incompletability
(ɪnkəmˈpliːtəbɪlɪtiː)
Also -ibility.
[f. incomplete a. + -bility.]
1. Incapability of being completed; = incompletableness.
| 1829 Carlyle Misc., Novalis (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 Math. 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 a. 2 b.
| 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 ― Methods of Logic (1952) §42. 248 Church's argument makes essential use of Gödel's theorem of the incompletability of number theory. 1962 [see Gödel]. |