18 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] |
21642 | If quantification is all substitutional, there is no ontology [Quine] |
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] |
10735 | Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach] |
1633 | Absolute ontological questions are meaningless, because the answers are circular definitions [Quine] |
18964 | Ontology is relative to both a background theory and a translation manual [Quine] |
18965 | We know what things are by distinguishing them, so identity is part of ontology [Quine] |
1634 | Two things are relative - the background theory, and translating the object theory into the background theory [Quine] |
10732 | If concepts are just recognitional, then general judgements would be impossible [Geach] |
10731 | For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach] |
10733 | The abstractionist cannot explain 'some' and 'not' [Geach] |
10734 | Only a judgement can distinguish 'striking' from 'being struck' [Geach] |
8470 | Reference is inscrutable, because we cannot choose between theories of numbers [Quine, by Orenstein] |
18963 | Indeterminacy translating 'rabbit' depends on translating individuation terms [Quine] |