Combining Texts
Ideas for
'Logical Pluralism', 'That Politics may be reduced to a Science' and 'Alfred Tarski: life and logic'
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16 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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13235
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Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall]
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13238
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Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall]
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5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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13234
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The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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13232
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Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall]
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5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
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13241
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The model theory of classical predicate logic is mathematics [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
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13253
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There are several different consequence relations [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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13240
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A sentence follows from others if they always model it [Beall/Restall]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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13236
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Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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10158
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A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
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10162
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Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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10159
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Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
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10160
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Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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10161
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If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
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5. Theory of Logic / K. Features of Logics / 7. Decidability
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10156
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'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
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10155
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Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
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13237
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Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall]
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