Gödeln.

Brit.

/ˈɡəːdl/, U.S.

/ˈɡədəl/

Forms: 1900s– Gödel, 1900s– Goedel.

Origin: From a proper name. Etymon: proper name Gödel.

Etymology: < the name of Kurt Gödel (1906–78), Austrian logician and mathematician, who published the theorem in 1931 ( Monatshefte f. Math. u. Physik 38 173).The form Goedel reflects the German convention of using oe instead of ö where a suitable letter type is not available.

Logic and Mathematics.

1. Gödel's theorem n. (also Gödel theorem) the demonstration that in any system of axioms there must be formulas which are true but neither provable nor disprovable within the system, thus making mathematics essentially incomplete; (also) the corollary that the consistency of such a system cannot be proved within that system; also called incompleteness theorem (see incompleteness n. b).

ΘΚΠ

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

1933 M. Black Nature of Math. 167 (heading) Note on Gödel's theorem.

1952 S. C. Kleene Introd. Metamath. viii. 204 We designate the first of these theorems, which entails the other as corollary, as ‘Gödel's theorem’.

1964 Philosophy 39 196 Machines could never be selfconscious in the way that human minds are, and..Gödel's theorem illustrates this.

1965 R. L. Wilder Introd. Found. Math. (ed. 2) xi. 275 In some of these systems, analogues of the Gödel theorems have been shown to hold.

1999 A. W. Neumann Should You read Shakespeare? vii. 79 Why do people want The X Files and UFOs when they've got Goedel's theorem, the Riemann conjecture and quantum theory?

2013 P. Smith Introd. Gödel's Theorems (ed. 2) Pref. p. xiii It has also frequently been claimed that Gödel's Theorems have a much wider impact on very general issues about language, truth and the mind.

2. attributive. Derived from or related to Gödel's theorem, esp. in Gödel number, Gödel numbering.

ΚΠ

1936 Jrnl. Symbolic Logic 1 40 A recursively defined function a of two positive integers..is the Gödel representation of the xth formula.

1952 S. C. Kleene Introd. Metamath. viii. 206 We call this a Gödel numbering, and the correlated number of a formal object its Gödel number.

1959 E. Nagel & J. R. Newman (title) Gödel's proof.

1991 J. L. Casti Searching for Certainty (1992) xii. 371 Gödel's Theorem says that there will always exist statements (or Gödel sentences) like G that are eternally doomed to a life in the shadow world of gray.

2009 M. Baaz et al. in H. Ono et al. Logic, Lang., Information & Computation 114 Let V be a Gödel set, we denote the G_V the Gödel logic based on the set of truth values V.

Derivatives

Göˈdelian adj.

Brit.

/ɡəːˈdiːlɪən/

U.S.

/ɡəˈdiliən/

ΘΚΠ

the world > relative properties > number > mathematics > [adjective] > characterized by theories of or approaches to

physico-mathematical1660

analytical1694

Bernoulli1749

analytic1761

Boolean1851

Sturmian1853

Bernoullian1876

Fermatian1887

Grassmannian1894

number-theoretic1899

Cantor1902

Cantorian1912

Tauberian1913

Thiessen1923

intuitionist1926

metamathematical1926

finitist1931

number-theoretical1936

finitistic1937

proof-theoretic1940

formalistic1941

Gödelian1942

constructivist1943

constructivistic1944

game-theoretical1946

game-theoretic1950

finitary1952

perturbation-theoretic1964

perturbation-theoretical1968

constructive1979

1942 Mind 51 259 (title) Goedelian sentences: a non-numerical approach.

1986 G. Johnson Machinery of Mind xv. 282 The mind is a system that can think about itself—perhaps some kind of Gödelian knot is at the heart of it.

2004 M. Potter Set Theory & its Philos. xiii. 220 The Gödelian considerations alluded to earlier tell us that there are sentences in the language of arithmetic..that are provable with the axiom of ordinals but not without.

This entry has been updated (OED Third Edition, June 2014; most recently modified version published online March 2022).

单词	gödel
释义	Gödeln. Brit. /ˈɡəːdl/, U.S. /ˈɡədəl/ Forms: 1900s– Gödel, 1900s– Goedel. Origin: From a proper name. Etymon: proper name Gödel. Etymology: < the name of Kurt Gödel (1906–78), Austrian logician and mathematician, who published the theorem in 1931 ( Monatshefte f. Math. u. Physik 38 173).The form Goedel reflects the German convention of using oe instead of ö where a suitable letter type is not available. Logic and Mathematics. 1. Gödel's theorem n. (also Gödel theorem) the demonstration that in any system of axioms there must be formulas which are true but neither provable nor disprovable within the system, thus making mathematics essentially incomplete; (also) the corollary that the consistency of such a system cannot be proved within that system; also called incompleteness theorem (see incompleteness n. b). ΘΚΠ 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 1933 M. Black Nature of Math. 167 (heading) Note on Gödel's theorem. 1952 S. C. Kleene Introd. Metamath. viii. 204 We designate the first of these theorems, which entails the other as corollary, as ‘Gödel's theorem’. 1964 Philosophy 39 196 Machines could never be selfconscious in the way that human minds are, and..Gödel's theorem illustrates this. 1965 R. L. Wilder Introd. Found. Math. (ed. 2) xi. 275 In some of these systems, analogues of the Gödel theorems have been shown to hold. 1999 A. W. Neumann Should You read Shakespeare? vii. 79 Why do people want The X Files and UFOs when they've got Goedel's theorem, the Riemann conjecture and quantum theory? 2013 P. Smith Introd. Gödel's Theorems (ed. 2) Pref. p. xiii It has also frequently been claimed that Gödel's Theorems have a much wider impact on very general issues about language, truth and the mind. 2. attributive. Derived from or related to Gödel's theorem, esp. in Gödel number, Gödel numbering. ΚΠ 1936 Jrnl. Symbolic Logic 1 40 A recursively defined function a of two positive integers..is the Gödel representation of the xth formula. 1952 S. C. Kleene Introd. Metamath. viii. 206 We call this a Gödel numbering, and the correlated number of a formal object its Gödel number. 1959 E. Nagel & J. R. Newman (title) Gödel's proof. 1991 J. L. Casti Searching for Certainty (1992) xii. 371 Gödel's Theorem says that there will always exist statements (or Gödel sentences) like G that are eternally doomed to a life in the shadow world of gray. 2009 M. Baaz et al. in H. Ono et al. Logic, Lang., Information & Computation 114 Let V be a Gödel set, we denote the G_V the Gödel logic based on the set of truth values V. Derivatives Göˈdelian adj. Brit. /ɡəːˈdiːlɪən/ , U.S. /ɡəˈdiliən/ ΘΚΠ the world > relative properties > number > mathematics > [adjective] > characterized by theories of or approaches to physico-mathematical1660 analytical1694 Bernoulli1749 analytic1761 Boolean1851 Sturmian1853 Bernoullian1876 Fermatian1887 Grassmannian1894 number-theoretic1899 Cantor1902 Cantorian1912 Tauberian1913 Thiessen1923 intuitionist1926 metamathematical1926 finitist1931 number-theoretical1936 finitistic1937 proof-theoretic1940 formalistic1941 Gödelian1942 constructivist1943 constructivistic1944 game-theoretical1946 game-theoretic1950 finitary1952 perturbation-theoretic1964 perturbation-theoretical1968 constructive1979 1942 Mind 51 259 (title) Goedelian sentences: a non-numerical approach. 1986 G. Johnson Machinery of Mind xv. 282 The mind is a system that can think about itself—perhaps some kind of Gödelian knot is at the heart of it. 2004 M. Potter Set Theory & its Philos. xiii. 220 The Gödelian considerations alluded to earlier tell us that there are sentences in the language of arithmetic..that are provable with the axiom of ordinals but not without. This entry has been updated (OED Third Edition, June 2014; most recently modified version published online March 2022). < n.1933
随便看	resinimpregnated resining resinise resinised resinises resinising resinite resinize resinized resinizes resinizing resink resino resino- resino-electric resino-extractive resino-vitreous resinoelectric resinoextractive resinographer resinographic resinographically resinography resinoid resinoid-bonded