Combining Philosophers

All the ideas for Prodicus, Menedemus and Gerhard Gentzen

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11 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]

19. Language / F. Communication / 3. Denial

1554	Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind]

23. Ethics / A. Egoism / 1. Ethical Egoism

3031	The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius]

28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique

1555	People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus]

28. God / C. Attitudes to God / 5. Atheism

535	The gods are just personified human benefits [Prodicus]

1543	He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus]