Combining Texts

All the ideas for 'fragments/reports', 'works' and 'Emergent Evolution'

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7 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.
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.
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
16051 Life has a new supervenient relation, which alters its underlying physical events [Morgan,L]
     Full Idea: When some new kind of relatedness is supervenient (say at the level of life), the way in which the physical events which are involved run their course is different in virtue of its presence.
     From: Lloyd Morgan (Emergent Evolution [1923], pp.15-16), quoted by Terence Horgan - From Supervenience to Superdupervenience 1
     A reaction: This is a clear assertion of 'downward causation' at the first introduction of 'supervenience', supporting 'emergentism' about life and mind. That is, the newly-emerged feature has new causal powers that affect the physical system from outside. Wrong!
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?