27 ideas
18369 | There are at least fourteen candidates for truth-bearers [Kirkham] |
19318 | A 'sequence' of objects is an order set of them [Kirkham] |
19319 | If one sequence satisfies a sentence, they all do [Kirkham] |
19320 | If we define truth by listing the satisfactions, the supply of predicates must be finite [Kirkham] |
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] |
19315 | In quantified language the components of complex sentences may not be sentences [Kirkham] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
19317 | An open sentence is satisfied if the object possess that property [Kirkham] |
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] |
19322 | Why can there not be disjunctive, conditional and negative facts? [Kirkham] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
20921 | How can we state relativism of sweet and sour, if they have no determinate nature? [Theophrastus] |
5990 | Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk] |