undecidableadj.
/ˌʌndᵻˈsʌɪdəbl/, U.S. /ˌəndəˈsaɪdəb(ə)l/, /ˌəndiˈsaɪdəb(ə)l/ a. Incapable of being decided.
ΘΚΠ
the mind > mental capacity > belief > uncertainty, doubt, hesitation > insecure knowledge, uncertainty > questionable state or quality > [adjective] > incapable of being decided
indeterminable1611
undeterminablea1639
undecidable1640
inconcludinga1644
indijudicable1660
undecisive1661
fallible1664
inconcludent1671
inconclusive1700
indecisive1726
1640 Bp. J. Hall Episcopacie iii. v. 244 Things so utterly undetermined, that they are indeed altogether undecidable.
1683 J. Moxon Mech. Exercises II. Pref. 1 An undecidable Controversie about the original Contriver..remains on foot.
1737 L. Clarke Compl. Hist. Bible II. vii. 224 The Question being undecidable among themselves, they appeal to Jerusalem.
1845 T. Carlyle in O. Cromwell Lett. & Speeches II. 531 As this matter of the Kingship is to me even now; very ‘dark’ and undecidable.
b. Logic and Mathematics. Of a proposition, theorem, etc.: incapable of being either proved or disproved.
ΘΚΠ
the world > relative properties > number > mathematics > [adjective] > relating to mathematical enquiry > of a proposition
decidable1935
undecidable1937
the mind > mental capacity > philosophy > logic > predicate or propositional logic > [adjective] > decidable or undecidable
decidable1935
undecidable1937
1937 Mind 46 60 Gödel has shown that the particular sentence in question is undecidable, i.e., neither it nor its negation is demonstrable.
1966 S. Beer Decision & Control x. 208 The network language which spans the gap between a problem situation and its conceptual model also contains undecidable sentences.
1979 Sci. Amer. Feb. 5/1 Logicians have been able to show that even simple and mathematically interesting statements may be undecidable.
Derivatives
ˌundecidaˈbility n. the property of being undecidable.
ΘΚΠ
the world > relative properties > number > mathematics > [noun] > mathematical property
irreductibility1865
utility1881
intransitivity1889
independence1902
non-linearity1904
connexity1905
analyticity1914
irredundance1925
irreflexiveness1933
decidability1936
non-emptiness1936
undecidability1942
irredundancy1952
irreflexivity1964
single-valuedness1968
the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > decidability or undecidability
decidability1936
undecidability1942
1942 Mind 51 260 It therefore raises the issue of undecidability in the arithmetical as well as in the linguistic realm.
1967 S. C. Kleene Math. Logic v. 279 By the essential undecidability of S, S2 is undecidable.
1971 Sci. 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.
Draft additions 1993
absol. or as n.
Something that cannot be decided; that which is undecidable.
ΘΚΠ
the mind > mental capacity > belief > uncertainty, doubt, hesitation > insecure knowledge, uncertainty > questionable state or quality > [noun] > something uncertain
uncertaintya1387
ambiguity1445
moot point1563
measuring cast1631
inconcludency1654
disputablea1657
undefinable1809
tertium quid1826
open question1837
question mark1870
inconclusion1886
disputability1892
borderliner1953
undecidable1965
1965 M. Davis (title) The undecidable: basic papers on undecidable propositions, unsolvable problems and computable functions.
1977 Dædalus 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.
1988 Mind 97 598 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.
This entry has not yet been fully updated (first published 1921; most recently modified version published online March 2022).
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adj.1640