Combining Texts
Ideas for
'What is Logic?st1=Ian Hacking', 'Rationality in Action' and 'Mere Possibilities'
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11 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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If complex logic requires rules, then so does basic logic [Searle]
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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The various logics are abstractions made from terms like 'if...then' in English [Hacking]
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5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
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First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
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A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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Second-order completeness seems to need intensional entities and possible worlds [Hacking]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
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We regiment to get semantic structure, for evaluating arguments, and understanding complexities [Stalnaker]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
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In 'S was F or some other than S was F', the disjuncts need S, but the whole disjunction doesn't [Stalnaker]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
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Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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In real reasoning semantics gives validity, not syntax [Searle]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843
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If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
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