Combining Philosophers

Ideas for B Hale / C Wright, Plato and Michael Dummett

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28 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11066 Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
9820 In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
19058 Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
8173 Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett]
8195 Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
7334 Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A]
8179 The law of excluded middle is the logical reflection of the principle of bivalence [Dummett]
9195 Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
19052 Natural language 'not' doesn't apply to sentences [Dummett]
18801 Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
13777 A name is a sort of tool [Plato]
13790 A name-giver might misname something, then force other names to conform to it [Plato]
13791 Things must be known before they are named, so it can't be the names that give us knowledge [Plato]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
9182 Ancient names like 'Obadiah' depend on tradition, not on where the name originated [Dummett]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
13789 Anyone who knows a thing's name also knows the thing [Plato]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
12230 Singular terms refer if they make certain atomic statements true [Hale/Wright]
5. Theory of Logic / G. Quantification / 1. Quantification
19057 Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
9186 First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
19063 Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett]
19059 In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett]
19062 Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9187 Logical truths and inference are characterized either syntactically or semantically [Dummett]
5. Theory of Logic / K. Features of Logics / 4. Completeness
19065 Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett]
5. Theory of Logic / L. Paradox / 2. Aporiai
11259 How can you seek knowledge of something if you don't know it? [Plato]
5. Theory of Logic / L. Paradox / 3. Antinomies
13986 Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle]
14150 Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
8194 Surely there is no exact single grain that brings a heap into existence [Dummett]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
10631 If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]