| 单词 | metamathematics |
| 释义 | metamathematics, n. pl. (const. as sing.)|ˌmɛtəmæθɪˈmætɪks|
[f. meta- 1 + mathematics n. pl., after G. metamathematik (D. Hilbert 1923, in Math. Ann. LXXXVIII. 153).]
The field of study concerned with the structure and formal properties of mathematics and similar formal systems.
1890in Cent. Dict. 1926Encycl. Brit. II. 831/1 The science on which Hilbert is now (1926) engaged, which takes for its subject matter the meaningless formulae of mathematics, he calls metamathematics, and believes it to be capable of establishing many important results relating to the multiplicative axiom or axiom of selections, and to the continuum problem. 1940Mind XLIX. 242 The investigation of calculi, in this light, independently of all regard for the ‘meaning’ of the component complex marks, was christened metamathematics. 1952S. C. Kleene Introd. Metamath. iii. 63 The formal systems which are studied in metamathematics are (usually) so chosen that they serve as models for parts of informal mathematics and logic with which we are already more or less familiar, and from which they arose by formalization. 1956E. H. Hutten Lang. Mod. Physics ii. 35 That we require a meta-mathematics in order to prove the consistency and completeness of mathematics..does not mean that we are confronted with the final break-down of logic and mathematics. 1963G. T. Kneebone Math. Logic 381 Metamathematics began as a study of particular formal systems, and it was initially concerned with questions of consistency and completeness of given sets of axioms. But it now embraces investigations of altogether wider scope, designed to yield fundamental information about entire classes of formal systems of some particular kind. 1966J. J. Katz Philos. of Lang. iii. 27 Metamathematics, as the general theory of the formal structure of the language of mathematics, was closely parallel to Carnap's idea of logical syntax, as the general theory of the formal structure of scientific and factual discourse. No wonder, then, that metamathematics appealed to Carnap as a model for his theory of logical syntax. |
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