Combining Texts
Ideas for
'Logical Consequence', 'Things' and 'The 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 / D. Assumptions for Logic / 2. Excluded Middle
9195
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Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
9186
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First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9187
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Logical truths and inference are characterized either syntactically or semantically [Dummett]
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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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