16 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] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 6237 | Fear of God is not conscience, which is a natural feeling of offence at bad behaviour [Shaftesbury] |
| 6234 | If an irrational creature with kind feelings was suddenly given reason, its reason would approve of kind feelings [Shaftesbury] |
| 6233 | A person isn't good if only tying their hands prevents their mischief, so the affections decide a person's morality [Shaftesbury] |
| 6236 | People more obviously enjoy social pleasures than they do eating and drinking [Shaftesbury] |
| 6235 | Self-interest is not intrinsically good, but its absence is evil, as public good needs it [Shaftesbury] |
| 6232 | Every creature has a right and a wrong state which guide its actions, so there must be a natural end [Shaftesbury] |
| 5642 | For Shaftesbury, we must already have a conscience to be motivated to religious obedience [Shaftesbury, by Scruton] |