12 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 21222 | Logicians presuppose a world, and ignore logic/world connections, so their logic is impure [Husserl, by Velarde-Mayol] |
| 21223 | Phenomenology grounds logic in subjective experience [Husserl, by Velarde-Mayol] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| 21224 | Pure mathematics is the relations between all possible objects, and is thus formal ontology [Husserl, by Velarde-Mayol] |
| 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] |