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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]
| 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] |
| 13936 | Questions about numbers are answered by analysis, and are analytic, and hence logically true [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] |
| 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] |
| 13939 | No possible evidence could decide the reality of numbers, so it is a pseudo-question [Carnap] |
| 13938 | A linguistic framework involves commitment to entities, so only commitment to the framework is in question [Carnap] |
| 13940 | All linguistic forms in science are merely judged by their efficiency as instruments [Carnap] |