31 ideas
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
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] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
3157 | T.H.Huxley gave the earliest clear statement of epiphenomenalism [Huxley, by Rey] |
3154 | Brain causes mind, but it doesn't seem that mind causes actions [Huxley] |