incompletenessn.

/ɪnkəmˈpliːtnɪs/

Etymology: < incomplete adj. + -ness suffix.

a. The quality or state of being incomplete; want of completeness.

ΘΚΠ

the world > relative properties > wholeness > incompleteness > [noun]

halfness1530

incompleteness1644

partialness1701

partiality1822

fragmentariness1836

partness1925

1644 J. Milton Doctr. Divorce (ed. 2) To Parl. sig. A2 Error..willingly accepts what he wants, and supplies what her incompleatnesse went seeking.

1665 R. Boyle New Exper. & Observ. Cold 74 The incompleteness of the Theory of Cold.

1845 R. C. Trench Fitness Holy Script. i. 10 A book..underlying the same..incompletenesses as every other work of men's hands.

1860 J. Tyndall Glaciers of Alps 33 I had often occasion to feel the incompleteness of my knowledge.

b. spec. in Logic and Mathematics (see incomplete adj. 2b) Also attributive in incompleteness theorem n. the mathematical proof of incompleteness (cf. Gödel n.).

ΘΚΠ

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

incompleteness1932

incompletability1940

incompleteness theorem1955

the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem

pons asinorum1718

Fermat's theorem1845

Bernoulli's theorem1865

Fermat's last theorem1865

Fourier's theorem1880

remainder theorem1886

Stokes' theorem1893

Jordan('s) (curve) theorem1900

Waring's theorem1920

Gödel's theorem1933

maximin1953

incompleteness theorem1955

Schwarz inequality1955

1932 C. I. Lewis & C. H. Langford Symbolic Logic xi. 365 This point of incompleteness can be brought out by contrasting examples.

1937 A. Smeaton tr. R. Carnap Logical Syntax Lang. iii. §34a. 100 In spite of this necessary incompleteness of the method of derivation.., the method retains its fundamental significance.

1955 K. 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.

1957 P. Suppes Introd. to 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.

1962 B. Meltzer tr. K. Gödel 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.

1971 G. Hunter Metalogic 257 This is Gödel's second incompleteness theorem.

This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2021).

单词	incompleteness
释义	incompletenessn. /ɪnkəmˈpliːtnɪs/ Etymology: < incomplete adj. + -ness suffix. a. The quality or state of being incomplete; want of completeness. ΘΚΠ the world > relative properties > wholeness > incompleteness > [noun] halfness1530 incompleteness1644 partialness1701 partiality1822 fragmentariness1836 partness1925 1644 J. Milton Doctr. Divorce (ed. 2) To Parl. sig. A2 Error..willingly accepts what he wants, and supplies what her incompleatnesse went seeking. 1665 R. Boyle New Exper. & Observ. Cold 74 The incompleteness of the Theory of Cold. 1845 R. C. Trench Fitness Holy Script. i. 10 A book..underlying the same..incompletenesses as every other work of men's hands. 1860 J. Tyndall Glaciers of Alps 33 I had often occasion to feel the incompleteness of my knowledge. b. spec. in Logic and Mathematics (see incomplete adj. 2b) Also attributive in incompleteness theorem n. the mathematical proof of incompleteness (cf. Gödel n.). ΘΚΠ the mind > mental capacity > philosophy > mathematical philosophy > [noun] > incompleteness incompleteness1932 incompletability1940 incompleteness theorem1955 the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem pons asinorum1718 Fermat's theorem1845 Bernoulli's theorem1865 Fermat's last theorem1865 Fourier's theorem1880 remainder theorem1886 Stokes' theorem1893 Jordan('s) (curve) theorem1900 Waring's theorem1920 Gödel's theorem1933 maximin1953 incompleteness theorem1955 Schwarz inequality1955 1932 C. I. Lewis & C. H. Langford Symbolic Logic xi. 365 This point of incompleteness can be brought out by contrasting examples. 1937 A. Smeaton tr. R. Carnap Logical Syntax Lang. iii. §34a. 100 In spite of this necessary incompleteness of the method of derivation.., the method retains its fundamental significance. 1955 K. 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. 1957 P. Suppes Introd. to 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. 1962 B. Meltzer tr. K. Gödel 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. 1971 G. Hunter Metalogic 257 This is Gödel's second incompleteness theorem. This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2021). < n.1644
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