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'works', 'Logic in Mathematics' and 'Alfred Tarski: life and logic'
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16 ideas
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
16867
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Logic not only proves things, but also reveals logical relations between them [Frege]
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5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
16863
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Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege]
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16862
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The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
4730
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For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
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5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
16865
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'Theorems' are both proved, and used in proofs [Frege]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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
10160
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Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
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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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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
16866
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Tracing inference backwards closes in on a small set of axioms and postulates [Frege]
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16868
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The essence of mathematics is the kernel of primitive truths on which it rests [Frege]
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16871
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A truth can be an axiom in one system and not in another [Frege]
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16870
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Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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
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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