38 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] |
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| 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] |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| 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] |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| 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] |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| 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] |
| 12131 | All concepts can be derived from a few basics, making possible one science of everything [Carnap, by Brody] |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| 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] |