17 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] |
| 10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| 10063 | Formalism is a bulwark of logical positivism [Musgrave] |
| 10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
| 6000 | The goal is rationality in the selection of things according to nature [Diogenes of Babylon, by Blank] |
| 5999 | The good is what is perfect by nature [Diogenes of Babylon, by Blank] |
| 6001 | Justice is a disposition to distribute according to desert [Diogenes of Babylon, by Blank] |