| 释义 |
intuˈitionist, n. (and a.)
[f. as prec. + -ist.]
One who holds the theory of intuitionism.
1. An adherent of the doctrine of Reid concerning immediate perception: see prec. 1. Also attrib.
1872Mill Exam. Hamilton's Philos. (ed. 4) xiv. 339 This..is the staple of the Intuitionist argument. 1890in Cent. Dict.
2. a. = intuitionalist 1. Used esp. in Math. Cf. intuitionism 3.
1855Miss Cobbe Intuit. Mor. 76 Where the Deductive Science of the Intuitionist stops, there the Inductive Science of the Experimentalist meets it. 1865Mill Exam. Hamilton 208 The most strenuous Intuitionist does not include this among the things that I know by direct intuition. 1879H. Spencer Data Ethics iv. §20. 55 Nor is it otherwise with the pure intuitionists, who hold that moral perceptions are innate in the original sense. 1913Bull. Amer. Math. Soc. XXV. 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. 1926Proc. London Math. Soc. 2nd Ser. XXV. 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. 1933M. Black Nature of Math. 195 The intuitionist recognises only the existence of denumerable sets. 1941[see formalist 5]. 1952R. M. Hare Lang. Morals iii. 30 The word ‘good’ is treated in the fashion that many intuitionists have treated it. 1959E. W. Beth Found. Math. xv. 421 The intuitionist..can point to the edifice of intuitionistic mathematics which has been built alongside classical mathematics. 1967S. C. Kleene Math. Logic §36. 196 To prove an existence statement {semE}xA(x), an intuitionist insists that it be shown how to find an x such that A(x). 1973Sci. 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. attrib. or as adj. Of or pertaining to intuitionism.
1885Athenæum 8 Aug. 170/3 He gives to the intuitionist theory as strong a position as can well be given to it. 1926[see formalist B]. 1933M. Black Nature of Math. 11 Intuitionist doctrines require the larger part of mathematics to be rewritten. Ibid., The intuitionists..are beginning to produce an intuitionist formal logic. 1960S. 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. Ibid., Every intuitionist proposition p, whether or not the (intuitionist-)negation occurs in it, is the record of a construction. 1970A. 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.
Hence intuitioˈnistic a., holding the theory of intuitionism; also intuitioˈnistically adv., in an intuitionistic manner.
1882W. G. Ward Ess. (1884) II. 155 And this criticism of Intuitionistic philosophers suggests a more general remark. 1940Mathematical 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. 1942D. D. Runes Dict. Philos. 150 The resulting disjunction becomes intuitionistically acceptable. 1944Mathematical 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. 1945E. T. Bell Devel. Math. (ed. 2) xxiii. 560 The ‘objects’ with which intuitionistic mathematics is concerned are said to be immediately apprehended in thought. 1946Nature 7 Sept. 323/1 Nevertheless, if ethics is to be scientific in this sense, some possible theories, particularly those commonly called intuitionistic, are excluded. 1957Encycl. Brit. XV. 82B/1 Most theorems of classical arithmetic can be established intuitionistically. 1962B. Meltzer tr. Gödel's On formally Undecidable Propositions 60 The following is demonstrated in an intuitionistically unobjectionable way. 1965Kleene & Vesley (title) The foundations of intuitionistic mathematics. 1967S. C. Kleene Math. Logic §44. 257 The consistency proof by a truth definition can even be managed intuitionistically. 1971R. 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. |