| 释义 |
metamathematical, a.|ˌmɛtəmæθɪˈmætɪkəl|
[f. as next, after mathematics, mathematical.]
a. Beyond the scope of mathematics. rare.
1833Sir W. R. Hamilton in R. P. Graves Life II. 68 In the application of the mathematics themselves there must (if I may venture on the word) be something meta-mathematical.
b. Of or pertaining to metamathematics.
1926F. P. Ramsey in Mathematical Gaz. XIII. 188 It is contended that the principles used in the metamathematical proof that the axioms of mathematics do not lead to contradiction, are so obviously true that not even the sceptics can doubt them. 1933M. Black Nature of Math. 150 It is extremely probable that a metamathematical proof of the consistency of the whole of pure mathematics is impossible. 1952S. C. Kleene Introd. Metamath. vi. 140 In either case, the rules of inference must have the character of schemata, i.e. they must employ metamathematical variables, since infinitely many applications have to be provided for. 1971Nature 8 Jan. 104/2 Hilbert's programme for demonstrating the consistency of arithmetic by metamathematical methods resulted in a new outburst of activity which culminated..with Gödel's incompleteness theorem.
Hence ˌmetamatheˈmatically adv., by means of, or from the point of view of, metamathematics.
1937Philos. of Sci. IV. 329 Gödel has proved metamathematically that there are surely theorems and problems about the natural numbers which cannot be proved or solved by elementary means. 1956J. H. Woodger tr. Tarski's Logic, Semantics, Metamath. 116 Let us now consider the situation metamathematically. 1967S. C. Kleene Math. Logic §39. 214 Ackermann in 1924–5 thought he had proved metamathematically the consistency of N. |