9 ideas
| 18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
| 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] |
| 19525 | If the only aim is to believe truths, that justifies recklessly believing what is unsupported (if it is right) [Conee/Feldman] |
| 19524 | We don't have the capacity to know all the logical consequences of our beliefs [Conee/Feldman] |