arithmetizev.
ΘΚΠ
the world > relative properties > number > arithmetic > do arithmetic [verb (intransitive)]
cipher1530
count1588
arithmetizea1658
to do one's sums1818
sum1838
figure1854
a1658 J. Cleveland Publick Faith in Wks. (1687) 201 But now the Cub can count, arithmatize.
2. Mathematics.
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.
ΘΚΠ
the world > relative properties > number > arithmetic > treat arithmetically [verb (transitive)]
state1657
cipher1825
to figure up1854
arithmeticize1878
arithmetize1892
1892 H. 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.
1937 Mind 46 311 A time in which there is genuine change or process can scarcely be ‘arithmetised’ or ‘logicised’ in its full meaning.
1948 H. C. Brodie & A. P. Coleman tr. L. Chwistek Limits of Sci. p. xxx Weierstrass and Kronecker..maintained that..it is logically possible to arithmetize all portions of mathematics.
1951 Ess. in Crit. 1 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.
ΘΚΠ
the world > relative properties > number > mathematics > mathematize [verb (intransitive)]
mathematize1719
mathematicize1875
arithmetize1937
the world > relative properties > number > mathematics > calculate or solve [verb (transitive)] > by specific method
arithmetize1937
1937 A. Smeaton tr. R. Carnap 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.
1940 Mind 49 240 The method of arithmetising axiom systems, used to such effect in Gödel's work, is fully explained.
Derivatives
aˈrithmetizing n. the action of the verb.
ΚΠ
1896 Bull. Amer. Math. Soc. 2 243 The arithmetizing of mathematics began originally..by ousting space intuition.
1919 B. 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.
This entry has not yet been fully updated (first published 1885; most recently modified version published online June 2019).
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