Combining Philosophers

All the ideas for Antoine Arnauld, Gottlob Schulze and Alan Musgrave

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10 ideas

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
No one can conceive of a possible substance, apart from those which God has created [Arnauld]
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 / 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 seems to exclude all creative, growing mathematics [Musgrave]
Formalism is a bulwark of logical positivism [Musgrave]
7. Existence / D. Theories of Reality / 2. Realism
Consciousness is not entirely representational, because there are pains, and the self [Schulze, by Pinkard]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]