Combining Philosophers

All the ideas for Myles F. Burnyeat, Alan Musgrave and Donald C. Williams

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12 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
10065 Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10050 A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
10049 Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
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 / 7. Formalism
10063 Formalism is a bulwark of logical positivism [Musgrave]
10062 Formalism seems to exclude all creative, growing mathematics [Musgrave]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
8508 A 'trope' is an abstract particular, the occurrence of an essence [Williams,DC]
8509 A world is completely constituted by its tropes and their connections [Williams,DC]
8510 'Socrates is wise' means a concurrence sum contains a member of a similarity set [Williams,DC]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060 Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
4377 Intellectualism is an excessive emphasis on reasoning in moral philosophy [Burnyeat]