Combining Philosophers

All the ideas for Hermarchus, Alan Musgrave and Stephen P. Schwartz

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13 ideas

2. Reason / D. Definition / 1. Definitions
The new view is that "water" is a name, and has no definition [Schwartz,SP]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP]
The traditional theory of names says some of the descriptions must be correct [Schwartz,SP]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is a bulwark of logical positivism [Musgrave]
Formalism seems to exclude all creative, growing mathematics [Musgrave]
18. Thought / C. Content / 8. Intension
The intension of "lemon" is the conjunction of properties associated with it [Schwartz,SP]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
25. Social Practice / F. Life Issues / 6. Animal Rights
Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]