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Awarded the 1988 Johnsonian Prize in Philosophy. Published with the aid of a grant from the National Endowment for the Humanities.
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J. R. Lucas argues against mechanism that an ideal, immortal agent whose mental activities could be mimicked by a Turing machine would be able, absurdly, to prove the Godel sentence for the set of arithmetical sentences she is able to... more
J. R. Lucas argues against mechanism that an ideal, immortal agent whose mental activities could be mimicked by a Turing machine would be able, absurdly, to prove the Godel sentence for the set of arithmetical sentences she is able to prove. There are two main objections: “The agent cannot know her own program” and “The agent cannot be sure the things she can prove are consistent.” It is argued that accepting the first objection would hand the anti-mechanist a roundabout victory, since for an ordinary finite mechanical system, one can determine what its program is, but that one need not accept the first objection. The second objection can only be thwarted by adopting a conception of “proof” that treats proof as veridical. This reduces Lucas’s argument to Montague’s theorem on the undefinability of epistemic necessity, which is, it is argued, an obstacle to naturalized epistemology.
L nary document. Nearly everyone can agree that it is a pro-foundly important piece of work, but scarcely anyone can agree where its importance lies. Its subject is the liar paradox, which is a problem of the utmost philosophical urgency.... more
L nary document. Nearly everyone can agree that it is a pro-foundly important piece of work, but scarcely anyone can agree where its importance lies. Its subject is the liar paradox, which is a problem of the utmost philosophical urgency. Unless we can overcome the liar ...
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This is not an overly ambitious paper. What I would like to do is to take a thesis that most people would regard as wildly implausible, and convince you that it is, in fact, false. What's worse, the argument I shall give is by no... more
This is not an overly ambitious paper. What I would like to do is to take a thesis that most people would regard as wildly implausible, and convince you that it is, in fact, false. What's worse, the argument I shall give is by no means airtight, though I hope it's reasonably convincing. The thesis has to do with the fuzzy boundaries of terms that refer to familiar middle-sized objects, terms like ‘Kilimanjaro’ and ‘the tallest mountain in Africa.’ It is intuitively clear (though not beyond doubt — see Timothy Williamson's book Vagueness) that Kilimanjaro has a fuzzy boundary, so that there are some clods of earth at the base of the mountain for which there isn't anything, either in our practices in using the word ‘Kilimanjaro’ or in the facts of geography, that determines an answer to the question whether the clod is a part of Kilimanjaro.
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... Page 2. 350 VANN MCGEE probabilistically valid, so there is a truth assignment r which gives each of the premisses a designated value and gives the conclusion an undesignated value. ... 351 NOTES 1 I would like to thank Ernest Adams... more
... Page 2. 350 VANN MCGEE probabilistically valid, so there is a truth assignment r which gives each of the premisses a designated value and gives the conclusion an undesignated value. ... 351 NOTES 1 I would like to thank Ernest Adams for his great help in preparing this paper. ...
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Research Interests: Formal Logic and Validity
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... Review: John Etchemendy, The Concept of Logical Consequence. Vann McGee. Source: J. Symbolic Logic Volume 57, Issue 1 (1992), 254-255. Reviewed Works: John Etchemendy, The Concept of Logical Consequence. Full ...
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We intend to develop an account of the relation between particulars and universals. Loosely derived from the work of Thomas Reid,' the account will be empiricist, in that it has our understanding of general concepts dependent upon... more
We intend to develop an account of the relation between particulars and universals. Loosely derived from the work of Thomas Reid,' the account will be empiricist, in that it has our understanding of general concepts dependent upon our prior acquaintance with particular individuals, ...
Van Aken James. Axioms for the set-theoretic hierarchy. The journal of symbolic logic, vol. 51 (1986), pp. 992–1004.Pollard Stephen. More axioms for the set-theoretic hierarchy. Logique et analyse, n.s. vol. 31 (1988), pp. 85–88.Potter Michael D.. Sets. An introduction. Clarendon Press, Oxford Un...more
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Robert Solovay [8] investigated the version of the modal sentential calculus one gets by taking “□ϕ” to mean “ϕ is true in every transitive model of Zermelo-Fraenkel set theory (ZF).” Defining an interpretation to be a function * taking... more
Robert Solovay [8] investigated the version of the modal sentential calculus one gets by taking “□ϕ” to mean “ϕ is true in every transitive model of Zermelo-Fraenkel set theory (ZF).” Defining an interpretation to be a function * taking formulas of the modal sentential calculus to sentences of the language of set theory that commutes with the Boolean connectives and sets (□ϕ)* equal to the statement that ϕ* is true in every transitive model of ZF, and stipulating that a modal formula ϕ is valid if and only if, for every interpretation *, ϕ* is true in every transitive model of ZF, Solovay obtained a complete and decidable set of axioms.In this paper, we stifle the hope that we might continue Solovay's program by getting an analogous set of axioms for the modal predicate calculus. The set of valid formulas of the modal predicate calculus is not axiomatizable; indeed, it is complete .We also look at a variant notion of validity according to which a formula ϕ counts as valid if and...
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The formalism of P(redicate) P(rovability) L(ogic) is the result of adjoining the unary operator □ to first-order logic without identity, constants, or function symbols. The term “provability” indicates that □ is to be “read” as “it is... more
The formalism of P(redicate) P(rovability) L(ogic) is the result of adjoining the unary operator □ to first-order logic without identity, constants, or function symbols. The term “provability” indicates that □ is to be “read” as “it is provable in P(eano) A(rithmetic) that…” and that the formulae of predicate provability logic are to be interpreted via formulae of PA as follows. Pr(x), alias Bew(x), is the standard provability predicate of PA. For any formula F of PA, Pr[F] is the formula of PA that expresses the PA-provability of F “of” the values of the variables free in F, i.e., it is the formula of PA with the same free variables as F that expresses the PA-provability of the result of substituting for each variable free in F the numeral for the value of that variable. For the details of the construction of Pr[F], the reader may consult [B2, p. 42]. If F is a sentence of PA, then Pr[F] = Pr(‘F’), the sentence that expresses the PA-provability of F. Let υ 1, υ 2,… be an enumeratio...
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Etchemendy John. The concept of logical consequence . An unaltered republication of JSL LVII 254. The David Hume series of philosophy and cognitive science reissues. Center for the Study of Language and Information, Stanford 1999, also distributed by Cambridge University Press, New York, vii + 17...more
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Research Interests: Philosophy and Synthese
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The theory of subjective probability can be understood either norma-tively or descriptively. As a descriptive account, the theory doesn't make it past the starting gate. The observed behavior of human betting agents does not even... more
The theory of subjective probability can be understood either norma-tively or descriptively. As a descriptive account, the theory doesn't make it past the starting gate. The observed behavior of human betting agents does not even resemble the behavior subjective probability ...
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Mathematical realism is the doctrine that mathematical objects really exist, that mathematical statements are either determinately true or determinately false, and that the accepted mathematical axioms are predominantly true. A realist... more
Mathematical realism is the doctrine that mathematical objects really exist, that mathematical statements are either determinately true or determinately false, and that the accepted mathematical axioms are predominantly true. A realist understanding of set theory has it that when the ...
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Tjrnest Adams (1965, 1975) has advanced a probabilistic ac-L count of conditionals, according to which the probability of a simple English indicative conditional is the conditional probability of the consequent given the antecedent. The... more
Tjrnest Adams (1965, 1975) has advanced a probabilistic ac-L count of conditionals, according to which the probability of a simple English indicative conditional is the conditional probability of the consequent given the antecedent. The theory describes what English speakers ...
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1. Cumulative Type Theory [*1933o]2 is the handwritten text of a lecture Godel delivered two years after the publication of his proof of the incompleteness theorems. The problem of giving a foundation for mathematics (ie, for 'the... more
1. Cumulative Type Theory [*1933o]2 is the handwritten text of a lecture Godel delivered two years after the publication of his proof of the incompleteness theorems. The problem of giving a foundation for mathematics (ie, for 'the totality of methods actually used by ...
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That reference is inscrutable is demonstrated, it is argued, not only by WV Quine's arguments but by Peter Unger's ''Problem of the Many.'' Applied to our own language, this is a... more
That reference is inscrutable is demonstrated, it is argued, not only by WV Quine's arguments but by Peter Unger's ''Problem of the Many.'' Applied to our own language, this is a paradoxical result, since nothing could be more obvious to speakers of English than that, when they ...
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Research Interests: Philosophy and Noûs
... most similar to the actual world in which Reagan did not win the election will be a world in whichCarter finished first ... VANN McGEE University of California at Berkeley KRIPKE ON WITTGENSTEIN ON RULES* THERE is no doubt that Ludwig... more
... most similar to the actual world in which Reagan did not win the election will be a world in whichCarter finished first ... VANN McGEE University of California at Berkeley KRIPKE ON WITTGENSTEIN ON RULES* THERE is no doubt that Ludwig Wittgenstein thought the topic of ...
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... Page 2. 350 VANN MCGEE probabilistically valid, so there is a truth assignment r which gives each of the premisses a designated value and gives the conclusion an undesignated value. ... 351 NOTES 1 I would like to thank Ernest Adams... more
... Page 2. 350 VANN MCGEE probabilistically valid, so there is a truth assignment r which gives each of the premisses a designated value and gives the conclusion an undesignated value. ... 351 NOTES 1 I would like to thank Ernest Adams for his great help in preparing this paper. ...