17 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
| 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] |
| 17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
| 17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
| 10369 | How fine-grained Kim's events are depends on how finely properties are individuated [Kim, by Schaffer,J] |
| 8976 | If events are ordered triples of items, such things seem to be sets, and hence abstract [Simons on Kim] |
| 8975 | Events cannot be merely ordered triples, but must specify the link between the elements [Kim, by Simons] |
| 8974 | Events are composed of an object with an attribute at a time [Kim, by Simons] |
| 8977 | Since properties like self-identity and being 2+2=4 are timeless, Kim must restrict his properties [Simons on Kim] |
| 8980 | Kim's theory results in too many events [Simons on Kim] |