intuitionistn.adj.

Etymology: < intuition n. + -ist suffix.Previous versions of the OED give the stress as: intuˈitionist.

One who holds the theory of intuitionism.

1. An adherent of the doctrine of Reid concerning immediate perception: see intuitionism n. 1. Also attributive.

ΘΚΠ

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

intuitionalist1869

intuitionist1872

1872 J. S. Mill Exam. Hamilton's Philos. (ed. 4) xiv. 339 This..is the staple of the Intuitionist argument.

1890 in Cent. Dict.

a. = intuitionalist n. 1. Used esp. in Mathematics. Cf. intuitionism n. 3.

ΘΚΠ

the mind > mental capacity > perception or cognition > intuition > [noun] > intuitive knowledge > one who works by

intuitionist1855

intuitive1907

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

intuitionist1855

intuitionalist1856

1855 F. P. Cobbe Ess. Intuitive Morals I. 76 Where the Deductive Science of the Intuitionist stops, there the Inductive Science of the Experimentalist meets it.

1865 J. S. Mill Exam. Hamilton's Philos. 208 The most strenuous Intuitionist does not include this among the things that I know by direct intuition.

1879 H. Spencer Data of Ethics iv. §20. 55 Nor is it otherwise with the pure intuitionists, who hold that moral perceptions are innate in the original sense.

1913 Bull. Amer. Math. Soc. 25 86 The intuitionist can never feel assured of the exactness of a mathematical theory by such guarantees as the proof of its being non-contradictory, the possibility of defining its concepts by a finite number of words or the practical certainty that it will never lead to a misunderstanding in human relations.

1926 Proc. London Math. Soc. 25 339 Apart from formalism, there are two main general attitudes to the foundation of mathematics: that of intuitionists or finitists..and that of the logicians.

1933 M. Black Nature of Math. 195 The intuitionist recognises only the existence of denumerable sets.

1941 R. Courant & H. E. Robbins What is Math.? iv. 216 The clash between the intuitionists and the formalists has been much publicized by passionate partisans of these schools.

1952 R. M. Hare Lang. Morals iii. 30 The word ‘good’ is treated in the fashion that many intuitionists have treated it.

1959 E. W. Beth Found. Math. xv. 421 The intuitionist..can point to the edifice of intuitionistic mathematics which has been built alongside classical mathematics.

1967 S. C. Kleene Math. Logic §36. 196 To prove an existence statement ∃xA(x), an intuitionist insists that it be shown how to find an x such that A(x).

1973 Sci. Amer. Mar. 103/2 As for intuitionists, they have in effect returned to the Pythagorean position that the natural numbers must be accepted without further analysis as the foundation of mathematics.

b. attributive or as adj. Of or pertaining to intuitionism.

ΘΚΠ

the mind > mental capacity > philosophy > epistemology > [adjective] > of cognition > of doctrines and adherents of cognition theories

representative1605

Lockean1765

intuitional1865

intuitionistic1882

intuitionist1885

imagist1948

the world > relative properties > number > mathematics > [adjective] > characterized by theories of or approaches to

physico-mathematical1660

analytical1694

Bernoulli1749

analytic1761

Boolean1851

Sturmian1853

Bernoullian1876

Fermatian1887

Grassmannian1894

number-theoretic1899

Cantor1902

Cantorian1912

Tauberian1913

Thiessen1923

intuitionist1926

metamathematical1926

finitist1931

number-theoretical1936

finitistic1937

proof-theoretic1940

formalistic1941

Gödelian1942

constructivist1943

constructivistic1944

game-theoretical1946

game-theoretic1950

finitary1952

perturbation-theoretic1964

perturbation-theoretical1968

constructive1979

1885 Athenæum 8 Aug. 170/3 He gives to the intuitionist theory as strong a position as can well be given to it.

1926 Proc. London Math. Soc. 25 339 I hold that mathematics is part of logic, and so belong to..the logical school as opposed to the formalist and intuitionist schools.

1933 M. Black Nature of Math. 11 Intuitionist doctrines require the larger part of mathematics to be rewritten.

1933 M. Black Nature of Math. 11 The intuitionists..are beginning to produce an intuitionist formal logic.

1960 S. Körner Philos. of Math. vi. 131 The intuitionist logic is a post factum record of the principles of reasoning which have been employed in mathematical constructions.

1960 S. Körner Philos. of Math. vi. 131 Every intuitionist proposition p, whether or not the (intuitionist-)negation occurs in it, is the record of a construction.

1970 A. Kino et al. Intuitionism & Proof Theory 19 That is the general way of accepting-on-faith in the domains of religion and philosophy, and in traditional intuitionist or constructivist mathematics also.

Derivatives

intuitioˈnistic adj. holding the theory of intuitionism.

ΘΚΠ

the mind > mental capacity > philosophy > epistemology > [adjective] > of cognition > of doctrines and adherents of cognition theories

representative1605

Lockean1765

intuitional1865

intuitionistic1882

intuitionist1885

imagist1948

1882 W. G. Ward Ess. (1884) II. 155 And this criticism of Intuitionistic philosophers suggests a more general remark.

1940 Math. Rev. Nov. 323/1 The treatment is ‘intuitionistic’ in the sense that it is purely algebraic, involving reference to order, absolute value, boundedness, etc., but not to limiting processes.

1945 E. T. Bell Devel. Math. (ed. 2) xxiii. 560 The ‘objects’ with which intuitionistic mathematics is concerned are said to be immediately apprehended in thought.

1946 Nature 7 Sept. 323/1 Nevertheless, if ethics is to be scientific in this sense, some possible theories, particularly those commonly called intuitionistic, are excluded.

1965 S. C. Kleene & R. E. Vesley (title) The foundations of intuitionistic mathematics.

1971 R. Schock Quasi-connectives vi. 58 The resulting quasi-connectives satisfy all the axioms of the intuitionistic sentential calculus, but not the principle of the excluded middle.

intuitioˈnistically adv. in an intuitionistic manner.

ΘΚΠ

the mind > mental capacity > philosophy > epistemology > [adverb] > as regards branches or doctrines and their adherents

particularistically1927

intuitionistically1942

intuitively1942

1942 D. D. Runes Dict. Philos. 150 The resulting disjunction becomes intuitionistically acceptable.

1944 Math. Rev. Sept. 198/2 The author proves intuitionistically seven theorems concerning the full product of a finite or denumerable number of virtually ordered sets, generalizing some results of Brouwer concerning the full products of sets of integers.

1957 Encycl. Brit. XV. 82 b/1 Most theorems of classical arithmetic can be established intuitionistically.

1962 B. Meltzer tr. K. Gödel On Formally Undecidable Propositions 60 The following is demonstrated in an intuitionistically unobjectionable way.

1967 S. C. Kleene Math. Logic §44. 257 The consistency proof by a truth definition can even be managed intuitionistically.

This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2019).

单词	intuitionist
释义	intuitionistn.adj. Etymology: < intuition n. + -ist suffix.Previous versions of the OED give the stress as: intuˈitionist. One who holds the theory of intuitionism. 1. An adherent of the doctrine of Reid concerning immediate perception: see intuitionism n. 1. Also attributive. ΘΚΠ the mind > mental capacity > philosophy > epistemology > [noun] > cognition > intuitionism > adherent of intuitionalist1869 intuitionist1872 1872 J. S. Mill Exam. Hamilton's Philos. (ed. 4) xiv. 339 This..is the staple of the Intuitionist argument. 1890 in Cent. Dict. 2. a. = intuitionalist n. 1. Used esp. in Mathematics. Cf. intuitionism n. 3. ΘΚΠ the mind > mental capacity > perception or cognition > intuition > [noun] > intuitive knowledge > one who works by intuitionist1855 intuitive1907 the mind > mental capacity > philosophy > pragmatism > [noun] > utilitarianism > intuitionism of Sidgwick > adherent of intuitionist1855 intuitionalist1856 1855 F. P. Cobbe Ess. Intuitive Morals I. 76 Where the Deductive Science of the Intuitionist stops, there the Inductive Science of the Experimentalist meets it. 1865 J. S. Mill Exam. Hamilton's Philos. 208 The most strenuous Intuitionist does not include this among the things that I know by direct intuition. 1879 H. Spencer Data of Ethics iv. §20. 55 Nor is it otherwise with the pure intuitionists, who hold that moral perceptions are innate in the original sense. 1913 Bull. Amer. Math. Soc. 25 86 The intuitionist can never feel assured of the exactness of a mathematical theory by such guarantees as the proof of its being non-contradictory, the possibility of defining its concepts by a finite number of words or the practical certainty that it will never lead to a misunderstanding in human relations. 1926 Proc. London Math. Soc. 25 339 Apart from formalism, there are two main general attitudes to the foundation of mathematics: that of intuitionists or finitists..and that of the logicians. 1933 M. Black Nature of Math. 195 The intuitionist recognises only the existence of denumerable sets. 1941 R. Courant & H. E. Robbins What is Math.? iv. 216 The clash between the intuitionists and the formalists has been much publicized by passionate partisans of these schools. 1952 R. M. Hare Lang. Morals iii. 30 The word ‘good’ is treated in the fashion that many intuitionists have treated it. 1959 E. W. Beth Found. Math. xv. 421 The intuitionist..can point to the edifice of intuitionistic mathematics which has been built alongside classical mathematics. 1967 S. C. Kleene Math. Logic §36. 196 To prove an existence statement ∃xA(x), an intuitionist insists that it be shown how to find an x such that A(x). 1973 Sci. Amer. Mar. 103/2 As for intuitionists, they have in effect returned to the Pythagorean position that the natural numbers must be accepted without further analysis as the foundation of mathematics. b. attributive or as adj. Of or pertaining to intuitionism. ΘΚΠ the mind > mental capacity > philosophy > epistemology > [adjective] > of cognition > of doctrines and adherents of cognition theories representative1605 Lockean1765 intuitional1865 intuitionistic1882 intuitionist1885 imagist1948 the world > relative properties > number > mathematics > [adjective] > characterized by theories of or approaches to physico-mathematical1660 analytical1694 Bernoulli1749 analytic1761 Boolean1851 Sturmian1853 Bernoullian1876 Fermatian1887 Grassmannian1894 number-theoretic1899 Cantor1902 Cantorian1912 Tauberian1913 Thiessen1923 intuitionist1926 metamathematical1926 finitist1931 number-theoretical1936 finitistic1937 proof-theoretic1940 formalistic1941 Gödelian1942 constructivist1943 constructivistic1944 game-theoretical1946 game-theoretic1950 finitary1952 perturbation-theoretic1964 perturbation-theoretical1968 constructive1979 1885 Athenæum 8 Aug. 170/3 He gives to the intuitionist theory as strong a position as can well be given to it. 1926 Proc. London Math. Soc. 25 339 I hold that mathematics is part of logic, and so belong to..the logical school as opposed to the formalist and intuitionist schools. 1933 M. Black Nature of Math. 11 Intuitionist doctrines require the larger part of mathematics to be rewritten. 1933 M. Black Nature of Math. 11 The intuitionists..are beginning to produce an intuitionist formal logic. 1960 S. Körner Philos. of Math. vi. 131 The intuitionist logic is a post factum record of the principles of reasoning which have been employed in mathematical constructions. 1960 S. Körner Philos. of Math. vi. 131 Every intuitionist proposition p, whether or not the (intuitionist-)negation occurs in it, is the record of a construction. 1970 A. Kino et al. Intuitionism & Proof Theory 19 That is the general way of accepting-on-faith in the domains of religion and philosophy, and in traditional intuitionist or constructivist mathematics also. Derivatives intuitioˈnistic adj. holding the theory of intuitionism. ΘΚΠ the mind > mental capacity > philosophy > epistemology > [adjective] > of cognition > of doctrines and adherents of cognition theories representative1605 Lockean1765 intuitional1865 intuitionistic1882 intuitionist1885 imagist1948 1882 W. G. Ward Ess. (1884) II. 155 And this criticism of Intuitionistic philosophers suggests a more general remark. 1940 Math. Rev. Nov. 323/1 The treatment is ‘intuitionistic’ in the sense that it is purely algebraic, involving reference to order, absolute value, boundedness, etc., but not to limiting processes. 1945 E. T. Bell Devel. Math. (ed. 2) xxiii. 560 The ‘objects’ with which intuitionistic mathematics is concerned are said to be immediately apprehended in thought. 1946 Nature 7 Sept. 323/1 Nevertheless, if ethics is to be scientific in this sense, some possible theories, particularly those commonly called intuitionistic, are excluded. 1965 S. C. Kleene & R. E. Vesley (title) The foundations of intuitionistic mathematics. 1971 R. Schock Quasi-connectives vi. 58 The resulting quasi-connectives satisfy all the axioms of the intuitionistic sentential calculus, but not the principle of the excluded middle. intuitioˈnistically adv. in an intuitionistic manner. ΘΚΠ the mind > mental capacity > philosophy > epistemology > [adverb] > as regards branches or doctrines and their adherents particularistically1927 intuitionistically1942 intuitively1942 1942 D. D. Runes Dict. Philos. 150 The resulting disjunction becomes intuitionistically acceptable. 1944 Math. Rev. Sept. 198/2 The author proves intuitionistically seven theorems concerning the full product of a finite or denumerable number of virtually ordered sets, generalizing some results of Brouwer concerning the full products of sets of integers. 1957 Encycl. Brit. XV. 82 b/1 Most theorems of classical arithmetic can be established intuitionistically. 1962 B. Meltzer tr. K. Gödel On Formally Undecidable Propositions 60 The following is demonstrated in an intuitionistically unobjectionable way. 1967 S. C. Kleene Math. Logic §44. 257 The consistency proof by a truth definition can even be managed intuitionistically. This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2019). < n.adj.1855
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