32 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] |
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] |
17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
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] |
17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
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] |
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] |