incompletabilityn.

/ɪnkəmˈpliːtəbɪlɪtiː/

Forms: Also incompletibility.

Etymology: < incomplete adj. + -bility suffix.

a. Incapability of being completed; = incompletableness n.

ΘΚΠ

the world > action or operation > completing > non-completion > [noun] > incapability of being finished

incompletability1829

the world > relative properties > wholeness > incompleteness > [noun] > inability to be completed

incompletability1829

incompletableness1898

1829 T. Carlyle Novalis in Crit. & Misc. Ess. (1872) II. 213 (tr. Novalis) Men often wondered at the stubborn Incompletibility of these two Sciences.

1898 Q. Rev. Apr. 86 This idea of the mysterious incompletability of existence.

b. Logic and Mathematics. The property, inherent in certain kinds of logical or mathematical system, of being incapable of providing a proof of every true proposition that can be formulated within the language of the system, no matter how many of these propositions be taken as extra axioms of the system. Cf. incomplete adj. 2b.

ΘΚΠ

the mind > mental capacity > philosophy > mathematical philosophy > [noun] > incompleteness

incompleteness1932

incompletability1940

incompleteness theorem1955

1940 W. V. Quine Math. Logic Pref. p. vii Gödel's theorem regarding the incompletability of logic and arithmetic is derived along novel lines.

1950 W. V. Quine Methods of Logic (1952) §42. 248 Church's argument makes essential use of Gödel's theorem of the incompletability of number theory.

1962 W. Kneale & M. Kneale Devel. Logic vii. 476 This discovery is closely akin to Gödel's theorem on the incompletability of formal arithmetic.

This entry has not yet been fully updated (first published 1976; most recently modified version published online December 2020).

单词	incompletability
释义	incompletabilityn. /ɪnkəmˈpliːtəbɪlɪtiː/ Forms: Also incompletibility. Etymology: < incomplete adj. + -bility suffix. a. Incapability of being completed; = incompletableness n. ΘΚΠ the world > action or operation > completing > non-completion > [noun] > incapability of being finished incompletability1829 the world > relative properties > wholeness > incompleteness > [noun] > inability to be completed incompletability1829 incompletableness1898 1829 T. Carlyle Novalis in Crit. & Misc. Ess. (1872) II. 213 (tr. Novalis) Men often wondered at the stubborn Incompletibility of these two Sciences. 1898 Q. Rev. Apr. 86 This idea of the mysterious incompletability of existence. b. Logic and Mathematics. The property, inherent in certain kinds of logical or mathematical system, of being incapable of providing a proof of every true proposition that can be formulated within the language of the system, no matter how many of these propositions be taken as extra axioms of the system. Cf. incomplete adj. 2b. ΘΚΠ the mind > mental capacity > philosophy > mathematical philosophy > [noun] > incompleteness incompleteness1932 incompletability1940 incompleteness theorem1955 1940 W. V. Quine Math. Logic Pref. p. vii Gödel's theorem regarding the incompletability of logic and arithmetic is derived along novel lines. 1950 W. V. Quine Methods of Logic (1952) §42. 248 Church's argument makes essential use of Gödel's theorem of the incompletability of number theory. 1962 W. Kneale & M. Kneale Devel. Logic vii. 476 This discovery is closely akin to Gödel's theorem on the incompletability of formal arithmetic. This entry has not yet been fully updated (first published 1976; most recently modified version published online December 2020). < n.1829
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