15 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 14263 | Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value [Fine,K] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| 23026 | We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz] |
| 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] |
| 14262 | Formal grounding needs transitivity of grounding, no self-grounding, and the existence of both parties [Fine,K] |
| 13189 | A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz] |
| 19432 | Intelligible truth is independent of any external things or experiences [Leibniz] |
| 19430 | We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz] |
| 19431 | There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz] |