15 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] |
| 15148 | Powers give explanations, without being necessary for some class membership [Chakravartty] |
| 15145 | A kind essence is the necessary and sufficient properties for membership of a class [Chakravartty] |
| 15147 | Cluster kinds are explained simply by sharing some properties, not by an 'essence' [Chakravartty] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 15144 | Explanation of causal phenomena concerns essential kinds - but also lack of them [Chakravartty] |
| 15146 | Some kinds, such as electrons, have essences, but 'cluster kinds' do not [Chakravartty] |
| 15151 | Many causal laws do not refer to kinds, but only to properties [Chakravartty] |