Combining Philosophers
Ideas for William W. Tait, Willard Quine and Anon (Bhag)
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52 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
9020
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My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine]
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13010
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In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
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5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9028
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Maybe logical truth reflects reality, but in different ways in different languages [Quine]
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
9002
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Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13639
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Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro]
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8789
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Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine]
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10014
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Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes]
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10828
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Quantifying over predicates is treating them as names of entities [Quine]
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13681
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Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
12219
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Whether a modal claim is true depends on how the object is described [Quine, by Fine,K]
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22437
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Logical languages are rooted in ordinary language, and that connection must be kept [Quine]
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5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10064
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Quine quickly dismisses If-thenism [Quine, by Musgrave]
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5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
20296
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Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
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8998
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Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
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8999
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Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
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9000
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If a convention cannot be communicated until after its adoption, what is its role? [Quine]
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5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
19043
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Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
9024
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Excluded middle has three different definitions [Quine]
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5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10012
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Quantification theory can still be proved complete if we add identity [Quine]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
22434
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Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it [Quine]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13829
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If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
12221
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'Corner quotes' (quasi-quotation) designate 'whatever these terms designate' [Quine]
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1618
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We study bound variables not to know reality, but to know what reality language asserts [Quine]
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5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
21698
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All relations, apart from ancestrals, can be reduced to simpler logic [Quine]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
8453
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If we had to name objects to make existence claims, we couldn't discuss all the real numbers [Quine]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
10925
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Failure of substitutivity shows that a personal name is not purely referential [Quine]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
19321
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We might do without names, by converting them into predicates [Quine, by Kirkham]
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8455
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Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein]
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8456
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Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein]
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9204
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Quine's arguments fail because he naively conflates names with descriptions [Fine,K on Quine]
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9016
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Names are not essential, because naming can be turned into predication [Quine]
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
1611
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Names can be converted to descriptions, and Russell showed how to eliminate those [Quine]
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5. Theory of Logic / G. Quantification / 1. Quantification
10926
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Quantifying into referentially opaque contexts often produces nonsense [Quine]
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10922
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Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine]
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10311
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No sense can be made of quantification into opaque contexts [Quine, by Hale]
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10538
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Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett]
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9015
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Universal quantification is widespread, but it is definable in terms of existential quantification [Quine]
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5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
10793
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Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)]
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10801
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Either reference really matters, or we don't need to replace it with substitutions [Quine]
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21642
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If quantification is all substitutional, there is no ontology [Quine]
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9025
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You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine]
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9026
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Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10705
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Putting a predicate letter in a quantifier is to make it the name of an entity [Quine]
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
12798
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Plurals can in principle be paraphrased away altogether [Quine]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9027
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A sentence is logically true if all sentences with that grammatical structure are true [Quine]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
13416
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Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C]
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5. Theory of Logic / L. Paradox / 3. Antinomies
21691
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Antinomies contradict accepted ways of reasoning, and demand revisions [Quine]
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5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
21690
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Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine]
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
9003
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Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
21689
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A barber shaves only those who do not shave themselves. So does he shave himself? [Quine]
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21694
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Membership conditions which involve membership and non-membership are paradoxical [Quine]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21692
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If we write it as '"this sentence is false" is false', there is no paradox [Quine]
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