15 ideas
| 13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
| 23476 | Logical constants seem to be entities in propositions, but are actually pure form [Russell] |
| 23477 | We use logical notions, so they must be objects - but I don't know what they really are [Russell] |
| 18273 | Logical truths are known by their extreme generality [Russell] |
| 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] |
| 22315 | There can't be a negative of a complex, which is negated by its non-existence [Potter on Russell] |
| 13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
| 13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
| 13408 | Intuition and thought-experiments embody substantial information about the world [Papineau] |
| 13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |