12 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 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] |
| 3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
| 22371 | Determinism threatens free will if actions can be causally traced to external factors [Foot] |
| 22372 | Not all actions need motives, but it is irrational to perform troublesome actions with no motive [Foot] |
| 22373 | People can act out of vanity without being vain, or even vain about this kind of thing [Foot] |