| 释义 |
Gödel|ˈgøːdəl|
The name of Kurt Gödel (born 1906), Austrian mathematician, used attrib. and in the possessive to designate his metamathematical theorems and related techniques and constituents; as Gödel number, Gödel numbering; Gödel's proof; Gödel('s) theorem, the demonstration (first published in Monatshefte f. Math. u. Physik (1931) XXXVIII) that in logic and in mathematics there must be true formulas which are neither provable nor disprovable, thus making mathematics essentially incomplete, and also the corollary that the consistency of such a system as arithmetic cannot be proved within that system. Also Gödelian |gœˈdiːlɪən|, a.
1933M. Black Nature of Math. 167 (heading) Note on Gödel's Theorem. 1942Mind LI. 259 (title) Goedelian sentences: a non-numerical approach. 1952S. C. Kleene Introd. Metamath. viii. 204 We designate the first of these theorems, which entails the other as corollary, as ‘Gödel's theorem’. Ibid. 206 We call this a Gödel numbering, and the correlated number of a formal object its Gödel number. 1956E. H. Hutten Lang. Mod. Physics ii. 34 Gödel's theorem, when first published in 1930, plunged many logicians and mathematicians into the pit of despair. 1959Nagel & Newman (title) Gödel's proof. 1962W. & M. Kneale Devel. Logic vii. 476 This discovery is closely akin to Gödel's theorem on the incompletability of formal arithmetic. 1964Philos. XXXIX. 196 Machines could never be selfconscious in the way that human minds are, and..Gödel's theorem illustrates this. 1965R. L. Wilder Introd. Found. Math. (ed. 2) xi. 275 In some of these systems, analogues of the Gödel theorems have been shown to hold. |