16 ideas
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
7413 | Without confidence in our beliefs, how should we actually live? [Tuck] |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |