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'fragments/reports', '(Nonsolipsistic) Conceptual Role Semantics' and 'Logic in Mathematics'
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10 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
12595
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We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman]
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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 / 2. Logical Connectives / d. and
12597
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I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman]
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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 / 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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