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Full Idea
I cannot think of any possible evidence that would be regarded as relevant by both nominalists and realists about numbers, and would decide the controversy, or make one side more probable. Hence I regard the external questions as pseudo-questions.
Gist of Idea
No possible evidence could decide the reality of numbers, so it is a pseudo-question
Source
Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 4)
Book Ref
Carnap,Rudolph: 'Meaning and Necessity (2nd ed)' [Chicago 1988], p.219
| 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] |