Combining Texts
Ideas for
'The Fixation of Belief', 'Logical Consequence' and 'Philosophy of Mathematics'
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9 ideas
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10690
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Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691
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Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10695
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Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 8. Material Implication
10689
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A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
23447
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In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10696
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A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10693
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Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
23443
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The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
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23444
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To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
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