Combining Philosophers

All the ideas for Archimedes, Terence Horgan and Alan Musgrave

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15 ideas

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 / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
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 / C. Structure of Existence / 5. Supervenience / b. Types of supervenience
'Superdupervenience' is supervenience that has a robustly materialistic explanation [Horgan,T]
'Global' supervenience is facts tracking varying physical facts in every possible world [Horgan,T]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
Don't just observe supervenience - explain it! [Horgan,T]
7. Existence / D. Theories of Reality / 6. Physicalism
Physicalism needs more than global supervenience on the physical [Horgan,T]
Materialism requires that physics be causally complete [Horgan,T]
14. Science / B. Scientific Theories / 3. Instrumentalism
Instrumentalism normally says some discourse is useful, but not genuinely true [Horgan,T]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]