79 ideas
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| 23000 | Vicious regresses force you to another level; non-vicious imply another level [Baron/Miller] |
| 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] |
| 10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
| 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] |
| 23024 | A traveller takes a copy of a picture into the past, gives it the artist, who then creates the original! [Baron/Miller] |
| 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] |
| 10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
| 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] |
| 10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
| 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] |
| 23008 | Grounding is intended as a relation that fits dependences between things [Baron/Miller] |
| 23018 | How does a changing object retain identity or have incompatible properties over time? [Baron/Miller] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 23011 | Modern accounts of causation involve either processes or counterfactuals [Baron/Miller] |
| 23013 | The main process theory of causation says it is transference of mass, energy, momentum or charge [Baron/Miller] |
| 23014 | If causes are processes, what is causation by omission? (Distinguish legal from scientific causes?) [Baron/Miller] |
| 23015 | The counterfactual theory of causation handles the problem no matter what causes actually are [Baron/Miller] |
| 23016 | Counterfactual theories struggle with pre-emption by a causal back-up system [Baron/Miller] |
| 23009 | There is no second 'law' of thermodynamics; it just reflects probabilities of certain microstates [Baron/Miller] |
| 23002 | In relativity space and time depend on one's motion, but spacetime gives an invariant metric [Baron/Miller] |
| 22988 | The block universe theory says entities of all times exist, and time is the B-series [Baron/Miller] |
| 22991 | How can we know this is the present moment, if other times are real? [Baron/Miller] |
| 22992 | If we are actually in the past then we shouldn't experience time passing [Baron/Miller] |
| 22994 | Erzatz Presentism allows the existence of other times, with only the present 'actualised' [Baron/Miller] |
| 22998 | How do presentists explain relations between things existing at different times? [Baron/Miller] |
| 23017 | Presentism needs endurantism, because other theories imply most of the object doesn't exist [Baron/Miller] |
| 23023 | How can presentists move to the next future moment, if that doesn't exist? [Baron/Miller] |
| 22995 | Most of the sciences depend on the concept of time [Baron/Miller] |
| 22993 | For abstractionists past times might still exist, althought their objects don't [Baron/Miller] |
| 23001 | The error theory of time's passage says it is either a misdescription or a false inference [Baron/Miller] |
| 22999 | It is meaningless to measure the rate of time using time itself, and without a rate there is no flow [Baron/Miller] |
| 22986 | The C-series rejects A and B, and just sees times as order by betweenness, without direction [Baron/Miller] |
| 22996 | The A-series has to treat being past, present or future as properties [Baron/Miller] |
| 23007 | The B-series can have a direction, as long as it does not arise from temporal flow [Baron/Miller] |
| 23003 | Static theories cannot account for time's obvious asymmetry, so time must be dynamic [Baron/Miller] |
| 23004 | The direction of time is either primitive, or reducible to something else [Baron/Miller] |
| 23005 | The kaon does not seem to be time-reversal invariant, unlike the rest of nature [Baron/Miller] |
| 23006 | Maybe the past is just the direction of decreasing entropy [Baron/Miller] |
| 23010 | We could explain time's direction by causation: past is the direction of causes, future of effects [Baron/Miller] |
| 22989 | Static time theory presents change as one property at t1, and a different property at t2 [Baron/Miller] |
| 23020 | If a time traveller kills his youthful grandfather, he both exists and fails to exist [Baron/Miller] |
| 23022 | Presentism means there no existing past for a time traveller to visit [Baron/Miller] |
| 22987 | The past (unlike the future) is fixed, along with truths about it, by the existence of past objects [Baron/Miller] |
| 22990 | The moving spotlight says entities can have properties of being present, past or future [Baron/Miller] |
| 22997 | The present moment is a matter of existence, not of acquiring a property [Baron/Miller] |