24 ideas
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
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] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
8337 | Some says mental causation is distinct because we can recognise single occurrences [Mackie] |
8342 | Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie] |
8343 | Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie] |
8385 | A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane] |
8335 | Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie] |
8336 | The INUS account interprets single events, and sequences, causally, without laws being known [Mackie] |
8333 | A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie] |
8395 | Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley] |
8334 | The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie] |