Combining Philosophers
Ideas for Galen, Michael Potter and Michael Dummett
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24 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11066
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Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna]
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
9820
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In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10704
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We can formalize second-order formation rules, but not inference rules [Potter]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
19058
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Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett]
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5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
22279
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Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter]
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5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
22291
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Deductivism can't explain how the world supports unconditional conclusions [Potter]
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5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
8173
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Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett]
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8195
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Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
7334
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Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A]
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8179
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The law of excluded middle is the logical reflection of the principle of bivalence [Dummett]
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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 / E. Structures of Logic / 2. Logical Connectives / c. not
19052
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Natural language 'not' doesn't apply to sentences [Dummett]
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18801
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Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
9182
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Ancient names like 'Obadiah' depend on tradition, not on where the name originated [Dummett]
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5. Theory of Logic / G. Quantification / 1. Quantification
19057
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Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [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 / H. Proof Systems / 3. Proof from Assumptions
10703
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Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
19059
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In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett]
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19062
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Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett]
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19063
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Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [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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22295
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Modern logical truths are true under all interpretations of the non-logical words [Potter]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
19065
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Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
8194
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Surely there is no exact single grain that brings a heap into existence [Dummett]
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