41 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] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
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] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
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] |
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] |
20429 | Most of us are too close to our own motives to understand them [Fry] |
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] |
20424 | Imaginative life requires no action, so new kinds of perception and values emerge in art [Fry] |
20427 | Everyone reveals an aesthetic attitude, looking at something which only exists to be seen [Fry] |
20433 | 'Beauty' can either mean sensuous charm, or the aesthetic approval of art (which may be ugly) [Fry] |
20430 | In life we neglect 'cosmic emotion', but it matters, and art brings it to the fore [Fry] |
20431 | Art needs a mixture of order and variety in its sensations [Fry] |
20423 | If graphic arts only aim at imitation, their works are only trivial ingenious toys [Fry] |
20428 | Popular opinion favours realism, yet most people never look closely at anything! [Fry] |
20432 | When viewing art, rather than flowers, we are aware of purpose, and sympathy with its creator [Fry] |
20425 | In the cinema the emotions are weaker, but much clearer than in ordinary life [Fry] |
20426 | For pure moralists art must promote right action, and not just be harmless [Fry] |