Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'The Semantic Tradition from Kant to Carnap' and 'Individuals in Aristotle'

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17 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]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
18270 Choice suggests that intensions are not needed to ensure classes [Coffa]
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]
9. Objects / E. Objects over Time / 9. Ship of Theseus
16157 Insurance on the original ship would hardly be paid out if the plank version was wrecked! [Frede,M]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
18263 The semantic tradition aimed to explain the a priori semantically, not by Kantian intuition [Coffa]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
18272 Platonism defines the a priori in a way that makes it unknowable [Coffa]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
18266 Mathematics generalises by using variables [Coffa]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
18279 Relativity is as absolutist about space-time as Newton was about space [Coffa]