16 ideas
10838 | To explain a concept, we need its purpose, not just its rules of usage [Dummett] |
13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
10837 | It is part of the concept of truth that we aim at making true statements [Dummett] |
10840 | We must be able to specify truths in a precise language, like winning moves in a game [Dummett] |
19171 | Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson] |
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] |
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] |
13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
13408 | Intuition and thought-experiments embody substantial information about the world [Papineau] |
10839 | You can't infer a dog's abstract concepts from its behaviour [Dummett] |
13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |