Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Gerhard Gentzen and John Richardson

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12 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Metaphysics generalises the data, to get at the ontology [Richardson]
Metaphysics aims at the essence of things, and a system to show how this explains other truths [Richardson]
Metaphysics needs systems, because analysis just obsesses over details [Richardson]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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
The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
The logical connectives are 'defined' by their introduction rules [Gentzen]
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
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
Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
Humans dominate because, unlike other animals, they have a synthesis of conflicting drives [Richardson]
26. Natural Theory / C. Causation / 7. Eliminating causation
A mind that could see cause and effect as a continuum would deny cause and effect [Richardson]