deduction (dedukshon)

[ A compleate deduction of the progre e of navigation and com'erce, from its first principle, to ye present age. Evelyn, To my Lord Treasurer. 2t. The act of deriving; derivation. To them [vowels), as is well known to etymologists, little regard is to be shewn in the deduction of one language from another. Johnson, Eng. Dict., Pref. 3. In logic, derivation as a result from a known principle; nece ary inference; also, the result itself, as so concluded. As a term of logic, it is a translation of Aristotle's ἀπαγωγή (translated deductio by Boëthius), and properly signifies an illative descent from a general principle to the result of that principle in a special case; it is specially used by Aristotle when there is a doubt whether the case truly comes under the principle. By the older logicians it is little used, and not with any exact signification. In modern times it has been chiefly employed by those who hold that all reasoning is either a descent from generals to particulars ( deduction ) or an ascent from particulars to generals ( induction ). See de ductive reasoning, under deductive. Probation may be either a proce of deduction -that is, the leading of proof out of one higher or more general proposition - or a proce of induction - that is, the leading of proof out of a plurality of lower or le general judgments. ... Sir W. Hamilton . Deduction. is the inverse proce of inferring a particular case from a law of cases a umed to be of like nature. G. H. Lewes, Probs. of Life and Mind, 1st ser., III. iv. § 47. It is astonishing how little of the real life of the time we learn from the Troubadours except by way of inference Lowell , Study Windows, p. 236. and deduction. deed He labours to introduce a secondary and deductive Atheism: that although men concede there is a God, yet they should deny his providence. Sir T. Browne, Vulg. Err., i. 10. Deductive method, in the logical system of J. S. Mill, that mode of investigation by which the law of an effect is ascertained from the consideration of the laws of the different tendencies of which it is the joint result. This method consists of three kinds of operation, the first direct induction, the second ratiocination, the third verification. To the deductive method , thus characterized in its three constituent parts of induction, ratiocination, and verification, the human mind is indebted for its most conspicuous triumphs in the investigation of nature. Mill , Logic, III. xi. § 6. Deductive reasoning is commonly opposed to induc tive, and is meant to include all nece ary reasoning (even mathematical induction), together with those probable reasonings which predict results as true in the long run, but excluding those inferences which are regarded as be ing open to correction in the long run. Thus, if, from counting the letters on a single page, one concludes the proportions of the different letters which will generally be needed in a font of type, the reasoning is inductive; but if, knowing what the proportions generally are, one concludes what will be needed in printing a particular book or page, the reasoning is deductive. deductively (dē-duktiv-li), adv. By deduction; in consequence of a general principle. There is scarce a popular errour pa ant in our days, which is not either directly expre ed or deductively contained in this work [Pliny's Natural History]. Sir T. Browne, Vulg. Err., i. 8.