Combining Texts
Ideas for
'Logical Pluralism', 'Ordinary Objects' and 'Principia Mathematica'
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14 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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13235
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Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall]
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13238
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Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall]
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5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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13234
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The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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13232
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Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall]
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5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
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13241
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The model theory of classical predicate logic is mathematics [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
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13253
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There are several different consequence relations [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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13240
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A sentence follows from others if they always model it [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 6. Entailment
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14471
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Analytical entailments arise from combinations of meanings and inference rules [Thomasson]
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5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
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8204
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Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
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9359
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Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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21707
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Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
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5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
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10036
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In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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13236
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Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
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13237
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Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall]
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