intuitionismn.

/ɪntjuːˈɪʃənɪz(ə)m/

Etymology: < intuition n. + -ism suffix.

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.

ΘΚΠ

the mind > mental capacity > philosophy > epistemology > [noun] > cognition > intuitionism

intuitionism1847

1847 Blackwood's Mag. 62 243 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 n.

ΘΚΠ

the mind > mental capacity > philosophy > pragmatism > [noun] > utilitarianism > intuitionism of Sidgwick

intuitionalism1850

intuitionism1874

1874 H. Sidgwick Methods of 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. Mathematics. 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 n. 5c); 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 n. 3.

ΘΚΠ

the world > relative properties > number > mathematics > [noun] > theories or branches of

menadry1570

pure mathematics1605

mechanics1612

residuation1846

chaos theory1880

number theory1901

formalism1913

intuitionism1913

replacement theory1914

biomathematics1923

proof theory1929

finitism1935

mereology1938

combinatorics1941

cryptarithmetic1943

game theory1945

numerical analysis1946

queueing theory1951

constructivism1959

complexity1963

catastrophe theory1971

chaology1985

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 E. T. Bell Devel. Math. xxiii. 527 Formalism denies logicalism and seeks to controvert the conclusions of intuitionism.

1941 R. Courant & H. E. 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 S. C. Kleene & R. E. 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.

This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2018).

单词	intuitionism
释义	intuitionismn. /ɪntjuːˈɪʃənɪz(ə)m/ Etymology: < intuition n. + -ism suffix. 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. ΘΚΠ the mind > mental capacity > philosophy > epistemology > [noun] > cognition > intuitionism intuitionism1847 1847 Blackwood's Mag. 62 243 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 n. ΘΚΠ the mind > mental capacity > philosophy > pragmatism > [noun] > utilitarianism > intuitionism of Sidgwick intuitionalism1850 intuitionism1874 1874 H. Sidgwick Methods of 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. Mathematics. 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 n. 5c); 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 n. 3. ΘΚΠ the world > relative properties > number > mathematics > [noun] > theories or branches of menadry1570 pure mathematics1605 mechanics1612 residuation1846 chaos theory1880 number theory1901 formalism1913 intuitionism1913 replacement theory1914 biomathematics1923 proof theory1929 finitism1935 mereology1938 combinatorics1941 cryptarithmetic1943 game theory1945 numerical analysis1946 queueing theory1951 constructivism1959 complexity1963 catastrophe theory1971 chaology1985 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 E. T. Bell Devel. Math. xxiii. 527 Formalism denies logicalism and seeks to controvert the conclusions of intuitionism. 1941 R. Courant & H. E. 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 S. C. Kleene & R. E. 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. This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2018). < n.1847
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