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'The Fixation of Belief', 'Logic in Mathematics' and 'works'
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12 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 / 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 / F. Referring in Logic / 1. Naming / a. Names
8453
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If we had to name objects to make existence claims, we couldn't discuss all the real numbers [Quine]
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5. Theory of Logic / G. Quantification / 1. Quantification
10311
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No sense can be made of quantification into opaque contexts [Quine, by Hale]
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10538
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Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett]
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5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
10793
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Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)]
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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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16870
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Axioms are truths which cannot be doubted, and for which no proof is needed [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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