15 ideas
| 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] |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| 15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
| 10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| 10063 | Formalism is a bulwark of logical positivism [Musgrave] |
| 10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
| 9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
| 18203 | Avoid non-predicative classifications and definitions [Poincaré] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
| 15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |