18 ideas
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| 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] |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 18033 | The meaning of a representation is its role in thought, perception or decisions [Block] |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |