[ad. L. contrāpositiōn-em (Boethius), n. of action from contrāpōnĕre to CONTRAPONE.]
1. A placing over against; antithesis, opposition, contrast. Phr. In contraposition to (or with).
1581. J. Bell, Haddon’s Answ. Osor., 332. A figure called contraposition betwixt the decrees of God and the Popes.
1642. Potter, On Numb. 666, 91 (T.). To shew how exact and exquisite an antithesis and contraposition there is between the apostles and cardinals.
1731. Hist. Litteraria, I. 150. ’Tis called the new Covenant, in Contraposition to that which our first Parents violated.
1846. Grote, Greece (1862), II. vi. 133. Placed in contraposition with the Spartan on one side, and with the Helot on the other.
1852. Fraser’s Mag., XLVI. 219. He lauds, in contraposition to this single man, the greatness of Rome.
2. Logic. A mode of conversion in which from a given proposition we infer another proposition having the contradictory of the original predicate for its subject; thus ‘All S is P’ by contraposition gives ‘All not-P is not-S’ or ‘No not-P is S.’ (Sometimes also called Conversion by Negation.) Applied also to a similar conversion of the antecedent and consequent of a hypothetical proposition.
The definition varies with logicians according to the form in which they state the contrapositive proposition. The quality of the proposition is changed in the one form, and remains unchanged in the other. With Boethius and the earlier logicians the quality remained unchanged. Cf. Boeth., De Syll. Cat., Wks. (ed. Migne), 804 Est enim per contrapositionem conversio, ut si dicas omnis homo animal est, omne non animal non homo est.
1551. T. Wilson, Logike, 21. A conuersion by contraposition is when the former part of the sentence is turned into the last rehearsed part, and the last rehearsed part turned into the former part of the sentence, both the propositions being uniuersall, and affirmatiue, sauing that in the second proposition there be certaine negatiues enterlaced.
1630. Bp. W. Bedell, in Usher’s Lett. (1686), 440. A false and absurd Contraposition.
1788. Reid, Aristotle’s Log., iv. § 3. Converting the major by contraposition.
1845. Whately, Logic (1872), 36. This may be named Conversion by negation; or as it is commonly called, by contra-position.
1869. Fowler, Ded. Logic (ed. 3), 78. The O proposition, when permuted from ‘Some X is not Y’ into ‘Some X is not-Y,’ may of course be converted into ‘Some not-Y is X.’ This combination of permutation and conversion is … styled ‘Conversion by contra-Position or Negation.’
1871. T. M. Lindsay, trans. Ueberweg’s Logic, 319. No conclusion follows by Contraposition from the particular affirmative judgment.
