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] |
| 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] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 12732 | Some necessary truths are brute, and others derive from final causes [Leibniz] |
| 19438 | Our large perceptions and appetites are made up tiny unconscious fragments [Leibniz] |
| 19415 | Passions reside in confused perceptions [Leibniz] |
| 12165 | Romantics say music expresses ideas, or the Will, or intuitions, or feelings [Scruton] |
| 12164 | Expressing melancholy is a good thing, but arousing it is a bad thing [Scruton] |
| 19439 | God produces possibilities, and thus ideas [Leibniz] |