35 ideas
| 22338 | An unexamined life can be virtuous [Murdoch] |
| 22337 | Philosophy must keep returning to the beginning [Murdoch] |
| 23563 | Philosophy moves continually between elaborate theories and the obvious facts [Murdoch] |
| 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] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 22341 | Literature is the most important aspect of culture, because it teaches understanding of living [Murdoch] |
| 22347 | Appreciating beauty in art or nature opens up the good life, by restricting selfishness [Murdoch] |
| 22339 | Love is a central concept in morals [Murdoch] |
| 22348 | Ordinary human love is good evidence of transcendent goodness [Murdoch] |
| 22343 | If I attend properly I will have no choices [Murdoch] |
| 22349 | Art trains us in the love of virtue [Murdoch] |
| 22340 | It is hard to learn goodness from others, because their virtues are part of their personal history [Murdoch] |
| 22350 | Only trivial virtues can be possessed on their own [Murdoch] |
| 22346 | Moral reflection and experience gradually reveals unity in the moral world [Murdoch] |
| 22342 | Kantian existentialists care greatly for reasons for action, whereas Surrealists care nothing [Murdoch] |
| 22351 | Only a philosopher might think choices create values [Murdoch] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| 22345 | Moral philosophy needs a central concept with all the traditional attributes of God [Murdoch] |