13 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
| 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] |
| 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] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
| 10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
| 594 | Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle] |
| 2632 | Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero] |