39 ideas
| 13939 | No possible evidence could decide the reality of numbers, so it is a pseudo-question [Carnap] |
| 16252 | Metaphysics uses empty words, or just produces pseudo-statements [Carnap] |
| 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] |
| 13342 | Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap] |
| 13251 | Each person is free to build their own logic, just by specifying a syntax [Carnap] |
| 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] |
| 13936 | Questions about numbers are answered by analysis, and are analytic, and hence logically true [Carnap] |
| 8748 | Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Carnap, by Shapiro] |
| 8960 | Internal questions about abstractions are trivial, and external ones deeply problematic [Carnap, by Szabó] |
| 13933 | Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework) [Carnap] |
| 13934 | To be 'real' is to be an element of a system, so we cannot ask reality questions about the system itself [Carnap] |
| 13938 | A linguistic framework involves commitment to entities, so only commitment to the framework is in question [Carnap] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 13935 | We only accept 'things' within a language with formation, testing and acceptance rules [Carnap] |
| 14305 | In the truth-functional account a burnt-up match was soluble because it never entered water [Carnap] |
| 13932 | Empiricists tend to reject abstract entities, and to feel sympathy with nominalism [Carnap] |
| 13937 | New linguistic claims about entities are not true or false, but just expedient, fruitful or successful [Carnap] |
| 18699 | Carnap tried to define all scientific predicates in terms of primitive relations, using type theory [Carnap, by Button] |
| 13940 | All linguistic forms in science are merely judged by their efficiency as instruments [Carnap] |
| 13048 | Good explications are exact, fruitful, simple and similar to the explicandum [Carnap, by Salmon] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 12131 | All concepts can be derived from a few basics, making possible one science of everything [Carnap, by Brody] |
| 11968 | The intension of a sentence is the set of all possible worlds in which it is true [Carnap, by Kaplan] |
| 18285 | All translation loses some content (but language does not create reality) [Carnap] |