Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Alan Musgrave and Graham Farmelo

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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
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 / 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
10062 Formalism seems to exclude all creative, growing mathematics [Musgrave]
10063 Formalism is a bulwark of logical positivism [Musgrave]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
20653 Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060 Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
21236 Instead of gravitational force, we now have a pervasive gravitational field [Farmelo]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
21235 The Schrödinger waves are just the maths of transforming energy values to positions [Farmelo]
27. Natural Reality / B. Modern Physics / 4. Standard Model / c. Particle properties
21234 Experiments show that fundamental particles of one type are identical [Farmelo]