38 ideas
| 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] |
| 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] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 22167 | Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas] |
| 22117 | Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews] |
| 23805 | Some explanations offer to explain a mystery by a greater mystery [Schulte] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 23806 | Naturalist accounts of representation must match the views of cognitive science [Schulte] |
| 23793 | On the whole, referential content is seen as broad, and sense content as narrow [Schulte] |
| 23796 | Naturalists must explain both representation, and what is represented [Schulte] |
| 23792 | Phenomenal and representational character may have links, or even be united [Schulte] |
| 23795 | Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte] |
| 23804 | Maybe we can explain mental content in terms of phenomenal properties [Schulte] |
| 23802 | Conceptual role semantics says content is determined by cognitive role [Schulte] |
| 23797 | Cause won't explain content, because one cause can produce several contents [Schulte] |
| 23799 | Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte] |
| 23800 | Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte] |
| 23798 | Information theories say content is information, such as smoke making fire probable [Schulte] |
| 22118 | Augustine created the modern concept of the will [Augustine, by Matthews] |
| 4348 | Love, and do what you will [Augustine] |
| 7821 | Pagans produced three hundred definitions of the highest good [Augustine, by Grayling] |
| 22119 | Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews] |
| 22116 | Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews] |
| 19338 | Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins] |