| 释义 |
incompleteness|ɪnkəmˈpliːtnɪs|
[f. as prec. + -ness.]
a. The quality or state of being incomplete; want of completeness.
1643Milton Divorce Introd., Error..willingly accepts what he wants, and supplies what her incompleatnesse went seeking. 1664–5Boyle Cause Condens. Air Wks. 1772 II. 499 The incompleteness of the theory of cold. 1845–6Trench Huls. Lect. Ser. i. i. 8 A book..underlying the same..incompletenesses as every other work of men's hands. 1860Tyndall Glac. 33, I had often occasion to feel the incompleteness of my knowledge.
b. spec. in Logic and Math. (see incomplete a. 2 b.) Also attrib. in incompleteness theorem, the mathematical proof of incompleteness (cf. Gödel).
1932Lewis & Langford Symbolic Logic xi. 365 This point of incompleteness can be brought out by contrasting examples. 1937A. Smeaton tr. Carnap's Logical Syntax of Lang. iii. §34a. 100 In spite of this necessary incompleteness of the method of derivation.., the method retains its fundamental significance. 1955K. R. Popper in P. A. Schilpp Philos. of R. Carnap (1963) 200 Gödel, by his two famous incompleteness theorems, had proved that one unified language would not be sufficiently universal for even the purposes of elementary number theory. 1957P. Suppes Introd. Logic iv. 70 Gödel's theorem on the incompleteness of elementary number theory is probably the most important theorem in the literature of modern logic. 1962B. Meltzer tr. Gödel's On Formally Undecidable Propositions 62 The true source of the incompleteness attaching to all formal systems of mathematics, is to be found..in the fact that the formation of ever higher types can be continued into the transfinite. 1971G. Hunter Metalogic 257 This is Gödel's second incompleteness theorem. |