15 ideas
| 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] |
| 21695 | The set scheme discredited by paradoxes is actually the most natural one [Quine] |
| 21693 | Russell's antinomy challenged the idea that any condition can produce a set [Quine] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| 21691 | Antinomies contradict accepted ways of reasoning, and demand revisions [Quine] |
| 21690 | Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine] |
| 21689 | A barber shaves only those who do not shave themselves. So does he shave himself? [Quine] |
| 21694 | Membership conditions which involve membership and non-membership are paradoxical [Quine] |
| 21692 | If we write it as '"this sentence is false" is false', there is no paradox [Quine] |
| 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] |
| 6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
| 6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |