34 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] |
4033 | Two pure spheres in non-absolute space are identical but indiscernible [Campbell,K] |
3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |
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] |