57 ideas
7973 | There is no longer anything on which there is nothing to say [Baudrillard] |
6841 | Some continental philosophers are relativists - Baudrillard, for example [Baudrillard, by Critchley] |
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
7975 | The task of philosophy is to unmask the illusion of objective reality [Baudrillard] |
7986 | Drunken boat pilots are less likely to collide than clearly focused ones [Baudrillard] |
7982 | Instead of thesis and antithesis leading to synthesis, they now cancel out, and the conflict is levelled [Baudrillard] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
7974 | Without God we faced reality: what do we face without reality? [Baudrillard] |
7987 | Nothing is true, but everything is exact [Baudrillard] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
7978 | There is no need to involve the idea of free will to make choices about one's life [Baudrillard] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
7980 | In modern times, being useless is the essential aesthetic ingredient for an object [Baudrillard] |
7983 | Good versus evil has been banefully reduced to happiness versus misfortune [Baudrillard] |
7981 | Whole populations are terrorist threats to authorities, who unite against them [Baudrillard] |
7976 | People like democracy because it means they can avoid power [Baudrillard] |
7977 | Only in the last 200 years have people demanded the democratic privilege of being individuals [Baudrillard] |
7979 | The arrival of the news media brought history to an end [Baudrillard] |
7984 | Suicide is ascribed to depression, with the originality of the act of will ignored [Baudrillard] |
7985 | Pascal says secular life is acceptable, but more fun with the hypothesis of God [Baudrillard] |