Combining Texts

All the ideas for 'Through the Looking Glass', 'works' and 'fragments/reports'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

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 / A. Nature of Existence / 3. Being / e. Being and nothing

21982	I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
	Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people."
	From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
	A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork.

10. Modality / A. Necessity / 8. Transcendental Necessity

490	Everything happens by reason and necessity [Leucippus]
	Full Idea: Nothing happens at random; everything happens out of reason and by necessity.
	From: Leucippus (fragments/reports [c.435 BCE], B002), quoted by (who?) - where?