12 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] |
| 21731 | Fields can be 'scalar', or 'vector', or 'tensor', or 'spinor' [Baggott] |
| 21730 | A 'field' is a property with a magnitude, distributed across all of space and time [Baggott] |
| 21732 | The current standard model requires 61 particles [Baggott] |
| 6011 | There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara] |