18 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] |
| 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] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 14193 | 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA] |
| 14195 | If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA] |
| 14196 | Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA] |
| 14198 | Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA] |
| 14190 | Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA] |
| 14191 | Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA] |
| 14192 | Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA] |
| 14197 | An object's modal properties don't determine its possibilities [Paul,LA] |
| 14189 | 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA] |
| 20581 | If men are born free, are women born slaves? [Astell] |