36 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] |
18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
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] |
20339 | Classes rarely share properties with their members - unlike universals and types [Wollheim] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
20338 | We often treat a type as if it were a sort of token [Wollheim] |
20342 | Interpretation is performance for some arts, and critical for all arts [Wollheim] |
20343 | A love of nature must precede a love of art [Wollheim] |
20348 | A criterion of identity for works of art would be easier than a definition [Wollheim] |
20347 | If beauty needs organisation, then totally simple things can't be beautiful [Wollheim] |
20345 | Some say art must have verbalisable expression, and others say the opposite! [Wollheim] |
20331 | It is claimed that the expressive properties of artworks are non-physical [Wollheim] |
20336 | Style can't be seen directly within a work, but appreciation needs a grasp of style [Wollheim] |
20337 | The traditional view is that knowledge of its genre to essential to appreciating literature [Wollheim] |
20333 | If artworks are not physical objects, they are either ideal entities, or collections of phenomena [Wollheim] |
20334 | The ideal theory says art is an intuition, shaped by a particular process, and presented in public [Wollheim] |
20335 | The ideal theory of art neglects both the audience and the medium employed [Wollheim] |
20340 | A musical performance has virtually the same features as the piece of music [Wollheim] |
20341 | An interpretation adds further properties to the generic piece of music [Wollheim] |
20332 | A drawing only represents Napoleon if the artist intended it to [Wollheim] |