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All the ideas for 'What is Logic?st1=Ian Hacking', 'fragments/reports' and 'Formal and Material Consequence'

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19 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
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
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]
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]
14187 If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read]
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 / B. Logical Consequence / 1. Logical Consequence
14188 Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read]
14182 If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read]
14183 Maybe arguments are only valid when suppressed premises are all stated - but why? [Read]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
14184 In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read]
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]
14186 Logical connectives contain no information, but just record combination relations between facts [Read]
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]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
6019 If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
14185 Conditionals are just a shorthand for some proof, leaving out the details [Read]