31 ideas
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
16951 | It was realised that possible worlds covered all modal logics, if they had a structure [Dummett] |
16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett] |
16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
16960 | If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett] |
16958 | In S4 the actual world has a special place [Dummett] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
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] |
10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
16957 | Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett] |
16959 | If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett] |
16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
16954 | Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett] |