68 ideas
2956 | There is nothing so obvious that a philosopher cannot be found to deny it [Lockwood] |
2963 | There may only be necessary and sufficient conditions (and counterfactuals) because we intervene in the world [Lockwood] |
2958 | No one has ever succeeded in producing an acceptable non-trivial analysis of anything [Lockwood] |
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] |
2959 | If something is described in two different ways, is that two facts, or one fact presented in two ways? [Lockwood] |
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] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
2969 | How does a direct realist distinguish a building from Buckingham Palace? [Lockwood] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
2970 | Dogs seem to have beliefs, and beliefs require concepts [Lockwood] |
2961 | Empiricism is a theory of meaning as well as of knowledge [Lockwood] |
2960 | Commonsense realism must account for the similarity of genuine perceptions and known illusions [Lockwood] |
2952 | A 1988 estimate gave the brain 3 x 10-to-the-14 synaptic junctions [Lockwood] |
2964 | How come unconscious states also cause behaviour? [Lockwood] |
2951 | Could there be unconscious beliefs and desires? [Lockwood] |
2953 | Fish may operate by blindsight [Lockwood] |
2967 | We might even learn some fundamental physics from introspection [Lockwood] |
2966 | Can phenomenal qualities exist unsensed? [Lockwood] |
2955 | If mental events occur in time, then relativity says they are in space [Lockwood] |
2950 | Only logical positivists ever believed behaviourism [Lockwood] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
2954 | Identity theory likes the identity of lightning and electrical discharges [Lockwood] |
16362 | An identity statement aims at getting the hearer to merge two mental files [Lockwood] |
2971 | Perhaps logical positivism showed that there is no dividing line between science and metaphysics [Lockwood] |
4054 | I may exist before I become a person, just as I exist before I become an adult [Lockwood] |
4056 | If the soul is held to leave the body at brain-death, it should arrive at the time of brain-creation [Lockwood] |
4055 | It isn't obviously wicked to destroy a potential human being (e.g. an ununited egg and sperm) [Lockwood] |
2962 | Maybe causation is a form of rational explanation, not an observation or a state of mind [Lockwood] |
2949 | We have the confused idea that time is a process of change [Lockwood] |