Combining Philosophers

All the ideas for Phil Dowe, Myles F. Burnyeat and Gerhard Gentzen

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10 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
11022 Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11065 The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
11023 The logical connectives are 'defined' by their introduction rules [Gentzen]
11213 Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13832 Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10067 Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by 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]
26. Natural Theory / C. Causation / 4. Naturalised causation
14586 Physical causation consists in transference of conserved quantities [Dowe, by Mumford/Anjum]
4787 Causation interaction is an exchange of conserved quantities, such as mass, energy or charge [Dowe, by Psillos]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
4788 Dowe commends the Conserved Quantity theory as it avoids mention of counterfactuals [Dowe, by Psillos]