25 ideas
10153 | In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski] |
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
19141 | Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
10048 | There is no clear boundary between the logical and the non-logical [Tarski] |
10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
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] |
10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
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] |
7566 | The Identity of Indiscernibles is really the same as the verification principle [Jolley] |