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All the ideas for 'fragments/reports', 'An Analysis of Knowledge and Valuation' and 'works'

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11 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined

23367	Even pointing a finger should only be done for a reason [Epictetus]
	Full Idea: Philosophy says it is not right even to stretch out a finger without some reason.
	From: Epictetus (fragments/reports [c.57], 15)
	A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!).

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.

12. Knowledge Sources / E. Direct Knowledge / 4. Memory

21500	We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI]
	Full Idea: When the whole range of empirical beliefs is taken into account, all of them more or less dependent on memorial knowledge, we find that those which are most credible can be assured by their mutual support, or 'congruence'.
	From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 334), quoted by Erik J. Olsson - Against Coherence 3.1
	A reaction: Lewis may be over-confident about this, and is duly attacked by Olson, but it seems to me roughly correct. How do you assess whether some unusual element in your memory was a dream or a real experience?

21501	If we doubt memories we cannot assess our doubt, or what is being doubted [Lewis,CI]
	Full Idea: To doubt our sense of past experience as founded in actuality, would be to lose any criterion by which either the doubt itself or what is doubted could be corroborated.
	From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 358), quoted by Erik J. Olsson - Against Coherence 3.3.1
	A reaction: Obviously scepticism about memory can come in degrees, but total rejection of short-term and clear memories looks like a non-starter. What could you put in its place? Hyper-rationalism? Even maths needs memory.

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism

6556	If anything is to be probable, then something must be certain [Lewis,CI]
	Full Idea: If anything is to be probable, then something must be certain.
	From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 186), quoted by Robert Fogelin - Walking the Tightrope of Reason Intro
	A reaction: Lewis makes this comment when facing infinite regress problems. It is a very nice slogan for foundationalism, which embodies the slippery slope view. Personally I feel the emotional pull of foundations, but acknowledge the very strong doubts about them.

13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism

21498	Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI]
	Full Idea: A set of statements, or a set of supposed facts asserted, will be said to be congruent if and only if they are so related that the antecedent probability of any one of them will be increased if the remainder of the set can be assumed as given premises.
	From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 338), quoted by Erik J. Olsson - Against Coherence 2.2
	A reaction: This thesis is vigorously attacked by Erik Olson, who works through the probability calculations. There seems an obvious problem without that. How else do you assess 'congruence', other than by evidence of mutual strengthening?

18. Thought / C. Content / 8. Intension

5828	Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI]
	Full Idea: "The denotation or extension of a term is the class of all actual or existent things which the term correctly applies to or names; the connotation or intension of a term is delimited by any correct definition of it." ..And intension determines extension.
	From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946]), quoted by Stephen P. Schwartz - Intro to Naming,Necessity and Natural Kinds §II
	A reaction: The last part is one of the big ideas in philosophy of language, which was rejected by Putnam and co. If you were to reverse the slogan, though, (to extension determines intension) how would you identify the members of the extension?