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Single Idea 13936

[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism ]

Full Idea

For the internal question like 'is there a prime number greater than a hundred?' the answers are found by logical analysis based on the rules for the new expressions. The answers here are analytic, i.e., logically true.

Clarification

See Idea 13933 for 'internal' questions

Gist of Idea

Questions about numbers are answered by analysis, and are analytic, and hence logically true

Source

Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2)

Book Ref

Carnap,Rudolph: 'Meaning and Necessity (2nd ed)' [Chicago 1988], p.209

Related Ideas

Idea 13933 Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework) [Carnap]

Idea 13236 Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall]

Idea 12521 We can only know a thing's powers when we have combined it with many things [Locke]

The 20 ideas from Rudolph Carnap

16252 Metaphysics uses empty words, or just produces pseudo-statements [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]
13932 Empiricists tend to reject abstract entities, and to feel sympathy with nominalism [Carnap]
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]
13936 Questions about numbers are answered by analysis, and are analytic, and hence logically true [Carnap]
13935 We only accept 'things' within a language with formation, testing and acceptance rules [Carnap]
13937 New linguistic claims about entities are not true or false, but just expedient, fruitful or successful [Carnap]
13938 A linguistic framework involves commitment to entities, so only commitment to the framework is in question [Carnap]
13939 No possible evidence could decide the reality of numbers, so it is a pseudo-question [Carnap]
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]
18699 Carnap tried to define all scientific predicates in terms of primitive relations, using type theory [Carnap, by Button]
13251 Each person is free to build their own logic, just by specifying a syntax [Carnap]
13342 Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap]
11968 The intension of a sentence is the set of all possible worlds in which it is true [Carnap, by Kaplan]
14305 In the truth-functional account a burnt-up match was soluble because it never entered water [Carnap]
18285 All translation loses some content (but language does not create reality) [Carnap]