge on a demonstrative basis by discovering the whole system of necessary truths, and by showing how all particular facts in the various fields could be derived from them; for this would afford the absolute cer tainty which science was supposed to demand, ie., every fact would be deduced as a neces sary consequence from some general principle. At this time the empirical conclusions reached by inductive reasoning were not regarded as worthy of the name of science, for they are not universal and necessary truths, but only particular and more or less probable.

The development of thought in recent times has, however, entirely revolutionized our ideal of knowledge, and at the same time broken down the sharp distinctions between necessary, or a priori principles, and empirical truth, as well as between induction and deduc tion as contrasted methods of reasoning. It

is now widely recognized that there are no a priori truths in the old sense; no propositions that are certain in themselves apart from their connection with the rest of experience. It is true, the principles of logic itself and of mathe matics, which is a branch of logic, may be said to partake of apriority to such an extent that we are justified, for most purposes, in treating them as quite a priori. No matter how ulti mate any truth may appear, or how necessary in itself, its certainty and necessity are mediated in and through its relation to other experienced facts with which it is connected in the organic unity of a system. It is only through this systematic connection of the parts of knowledge that any inference is possible. For it is only in a whole, where the parts are systematically connected, that the nature of one part enables us to say what the other parts must be. And when it is seen that reasoning consists in making explicit the sys tematic connections of facts, the contrast between induction and deduction falls away. The structure of every inference is essentially the same; every inference is constituted by the relating of facts through a general principle. In deduction, as we have seen, the general truth is the starting point and we go on to explicate it in its application to some particular group of facts. On the other hand, the problem may be to find some relating principle for a given group of facts; and here we have to work in the reverse direction, beginning with the particulars and by the use of inductive methods seeking to bring to light some universal prin ciples of connection. There are no sciences which use exclusively either one of these methods. Even mathematics, which popu larly is supposed to employ only deduct ive reasoning, depends for a very essential class of demonstrations, known as existence proofs, on a more or less direct reference to concrete experience; and, on the other hand, the so-called observational sciences reason deductively in tracing out the application of the laws which have already been discovered and the consequences of the hypotheses which are employed. In every field thought uses all the means and methods which it can command to aid in solving its problems. Induction and deduction, observation and reasoning, are not separate and isolated processes, but functions of the knowledge-process which are supple mentary and go hand in hand. See braucnott,