metamathematicsn.
/ˌmɛtəˌmaθ(ə)ˈmatɪks/, U.S. /ˈˌmɛdəˌmæθ(ə)ˈmædɪks/ With singular agreement. The analysis of the nature, methodology, and philosophical implications of mathematics. Now usually: spec. the study of the structure and formal properties of mathematical theories and systems; proof theory.
ΘΚΠ
the mind > mental capacity > philosophy > mathematical philosophy > [noun]
mathematical philosophy1832
metamathematics1890
1890 Cent. Dict. Metamathematics, the metaphysics of mathematics; the philosophy of non-Euclidean geometry and the like.
1895 Mind 38 340 In meta-mathematics there is a possibility of some solid result.
1926 Encycl. 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.
1944 A. Tarski in Philos. & Phenomenol. Res. 4 368 As regards the applicability of semantics to mathematical sciences and their methodology, i.e., to meta-mathematics, we are in a much more favorable position.
1966 J. J. Katz Philos. 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.
1972 M. Kline Math. Thought li. 1207 The above arguments do not exclude the possibility of new methods of proof that would go beyond what Hilbert's metamathematics permit.
1991 C. B. Boyer & U. C. Merzbach Hist. Math. (ed. 2) xxvii. 612 If arithmetic cannot lift itself from the quagmire of possible inconsistency, perhaps metamathematics, standing outside the arithmetic bog, can save the day by other means.
This entry has been updated (OED Third Edition, December 2001; most recently modified version published online March 2022).
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