13 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] |
| 8510 | 'Socrates is wise' means a concurrence sum contains a member of a similarity set [Williams,DC] |
| 8508 | A 'trope' is an abstract particular, the occurrence of an essence [Williams,DC] |
| 8509 | A world is completely constituted by its tropes and their connections [Williams,DC] |
| 12719 | Clearly, force is that from which action follows, when unimpeded [Leibniz] |
| 12720 | Time doesn't exist, since its parts don't coexist [Leibniz] |