15 ideas
| 18261 | A simplification which is complete constitutes a definition [Kant] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
| 13365 | Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell] |
| 10711 | Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell] |
| 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] |
| 9127 | Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen] |
| 18260 | If we knew what we know, we would be astonished [Kant] |
| 7531 | We don't assert private thoughts; the objects are part of what we assert [Russell] |