Ideas of Charles Parsons, by Theme

[American, fl. 1980, Professor at Columbia University, then Harvard University.]

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4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
Modal logic is not an extensional language
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The old problems with the axiom of choice are probably better ascribed to the law of excluded middle
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true
Substitutional existential quantifier may explain the existence of linguistic entities
6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
General principles can be obvious in mathematics, but bold speculations in empirical science
6. Mathematics / C. Sources of Mathematics / 8. Finitism
If functions are transfinite objects, finitists can have no conception of them
7. Existence / D. Theories of Reality / 10. Ontological Commitment / e. Ontological commitment problems
If a mathematical structure is rejected from a physical theory, it retains its mathematical status