32 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] |
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] |
17292 | Avoid 'in virtue of' for grounding, since it might imply a reflexive relation such as identity [Audi,P] |
17295 | Ground relations depend on the properties [Audi,P] |
17297 | A ball's being spherical non-causally determines its power to roll [Audi,P] |
17302 | Ground is irreflexive, asymmetric, transitive, non-monotonic etc. [Audi,P] |
17303 | The best critique of grounding says it is actually either identity or elimination [Audi,P] |
17294 | Grounding is a singular relation between worldly facts [Audi,P] |
17300 | If grounding relates facts, properties must be included, as well as objects [Audi,P] |
17296 | We must accept grounding, for our important explanations [Audi,P] |
17301 | Reduction is just identity, so the two things are the same fact, so reduction isn't grounding [Audi,P] |
17293 | Worldly facts are obtaining states of affairs, with constituents; conceptual facts also depend on concepts [Audi,P] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
17298 | Two things being identical (like water and H2O) is not an explanation [Audi,P] |
17299 | There are plenty of examples of non-causal explanation [Audi,P] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |