15 ideas
2676 | Didactic argument starts from the principles of the subject, not from the opinions of the learner [Aristotle] |
2675 | Reasoning is a way of making statements which makes them lead on to other statements [Aristotle] |
2677 | Dialectic aims to start from generally accepted opinions, and lead to a contradiction [Aristotle] |
2674 | Competitive argument aims at refutation, fallacy, paradox, solecism or repetition [Aristotle] |
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] |
16967 | 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
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] |
3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
16149 | Generic terms like 'man' are not substances, but qualities, relations, modes or some such thing [Aristotle] |
11840 | Only if two things are identical do they have the same attributes [Aristotle] |
3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |