Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Benjamin Franklin and Gerhard Gentzen

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9 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]
	Full Idea: Gentzen introduced a natural deduction calculus (NK) in 1934.
	From: report of Gerhard Gentzen (works [1938]) by Stephen Read - Thinking About Logic Ch.8

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]
	Full Idea: Gentzen argued that the inferential role of a logical constant constitutes its meaning.
	From: report of Gerhard Gentzen (works [1938]) by Robert Hanna - Rationality and Logic 5.3
	A reaction: Possibly inspired by Wittgenstein's theory of meaning as use? This idea was the target of Prior's famous connective 'tonk', which has the role of implying anything you like, proving sentences which are not logical consequences.

11023	The logical connectives are 'defined' by their introduction rules [Gentzen]
	Full Idea: The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions.
	From: Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8
	A reaction: If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here?

11213	Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
	Full Idea: To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these.
	From: Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III
	A reaction: [1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives.

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]
	Full Idea: Gentzen thought that his natural deduction gets at the heart of logical reasoning, and used the sequent calculus only as a convenient tool for proving his chief results.
	From: report of Gerhard Gentzen (Investigations into Logical Deduction [1935]) by Ian Hacking - What is Logic? §05

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]
	Full Idea: Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic.
	From: report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5
	A reaction: This does not contradict Gödel's famous result, but reinforces it. The interesting question is what assumptions Gentzen felt he had to make.

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]
	Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles.
	From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro'
	A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture?

23. Ethics / B. Contract Ethics / 8. Contract Strategies

20721	Punctuality and justice in dealings are excellent for raising a man in the world [Franklin]
	Full Idea: After industry and frugality, nothing contributes more to raising a young man in the world than punctuality and justice in all his dealings.
	From: Benjamin Franklin (Advice to a Young Tradesman [1748], p.87-), quoted by Max Weber - The Protestant Ethic and the Spirit of Capitalism 2
	A reaction: A perfect illustration of the self-interest that drives morality in the social contract view.

24. Political Theory / D. Ideologies / 11. Capitalism

20720	Time is money, ..credit is money, ..and money breeds more money [Franklin]
	Full Idea: Remember that time is money, …and that credit is money, …and that money can beget money.
	From: Benjamin Franklin (Advice to a Young Tradesman [1748], p.87-), quoted by Max Weber - The Protestant Ethic and the Spirit of Capitalism 2
	A reaction: [snippets] A wonderful quotation rescued by Max Weber, showing that Franklin understood capitalism with crystal clarity, before it had even barely begun