19 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] |
| 14329 | Some dispositional properties (such as mental ones) may have no categorical base [Price,HH] |
| 9032 | Before we can abstract from an instance of violet, we must first recognise it [Price,HH] |
| 9035 | If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH] |
| 9034 | There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH] |
| 9036 | There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH] |
| 9037 | Intelligent behaviour, even in animals, has something abstract about it [Price,HH] |
| 9033 | Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH] |
| 9030 | Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH] |
| 9029 | If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH] |
| 9031 | The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH] |
| 22307 | Propositions don't name facts, because two opposed propositions can match one fact [Russell] |