43 ideas
| 11147 | Naturalistic philosophers oppose analysis, preferring explanation to a priori intuition [Margolis/Laurence] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 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] |
| 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] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 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] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 8978 | Events are made of other things, and are not fundamental to ontology [Bennett] |
| 11141 | Modern empiricism tends to emphasise psychological connections, not semantic relations [Margolis/Laurence] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 11142 | Body-type seems to affect a mind's cognition and conceptual scheme [Margolis/Laurence] |
| 11121 | Language of thought has subject/predicate form and includes logical devices [Margolis/Laurence] |
| 11120 | Concepts are either representations, or abilities, or Fregean senses [Margolis/Laurence] |
| 11122 | A computer may have propositional attitudes without representations [Margolis/Laurence] |
| 11124 | Do mental representations just lead to a vicious regress of explanations [Margolis/Laurence] |
| 11123 | Maybe the concept CAT is just the ability to discriminate and infer about cats [Margolis/Laurence] |
| 11125 | The abilities view cannot explain the productivity of thought, or mental processes [Margolis/Laurence] |
| 11140 | Concept-structure explains typicality, categories, development, reference and composition [Margolis/Laurence] |
| 11128 | Classically, concepts give necessary and sufficient conditions for falling under them [Margolis/Laurence] |
| 11129 | The classical theory explains acquisition, categorization and reference [Margolis/Laurence] |
| 11130 | Typicality challenges the classical view; we see better fruit-prototypes in apples than in plums [Margolis/Laurence] |
| 11131 | It may be that our concepts (such as 'knowledge') have no definitional structure [Margolis/Laurence] |
| 11134 | People don't just categorise by apparent similarities [Margolis/Laurence] |
| 11136 | Many complex concepts obviously have no prototype [Margolis/Laurence] |
| 11133 | Prototype theory categorises by computing the number of shared constituents [Margolis/Laurence] |
| 11135 | Complex concepts have emergent properties not in the ingredient prototypes [Margolis/Laurence] |
| 11132 | The prototype theory is probabilistic, picking something out if it has sufficient of the properties [Margolis/Laurence] |
| 11137 | The theory theory of concepts says they are parts of theories, defined by their roles [Margolis/Laurence] |
| 11138 | The theory theory is holistic, so how can people have identical concepts? [Margolis/Laurence] |
| 11139 | Maybe concepts have no structure, and determined by relations to the world, not to other concepts [Margolis/Laurence] |
| 11146 | People can formulate new concepts which are only named later [Margolis/Laurence] |
| 10364 | Facts are about the world, not in it, so they can't cause anything [Bennett] |