Ideas from 'Empiricism, Semantics and Ontology' by Rudolph Carnap [1950], by Theme Structure

[found in 'Meaning and Necessity (2nd ed)' by Carnap,Rudolph [Chicago 1988,0-226-09347-6]].

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1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
No possible evidence could decide the reality of numbers, so it is a pseudo-question
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Shapiro]
Questions about numbers are answered by analysis, and are analytic, and hence logically true
7. Existence / A. Nature of Existence / 1. Nature of Existence
Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework)
7. Existence / A. Nature of Existence / 4. Abstract Existence
Internal questions about abstractions are trivial, and external ones deeply problematic [Szabó]
7. Existence / D. Theories of Reality / 2. Reality
To be 'real' is to be an element of a system, so we cannot ask reality questions about the system itself
7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
A linguistic framework involves commitment to entities, so only commitment to the framework is in question
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
We only accept 'things' within a language with formation, testing and acceptance rules
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Empiricists tend to reject abstract entities, and to feel sympathy with nominalism
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
New linguistic claims about entities are not true or false, but just expedient, fruitful or successful
14. Science / B. Scientific Theories / 3. Instrumentalism
All linguistic forms in science are merely judged by their efficiency as instruments