28 ideas
5784 | In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell] |
5777 | The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell] |
5783 | Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell] |
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] |
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] |
5780 | The three questions about belief are its contents, its success, and its character [Russell] |
5778 | If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell] |
5779 | There are distinct sets of psychological and physical causal laws [Russell] |
5781 | Our important beliefs all, if put into words, take the form of propositions [Russell] |
5782 | A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell] |
5776 | A proposition is what we believe when we believe truly or falsely [Russell] |
23688 | Noncognitivism tries to avoid both naturalism and mysterious morality [Hacker-Wright] |