118 PART II. SOME IMPORTANT METHODOLOGICAL TERMS. 



SECTION XV. DEDUCTION. 



49. In a generalised statement much is often comprised 

 which was not suspected at first. 1 In consequence, when we 

 have reached our plain generalisation, and have embodied it 

 in a transparent definition, we begin to seek for all that it 

 involves. Here we do not rise from the minor to the major, 

 as in induction, but we descend from the major to the minor. 

 This process is named deduction, and is often of paramount 

 significance. Theoretically we might imagine a complete induc- 

 tion which exhausts every possible aspect, even to the past 

 and the future; in practice, however, comparatively few aspects 

 can be taken into consideration in an enquiry by a single 

 scholar. When, then, a generalisation is proposed or established, 

 we may descend in various ways to groups of particulars. 

 Manifestly, deductive reasoning forms an essential component 

 of the scientific process of investigation, and science would be 

 decidedly the poorer if the deductive process were discarded. 

 We may define deduction as that portion of a scientific enquiry 

 which, starting from a given statement, seeks to draw out its 

 implications in a desired direction or generally. 



Deduction is especially fruitful and safe where exact and 

 quantitative determinations have been reached. Here the pre- 

 cise form of the generalisation allows of the fullest and minutest 

 deduction, as, for instance, in astronomy and mechanics. Mathe- 

 matics is, therefore, of increasing value as science progresses, 

 and accordingly, when most developed, science tends to clothe 

 itself in mathematical garb, i.e., tends to become deductive. 

 This is no reflection, as is often assumed, on the inductive and 

 reputedly non-mathematical method, for this method not only 

 prevails, but is necessarily supreme, in all but the last stages 

 of a science. We must be first cognisant of the rudimentary 

 facts yielded by an examination of relevant data, then reach 

 a sufficient number of wide generalisations, then embody these 

 in a crisp definition, and only after this can we securely and 

 with distinct advantage proceed deductively when weighty issues 

 are involved. Hence observation, generalisation, definition, and 

 deduction form interrelated component parts of one method. 



Descartes searched in his mind for a clear and distinct idea 

 which he finally imagined that he had discovered. This dis- 

 covery he expressed in the now celebrated postulate Cogito, 



- 1 "Axioms, duly and orderly formed from particulars, easily discover the 

 way to new particulars, and thus render sciences active." (Bacon, Novuin 

 Organum, bk. 1, 24.) "All true and fruitful natural philosophy hath a double 

 scale or ladder, ascendent and descendent, ascending from experiments, to 

 the invention of causes; and descending from causes, to the invention of 

 new experiments." (Bacon, Advancement of Learning, bk. 2.) And, rightly, 

 "that method of discovery and proof according to which the most general 

 principles are first established, and then intermediate axioms are tried and 

 proved by them, is the parent of error and the curse of all science". (Novuin 

 Organum, bk. 1, 69.) "The deductive method . . . consists of three operations 



