60 ideas
| 1798 | He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius] |
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| 1800 | Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, by Diog. Laertius] |
| 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] |
| 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] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 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] |
| 19691 | Unlike knowledge, you can achieve understanding through luck [Grimm] |
| 19690 | 'Grasping' a structure seems to be modal, because we must anticipate its behaviour [Grimm] |
| 19692 | You may have 'weak' understanding, if by luck you can answer a set of 'why questions' [Grimm] |
| 6595 | If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin] |
| 6593 | The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin] |
| 6592 | Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin] |
| 1808 | Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius] |
| 1802 | Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius] |
| 1807 | Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius] |
| 1801 | Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius] |
| 1805 | Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius] |
| 1809 | Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius] |
| 1806 | Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius] |
| 1804 | Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius] |
| 1810 | Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius] |
| 1803 | Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 3062 | There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius] |
| 3063 | Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius] |