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All the ideas for 'What is Logic?st1=Ian Hacking', 'works' and 'On Referring'

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24 ideas

2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
13834 Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
13835 Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
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 / A. Overview of Logic / 4. Pure Logic
13845 The various logics are abstractions made from terms like 'if...then' in English [Hacking]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840 First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
13844 A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13842 Second-order completeness seems to need intensional entities and possible worlds [Hacking]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
8358 There are no rules for the exact logic of ordinary language, because that doesn't exist [Strawson,P]
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]
13837 With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839 Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
6413 'The present King of France is bald' presupposes existence, rather than stating it [Strawson,P, by Grayling]
8354 Russell asks when 'The King of France is wise' would be a true assertion [Strawson,P]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [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 / A. Nature of Meaning / 6. Meaning as Use
8356 The meaning of an expression or sentence is general directions for its use, to refer or to assert [Strawson,P]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
10430 Reference is mainly a social phenomenon [Strawson,P, by Sainsbury]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
10448 If an expression can refer to anything, it may still instrinsically refer, but relative to a context [Bach on Strawson,P]
19. Language / B. Reference / 5. Speaker's Reference
8355 Expressions don't refer; people use expressions to refer [Strawson,P]
8357 If an utterance fails to refer then it is a pseudo-use, though a speaker may think they assert something [Strawson,P]