contraposition
(ˌkɒntrəpəˈzɪʃən)
[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. 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 tr. Ueberweg's Logic 319 No conclusion follows by Contraposition from the particular affirmative judgment. |