Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'Critique of the Gotha Program' and 'An Axiomatization of Set Theory'

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18 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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
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 / 2. Logical Connectives / a. Logical connectives
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 / 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 / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory [Neumann]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
22971 In moving from capitalism to communism a revolutionary dictatorship of the proletariat is needed [Marx]
24. Political Theory / D. Ideologies / 9. Communism
22969 People who only have their labour power are the slaves of those permitting them to work [Marx]
22000 From each according to his ability, to each according to his need [Marx]
22970 Freedom is making the state subordinate to its society [Marx]
25. Social Practice / A. Freedoms / 2. Freedom of belief
22972 Bourgeois 'freedom of conscience' just tolerates all sorts of religious intolerance [Marx]