14 ideas
| 12302 | Definitions formed an abstract hierarchy for Aristotle, as sets do for us [Fine,K] |
| 14266 | Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets) [Fine,K] |
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
| 10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
| 10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
| 10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
| 10063 | Formalism is a bulwark of logical positivism [Musgrave] |
| 10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
| 14268 | Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K] |
| 14267 | There is no distinctive idea of constitution, because you can't say constitution begins and ends [Fine,K] |
| 14264 | Is there a plausible Aristotelian notion of constitution, applicable to both physical and non-physical? [Fine,K] |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
| 14265 | The components of abstract definitions could play the same role as matter for physical objects [Fine,K] |