non-theoremn.

Brit.

/nɒnˈθɪərəm/, U.S.

/nɑnˈθɪrəm/

Origin: Formed within English, by derivation. Etymons: non- prefix, theorem n.

Etymology: < non- prefix + theorem n.

Logic.

A proposition or formula that is not provable within a given system.

ΚΠ

1940 W. V. Quine Math. Logic vii. 292 The notion of a non-theorem, e.g., is protosyntactically definable, yet presumably not constructive.

1954 I. M. Copi Symbolic Logic vi. 185 A purely formal criterion for distinguishing between theorems and non-theorems of the system.

1972 A. Church in R. Rudner & I. Scheffler Logic & Art x. 198 The expected consequences of any assertion, even of a non-theorem.

1996 Philos. Q. 46 111 Any theorem has a finite proof in the recursive axiomatization above, while any non-theorem is refuted by some finite model.

This entry has been updated (OED Third Edition, December 2003; most recently modified version published online March 2022).

单词	non-theorem
释义	non-theoremn. Brit. /nɒnˈθɪərəm/, U.S. /nɑnˈθɪrəm/ Origin: Formed within English, by derivation. Etymons: non- prefix, theorem n. Etymology: < non- prefix + theorem n. Logic. A proposition or formula that is not provable within a given system. ΚΠ 1940 W. V. Quine Math. Logic vii. 292 The notion of a non-theorem, e.g., is protosyntactically definable, yet presumably not constructive. 1954 I. M. Copi Symbolic Logic vi. 185 A purely formal criterion for distinguishing between theorems and non-theorems of the system. 1972 A. Church in R. Rudner & I. Scheffler Logic & Art x. 198 The expected consequences of any assertion, even of a non-theorem. 1996 Philos. Q. 46 111 Any theorem has a finite proof in the recursive axiomatization above, while any non-theorem is refuted by some finite model. This entry has been updated (OED Third Edition, December 2003; most recently modified version published online March 2022). < n.1940
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