44 ideas
| 6575 | Philosophy may never find foundations, and may undermine our lives in the process [Fogelin] |
| 6585 | Rationality is threatened by fear of inconsistency, illusions of absolutes or relativism, and doubt [Fogelin] |
| 6557 | Humans may never be able to attain a world view which is both rich and consistent [Fogelin] |
| 6568 | A game can be played, despite having inconsistent rules [Fogelin] |
| 6560 | The law of noncontradiction is traditionally the most basic principle of rationality [Fogelin] |
| 6565 | The law of noncontradiction makes the distinction between asserting something and denying it [Fogelin] |
| 6574 | Legal reasoning is analogical, not deductive [Fogelin] |
| 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] |
| 16678 | Without magnitude a thing would retain its parts, but they would have no location [Buridan] |
| 16793 | A thing is (less properly) the same over time if each part is succeeded by another [Buridan] |
| 6582 | Conventions can only work if they are based on something non-conventional [Fogelin] |
| 6576 | My view is 'circumspect rationalism' - that only our intellect can comprehend the world [Fogelin] |
| 6589 | Knowledge is legitimate only if all relevant defeaters have been eliminated [Fogelin] |
| 6596 | For coherentists, circularity is acceptable if the circle is large, rich and coherent [Fogelin] |
| 6597 | A rule of justification might be: don't raise the level of scrutiny without a good reason [Fogelin] |
| 6588 | Scepticism is cartesian (sceptical scenarios), or Humean (future), or Pyrrhonian (suspend belief) [Fogelin] |
| 6590 | Scepticism deals in remote possibilities that are ineliminable and set the standard very high [Fogelin] |
| 6583 | Radical perspectivism replaces Kant's necessary scheme with many different schemes [Fogelin] |
| 16577 | Induction is not demonstration, because not all of the instances can be observed [Buridan] |
| 16576 | Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 6555 | We are also irrational, with a unique ability to believe in bizarre self-created fictions [Fogelin] |
| 6605 | Critics must be causally entangled with their subject matter [Fogelin] |
| 6607 | The word 'beautiful', when deprived of context, is nearly contentless [Fogelin] |
| 6604 | Saying 'It's all a matter to taste' ignores the properties of the object discussed [Fogelin] |
| 6586 | Cynics are committed to morality, but disappointed or disgusted by human failings [Fogelin] |
| 6572 | Deterrence, prevention, rehabilitation and retribution can come into conflict in punishments [Fogelin] |
| 6573 | Retributivists say a crime can be 'paid for'; deterrentists still worry about potential victims [Fogelin] |