12 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 18946 | Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer] |
| 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] |
| 21375 | Reason can be vicious, and great crimes have to be rational [Schopenhauer] |
| 21379 | Man's three basic ethical incentives are egoism, malice and compassion [Schopenhauer] |
| 21376 | Philosophy treats animals as exploitable things, ignoring the significance of their lives [Schopenhauer] |