11 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] |
| 13745 | Supervenience is not a dependence relation, on the lines of causal, mereological or semantic dependence [Kim] |
| 13746 | Supervenience is just a 'surface' relation of pattern covariation, which still needs deeper explanation [Kim] |
| 19347 | Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins] |