Combining Texts
Ideas for
'What is Logic?st1=Ian Hacking', 'Introduction to the Theory of Logic' and 'Facts and Propositions'
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19 ideas
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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13845
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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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13840
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First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
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13844
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A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
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10897
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A first-order 'sentence' is a formula with no free variables [Zalabardo]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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13842
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Second-order completeness seems to need intensional entities and possible worlds [Hacking]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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10899
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Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
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10893
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Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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13837
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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 / b. Basic connectives
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10896
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Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
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13839
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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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10898
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The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
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10902
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We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
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5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
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10892
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We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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10895
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'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
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10900
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Logically true sentences are true in all structures [Zalabardo]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
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10894
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A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
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10901
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Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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10903
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A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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13843
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If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
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