intuitionism
(ɪntjuːˈɪʃənɪz(ə)m)
[f. intuition + -ism.]
1. The doctrine of Reid and other philosophers of the Scottish school, that in perception, external objects are known immediately, without the intervention of a vicarious phenomenon.
| 1847 Blackw. Mag. LXII. 243 Representationism could not possibly be avoided, neither could intuitionism be possibly fallen in with, on the analytic road which he took. 1874 W. G. Ward Ess. (1884) I. 204 He [Mill] accounted the controversy between intuitionism and phenomenism far more fundamental than any other, in matters no less of social than of strictly philosophical speculation. 1896 G. M. Sloane Life James M'Cosh viii. 103 His philosophic creed, being the intuitionism of the Scottish School. |
2. = intuitionalism.
| 1874 Sidgwick Meth. Ethics i. 9 What we may call Intuitionism. 1884 Athenæum 11 Oct. 461/3 Prof. Sidgwick..showed his strong preference for utilitarianism over the other two methods, egoism and intuitionism, which completed his trio of possible schemes of ethical study by logical processes. |
3. Math. The theory put forward by L. E. J. Brouwer (1908) that mathematics is founded on extra-linguistic constructs based on pure intuition (in the Kantian sense, cf. intuition 5 c); that space geometry is reducible to arithmetic and that therefore the law of the excluded middle, applying to finite classes, might not be valid for infinite classes. Cf. formalism 3.
| 1913 tr. L. E. J. Brouwer in Bull. Amer. Math. Soc. XXV. 86 From the present point of view of intuitionism..all mathematical sets of units..can be developed out of the basal intuition, and this can only be done by combining a finite number of times the two operations: ‘to create a finite ordinal number’ and ‘to create the infinite ordinal number ω’. 1940 [see formalism 3 a]. 1941 Courant & Robbins What is Math.? i. 87 Some distinguished mathematicians have recently advocated the more or less complete banishment from mathematics of all non-constructive proofs... The school of ‘intuitionism’, which has adopted this program, has met with strong resistance. 1959 E. W. Beth Found. Math. xv. 413 One of the most spectacular features in Brouwer's intuitionism is..his rejection of the unrestricted application of the principle of the excluded third in mathematical reasoning. 1965 Kleene & Vesley Found. Intuitionistic Math. i. 1 Modern intuitionism, founded by Brouwer, constitutes a vigorous manifestation of the constructive tendency. 1973 Sci. Amer. Mar. 103/2 Three modern schools of mathematical thought: logicism, formalism and intuitionism. |