10 ideas
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
10670 | A 'singulariser' converts a plural like 'number of' to a syntactically neutral form [Cartwright,H, by Hossack] |
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] |
18424 | If two people can have phenomenally identical experiences, they can't involve the self [Brogaard] |