13 ideas
| 17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| 15533 | We can quantify over fictions by quantifying for real over their names [Lewis] |
| 15534 | We could quantify over impossible objects - as bundles of properties [Lewis] |
| 10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
| 10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [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] |
| 15532 | 'Allists' embrace the existence of all controversial entities; 'noneists' reject all but the obvious ones [Lewis] |
| 15535 | We can't accept a use of 'existence' that says only some of the things there are actually exist [Lewis] |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |