27 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] |
10397 | Abelard's mereology involves privileged and natural divisions, and principal parts [Abelard, by King,P] |
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] |
10395 | Abelard was an irrealist about virtually everything apart from concrete individuals [Abelard, by King,P] |
10396 | If 'animal' is wholly present in Socrates and an ass, then 'animal' is rational and irrational [Abelard, by King,P] |
15384 | Only words can be 'predicated of many'; the universality is just in its mode of signifying [Abelard, by Panaccio] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
8481 | The de dicto-de re modality distinction dates back to Abelard [Abelard, by Orenstein] |
15385 | Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard] |
15383 | Nothing external can truly be predicated of an object [Abelard, by Panaccio] |
23996 | Akrasia is intelligible in hindsight, when we revisit our previous emotions [Blackburn] |
10398 | Natural kinds are not special; they are just well-defined resemblance collections [Abelard, by King,P] |