14 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] |
| 23111 | If we say that freedom depends on rationality, the irrational actions are not free [Sidgwick] |
| 23059 | Self-interest is not rational, if the self is just a succession of memories and behaviour [Sidgwick, by Gray] |
| 4129 | It is self-evident (from the point of view of the Universe) that no individual has more importance than another [Sidgwick] |
| 20588 | Sidwick argues for utilitarian institutions, rather than actions [Sidgwick, by Tuckness/Wolf] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 6610 | I believe because it is absurd [Tertullian] |