31 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] |
17867 | If a concept is not compact, it will not be presentable to finite minds [Almog] |
17877 | The number series is primitive, not the result of some set theoretic axioms [Almog] |
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] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
17871 | Fregean meanings are analogous to conceptual essence, defining a kind [Almog] |
17866 | Essential definition aims at existence conditions and structural truths [Almog] |
17868 | Surface accounts aren't exhaustive as they always allow unintended twin cases [Almog] |
17872 | Definitionalists rely on snapshot-concepts, instead of on the real processes [Almog] |
17870 | Alien 'tigers' can't be tigers if they are not related to our tigers [Almog] |
17869 | Kripke and Putnam offer an intermediary between real and nominal essences [Almog] |
17876 | Individual essences are just cobbled together classificatory predicates [Almog] |
14366 | An explanation is a table of statistical information [Salmon, by Strevens] |
17873 | Water must be related to water, just as tigers must be related to tigers [Almog] |
17864 | Defining an essence comes no where near giving a thing's nature [Almog] |
17863 | Essences promise to reveal reality, but actually drive us away from it [Almog] |