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
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13939
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No possible evidence could decide the reality of numbers, so it is a pseudo-question
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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13936
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Questions about numbers are answered by analysis, and are analytic, and hence logically true
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8748
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Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Shapiro]
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7. Existence / A. Nature of Existence / 4. Abstract Existence
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8960
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Internal questions about abstractions are trivial, and external ones deeply problematic [Szabó]
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7. Existence / D. Theories of Reality / 1. Ontologies
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13933
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Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework)
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7. Existence / D. Theories of Reality / 3. Reality
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13934
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To be 'real' is to be an element of a system, so we cannot ask reality questions about the system itself
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7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
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13938
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A linguistic framework involves commitment to entities, so only commitment to the framework is in question
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9. Objects / A. Existence of Objects / 6. Nihilism about Objects
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13935
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We only accept 'things' within a language with formation, testing and acceptance rules
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12. Knowledge Sources / D. Empiricism / 1. Empiricism
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13932
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Empiricists tend to reject abstract entities, and to feel sympathy with nominalism
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12. Knowledge Sources / D. Empiricism / 3. Pragmatism
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13937
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New linguistic claims about entities are not true or false, but just expedient, fruitful or successful
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14. Science / B. Scientific Theories / 3. Instrumentalism
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13940
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All linguistic forms in science are merely judged by their efficiency as instruments
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