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] |
| 16078 | Clay is intrinsically and atomically the same as statue (and that lacks 'modal properties') [Rudder Baker] |
| 16077 | The clay is not a statue - it borrows that property from the statue it constitutes [Rudder Baker] |
| 16080 | Is it possible for two things that are identical to become two separate things? [Rudder Baker] |
| 16076 | Constitution is not identity, as consideration of essential predicates shows [Rudder Baker] |
| 16081 | The constitution view gives a unified account of the relation of persons/bodies, statues/bronze etc [Rudder Baker] |
| 16082 | Statues essentially have relational properties lacked by lumps [Rudder Baker] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |