| 释义 |
aˈrithmetize, v.
[f. arithmet-ic + -ize.]
†1. To work sums in arithmetic, to cipher. Obs.
a1658Cleveland Publ. Faith 33 But now the Cub can count, arithmatize.
2. Math.
a. To reduce (any other part of mathematics) to arithmetic, by defining mathematical entities and operations in terms of the natural numbers and their properties. Hence gen., to express in a numerical form.
1892H. B. Fine in Bull. N.Y. Math. Soc. I. 175 It is not merely that the purely arithmetical problems growing out of algebra were attractive to him [sc. Kronecker]—he ‘arithmetized’ algebra itself. 1937Mind XLVI. 311 A time in which there is genuine change or process can scarcely be ‘arithmetised’ or ‘logicised’ in its full meaning. 1948Brodie & Coleman tr. L. Chwistek's Limits of Sci. p. xxx, Weierstrass and Kronecker..maintained that..it is logically possible to arithmetize all portions of mathematics. 1951Ess. in Criticism I. 5 There has been a strong tendency in modern times to arithmetize criticism.
b. To apply the metamathematical method invented by Kurt Gödel of assigning a special number to each part of an utterance in order to formulate mathematical proofs about its properties.
1937A. Smeaton tr. R. Carnap's Logical Syntax Lang. §19. 57 The definitions and sentences of syntax arithmetized in this way do not differ fundamentally from the other definitions and sentences of arithmetic. 1940Mind XLIX. 240 The method of arithmetising axiom systems, used to such effect in Gödel's work, is fully explained.
Hence aˈrithmetizing vbl. n., the action of the verb.
1896Bull. Amer. Math. Soc. II. 243 The arithmetizing of mathematics began originally..by ousting space intuition. 1919B. Russell Introd. Math. Philos. i. 4 Pythagoras..was the discoverer of the most serious obstacle in the way of what is called the ‘arithmetising’ of mathematics. |