| 释义 |
undeˈcidable, a.
[un-1 7 b.]
a. Incapable of being decided.
1640Bp. Hall Episc. iii. v. 244 Things so utterly undetermined, that they are indeed altogether undecidable. 1683Moxon Mech. Exerc., Printing 1 An undecidable Controversie about the original Contriver..remains on foot. 1737L. Clarke Hist. Bible (1740) II. 224 The question being undecidable among themselves, they appeal to Jerusalem. 1845Carlyle Cromwell (1872) V. 16 As this matter of the Kingship is to me even now, very ‘dark’ and undecidable!
b. Logic and Math. Of a proposition, theorem, etc.: incapable of being either proved or disproved.
1937Mind XLVI. 60 Gödel has shown that the particular sentence in question is undecidable, i.e., neither it nor its negation is demonstrable. 1966S. Beer Decision & Control x. 208 The network language which spans the gap between a problem situation and its conceptual model also contains undecidable sentences. 1979Sci. Amer. Feb. 5/1 Logicians have been able to show that even simple and mathematically interesting statements may be undecidable.
Hence ˌundecidaˈbility, the property of being undecidable.
1942Mind LI. 260 It therefore raises the issue of undecidability in the arithmetical as well as in the linguistic realm. 1967S. C. Kleene Math. Logic v. 279 By the essential undecidability of S, S2 is undecidable. 1971Sci. Amer. Aug. 99/1 In contrast, the Platonists, who count among their number even Gödel himself, believe (like Einstein) that the undecidability in mathematics is a statement about the inherent limitations of our present axiomatic mode of investigation and not about the mathematical objects themselves.
Add:B. absol. or as n. Something that cannot be decided; that which is undecidable.
1965M. Davis (title) The undecidable: basic papers on undecidable propositions, unsolvable problems and computable functions. 1977Dædalus Fall 109 The paradoxes and undecidables which this perspective discloses as the unavoidable bases of language and thought are more familiar and more easily exemplified in the realm of literature than elsewhere. 1988Mind XCVII. 598 We are in the first case when it comes to undecidables: our understanding of them..is given substance by its completely consisting in a particular practical capacity. |