27 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] |
| 10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
| 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] |
| 11897 | A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P] |
| 11898 | Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P] |
| 11883 | A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P] |
| 11889 | Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P] |
| 11877 | An individual essence is the properties the object could not exist without [Mackie,P] |
| 11882 | No other object can possibly have the same individual essence as some object [Mackie,P] |
| 11886 | There are problems both with individual essences and without them [Mackie,P] |
| 11909 | Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P] |
| 11899 | Why are any sortals essential, and why are only some of them essential? [Mackie,P] |
| 11906 | The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P] |
| 11894 | Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P] |
| 11887 | Transworld identity without individual essences leads to 'bare identities' [Mackie,P] |
| 11890 | De re modality without bare identities or individual essence needs counterparts [Mackie,P] |
| 11892 | Things may only be counterparts under some particular relation [Mackie,P] |
| 11893 | Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P] |
| 11884 | The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P] |
| 11905 | Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P] |
| 11907 | Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P] |