21 ideas
13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
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] |
10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
10635 | Second-order quantification and plural quantification are different [Linnebo] |
10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
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] |
10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
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] |
13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |