29 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] |
18253 | I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege] |
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] |
18166 | The loss of my Rule V seems to make foundations for arithmetic impossible [Frege] |
17954 | Essence is a thing's necessities, but what about its possibilities (which may not be realised)? [Vetter] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
18269 | Logical objects are extensions of concepts, or ranges of values of functions [Frege] |
17953 | Real definition fits abstracta, but not individual concrete objects like Socrates [Vetter] |
17952 | Modal accounts make essence less mysterious, by basing them on the clearer necessity [Vetter] |
17959 | Metaphysical necessity is even more deeply empirical than Kripke has argued [Vetter] |
17955 | Possible worlds allow us to talk about degrees of possibility [Vetter] |
17957 | Maybe possibility is constituted by potentiality [Vetter] |
17958 | The apparently metaphysically possible may only be epistemically possible [Vetter] |
17956 | Closeness of worlds should be determined by the intrinsic nature of relevant objects [Vetter] |