39 ideas
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 8525 | Relations need terms, so they must be second-order entities based on first-order tropes [Campbell,K] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 8518 | Events are trope-sequences, in which tropes replace one another [Campbell,K] |
| 8513 | Two red cloths are separate instances of redness, because you can dye one of them blue [Campbell,K] |
| 8514 | Red could only recur in a variety of objects if it was many, which makes them particulars [Campbell,K] |
| 8522 | Tropes solve the Companionship Difficulty, since the resemblance is only between abstract particulars [Campbell,K] |
| 8523 | Tropes solve the Imperfect Community problem, as they can only resemble in one respect [Campbell,K] |
| 8524 | Trope theory makes space central to reality, as tropes must have a shape and size [Campbell,K] |
| 8521 | Nominalism has the problem that without humans nothing would resemble anything else [Campbell,K] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 8515 | Tropes are basic particulars, so concrete particulars are collections of co-located tropes [Campbell,K] |
| 8519 | Bundles must be unique, so the Identity of Indiscernibles is a necessity - which it isn't! [Campbell,K] |
| 13437 | A CAR and its major PART can become identical, yet seem to have different properties [Gallois] |
| 16233 | Gallois hoped to clarify identity through time, but seems to make talk of it impossible [Hawley on Gallois] |
| 16025 | If things change they become different - but then no one thing undergoes the change! [Gallois] |
| 16026 | 4D: time is space-like; a thing is its history; past and future are real; or things extend in time [Gallois] |
| 14755 | Gallois is committed to identity with respect to times, and denial of simple identity [Gallois, by Sider] |
| 16231 | Occasional Identity: two objects can be identical at one time, and different at others [Gallois, by Hawley] |
| 16027 | If two things are equal, each side involves a necessity, so the equality is necessary [Gallois] |
| 4033 | Two pure spheres in non-absolute space are identical but indiscernible [Campbell,K] |
| 8512 | Abstractions come before the mind by concentrating on a part of what is presented [Campbell,K] |
| 8517 | Causal conditions are particular abstract instances of properties, which makes them tropes [Campbell,K] |
| 8516 | Davidson can't explain causation entirely by events, because conditions are also involved [Campbell,K] |