Combining Philosophers

All the ideas for Charles Parsons, Noam Chomsky and Alan Musgrave

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20 ideas

2. Reason / F. Fallacies / 8. Category Mistake / c. Category mistake as semantic
18009 Chomsky established the view that category mistakes are well-formed but meaningless [Chomsky, by Magidor]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9470 Modal logic is not an extensional language [Parsons,C]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13418 The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10065 Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9469 Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
9468 On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10049 Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
10050 A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
10058 No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
18201 General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
10063 Formalism is a bulwark of logical positivism [Musgrave]
10062 Formalism seems to exclude all creative, growing mathematics [Musgrave]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
13419 If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
13417 If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
6649 Chomsky now says concepts are basically innate, as well as syntax [Chomsky, by Lowe]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060 Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
19. Language / C. Assigning Meanings / 1. Syntax
18007 Syntax is independent of semantics; sentences can be well formed but meaningless [Chomsky, by Magidor]
18006 Chomsky's 'interpretative semantics' says syntax comes first, and is then interpreted [Chomsky, by Magidor]