Combining Philosophers

All the ideas for Aeschylus, Gerhard Gentzen and William Davies

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12 ideas

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]
24. Political Theory / D. Ideologies / 11. Capitalism
Markets are transparent, with known prices and activity, and minimal profits [Davies,W]
Capitalists use their exceptional power to impose their own rules, and make the state their ally [Davies,W]
Economies have material, economic and capitalist layers [Davies,W]
Capitalism must mainly rely either on the labour market, or on the financial markets [Davies,W]
Capitalism is the anti-market, with opacity, monopolies, powers, exceptional profits and wealth [Davies,W]
25. Social Practice / D. Justice / 2. The Law / b. Rule of law
The 'Eumenides' of Aeschylus shows blood feuds replaced by law [Aeschylus, by Grayling]