13 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 10196 | The Axiom of Choice needs a criterion of choice [Black] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| 6303 | Sets are positions in patterns [Resnik] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| 10194 | Two things can only be distinguished by a distinct property or a distinct relation [Black] |
| 10193 | The 'property' of self-identity is uselessly tautological [Black] |
| 10195 | If the universe just held two indiscernibles spheres, that refutes the Identity of Indiscernibles [Black] |
| 20363 | Leaves are unequal, but we form the concept 'leaf' by discarding their individual differences [Nietzsche] |