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Roy T. Cook [86]Roy Thomas Cook [1]
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Roy T. Cook
University of Minnesota
  1. Let a thousand flowers Bloom: A tour of logical pluralism.Roy T. Cook - 2010 - Philosophy Compass 5 (6):492-504.
    Logical pluralism is the view that there is more than one correct logic. In this article, I explore what logical pluralism is, and what it entails, by: (i) distinguishing clearly between relativism about a particular domain and pluralism about that domain; (ii) distinguishing between a number of forms logical pluralism might take; (iii) attempting to distinguish between those versions of pluralism that are clearly true and those that are might be controversial; and (iv) surveying three prominent attempts to argue for (...)
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  2.  54
    The Yablo Paradox: An Essay on Circularity.Roy T. Cook - 2012 - Oxford, England: Oxford University Press.
    Roy T Cook examines the Yablo paradox--a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others that follow it. He focuses on questions of characterization, circularity, and generalizability, and pays special attention to the idea that it provides us with a semantic paradox that involves no circularity.
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  3. Patterns of paradox.Roy T. Cook - 2004 - Journal of Symbolic Logic 69 (3):767-774.
  4.  86
    Cardinality and Acceptable Abstraction.Roy T. Cook & Øystein Linnebo - 2018 - Notre Dame Journal of Formal Logic 59 (1):61-74.
    It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that a fix proposed by Heck fails but we analyze the interesting idea on which it is based, namely that an acceptable abstraction has to “generate” the objects that it requires. We also correct and complete the classification of proposed criteria for acceptable abstraction.
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  5. There is No Paradox of Logical Validity.Roy T. Cook - 2014 - Logica Universalis 8 (3-4):447-467.
    A number of authors have argued that Peano Arithmetic supplemented with a logical validity predicate is inconsistent in much the same manner as is PA supplemented with an unrestricted truth predicate. In this paper I show that, on the contrary, there is no genuine paradox of logical validity—a completely general logical validity predicate can be coherently added to PA, and the resulting system is consistent. In addition, this observation lead to a number of novel, and important, insights into the nature (...)
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  6.  91
    Possible predicates and actual properties.Roy T. Cook - 2019 - Synthese 196 (7):2555-2582.
    In “Properties and the Interpretation of Second-Order Logic” Bob Hale develops and defends a deflationary conception of properties where a property with particular satisfaction conditions actually exists if and only if it is possible that a predicate with those same satisfaction conditions exists. He argues further that, since our languages are finitary, there are at most countably infinitely many properties and, as a result, the account fails to underwrite the standard semantics for second-order logic. Here a more lenient version of (...)
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  7. Abstraction and identity.Roy T. Cook & Philip A. Ebert - 2005 - Dialectica 59 (2):121–139.
    A co-authored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.
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  8.  26
    Embracing intensionality: Paradoxicality and semi-truth operators in fixed point models.Nicholas Tourville & Roy T. Cook - 2020 - Logic Journal of the IGPL 28 (5):747-770.
    The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook, Cook, Schlenker, and Tourville and Cook via the addition of intensional operators such as ``is paradoxical''. In this extended framework we are able (...)
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  9. Vagueness and mathematical precision.Roy T. Cook - 2002 - Mind 111 (442):225-247.
    One of the main reasons for providing formal semantics for languages is that the mathematical precision afforded by such semantics allows us to study and manipulate the formalization much more easily than if we were to study the relevant natural languages directly. Michael Tye and R. M. Sainsbury have argued that traditional set-theoretic semantics for vague languages are all but useless, however, since this mathematical precision eliminates the very phenomenon (vagueness) that we are trying to capture. Here we meet this (...)
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  10.  68
    Conservativeness, Stability, and Abstraction.Roy T. Cook - 2012 - British Journal for the Philosophy of Science 63 (3):673-696.
    One of the main problems plaguing neo-logicism is the Bad Company challenge: the need for a well-motivated account of which abstraction principles provide legitimate definitions of mathematical concepts. In this article a solution to the Bad Company challenge is provided, based on the idea that definitions ought to be conservative. Although the standard formulation of conservativeness is not sufficient for acceptability, since there are conservative but pairwise incompatible abstraction principles, a stronger conservativeness condition is sufficient: that the class of acceptable (...)
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  11. What’s Wrong with Tonk.Roy T. Cook - 2005 - Journal of Philosophical Logic 34 (2):217 - 226.
    In “The Runabout Inference Ticket” AN Prior (1960) examines the idea that logical connectives can be given a meaning solely in virtue of the stipulation of a set of rules governing them, and thus that logical truth/consequence.
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  12.  77
    Abstraction and Four Kinds of Invariance.Roy T. Cook - 2017 - Philosophia Mathematica 25 (1):3–25.
    Fine and Antonelli introduce two generalizations of permutation invariance — internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most fine-grained abstraction principle that is invariant in each sense. Hume’s Principle is the most fine-grained abstraction principle invariant in both senses. I conclude by suggesting that this partially explains the success of Hume’s Principle, and the comparative lack (...)
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  13. Embracing revenge: on the indefinite extendibility of language.Roy T. Cook - 2007 - In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press. pp. 31.
     
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  14. What is a Truth Value And How Many Are There?Roy T. Cook - 2009 - Studia Logica 92 (2):183-201.
    Truth values are, properly understood, merely proxies for the various relations that can hold between language and the world. Once truth values are understood in this way, consideration of the Liar paradox and the revenge problem shows that our language is indefinitely extensible, as is the class of truth values that statements of our language can take – in short, there is a proper class of such truth values. As a result, important and unexpected connections emerge between the semantic paradoxes (...)
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  15. There Are Non-circular Paradoxes (But Yablo’s Isn't One of Them!).Roy T. Cook - 2006 - The Monist 89 (1):118-149.
  16.  8
    A Dictionary of Philosophical Logic.Roy T. Cook - 2009 - Edinburgh University Press.
    This dictionary introduces undergraduate and post-graduate students in philosophy, mathematics, and computer science to the main problems and positions in philosophical logic. Coverage includes not only key figures, positions, terminology, and debates within philosophical logic itself, but issues in related, overlapping disciplines such as set theory and the philosophy of mathematics as well. Entries are extensively cross-referenced, so that each entry can be easily located within the context of wider debates, thereby providing a valuable reference both for tracking the connections (...)
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  17.  31
    Iteration one more time.Roy T. Cook - 2003 - Notre Dame Journal of Formal Logic 44 (2):63--92.
    A neologicist set theory based on an abstraction principle (NewerV) codifying the iterative conception of set is investigated, and its strength is compared to Boolos's NewV. The new principle, unlike NewV, fails to imply the axiom of replacement, but does secure powerset. Like NewV, however, it also fails to entail the axiom of infinity. A set theory based on the conjunction of these two principles is then examined. It turns out that this set theory, supplemented by a principle stating that (...)
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  18.  87
    Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures.Roy T. Cook - 2004 - Mind 113 (449):154-157.
  19.  43
    An Intensional Theory of Truth: An Informal Report.Roy T. Cook - 2020 - Philosophical Forum 51 (2):115-126.
  20.  8
    Paradoxes.Roy T. Cook - 2013 - Malden, MA: Polity.
    Paradoxes are arguments that lead from apparently true premises, via apparently uncontroversial reasoning, to a false or even contradictory conclusion. Paradoxes threaten our basic understanding of central concepts such as space, time, motion, infinity, truth, knowledge, and belief. In this volume Roy T Cook provides a sophisticated, yet accessible and entertaining, introduction to the study of paradoxes, one that includes a detailed examination of a wide variety of paradoxes. The book is organized around four important types of paradox: the semantic (...)
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  21. The state of the economy: Neo-logicism and inflation.Roy T. Cook - 2002 - Philosophia Mathematica 10 (1):43-66.
    In this paper I examine the prospects for a successful neo–logicist reconstruction of the real numbers, focusing on Bob Hale's use of a cut-abstraction principle. There is a serious problem plaguing Hale's project. Natural generalizations of this principle imply that there are far more objects than one would expect from a position that stresses its epistemological conservativeness. In other words, the sort of abstraction needed to obtain a theory of the reals is rampantly inflationary. I also indicate briefly why this (...)
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  22.  7
    There Are Non-circular Paradoxes (But Yablo’s Isn't One of Them!).Roy T. Cook - 2006 - The Monist 89 (1):118-149.
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  23.  98
    Alethic pluralism, generic truth, and mixed conjunctions.Roy T. Cook - 2011 - Philosophical Quarterly 61 (244):624-629.
    A difficulty for alethic pluralism has been the idea that semantic evaluation of conjunctions whose conjuncts come from discourses with distinct truth properties requires a third notion of truth which applies to both of the original discourses. But this line of reasoning does not entail that there exists a single generic truth property that applies to all statements and all discourses, unless it is supplemented with additional, controversial, premises. So the problem of mixed conjunctions, while highlighting other aspects of alethic (...)
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  24. Knights, knaves and unknowable truths.Roy T. Cook - 2006 - Analysis 66 (1):10-16.
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  25.  44
    Embracing the technicalities: Expressive completeness and revenge.Nicholas Tourville & Roy T. Cook - 2016 - Review of Symbolic Logic 9 (2):325-358.
    The Revenge Problem threatens every approach to the semantic paradoxes that proceeds by introducing nonclassical semantic values. Given any such collection Δ of additional semantic values, one can construct a Revenge sentence:This sentence is either false or has a value in Δ.TheEmbracing Revengeview, developed independently by Roy T. Cook and Phlippe Schlenker, addresses this problem by suggesting that the class of nonclassical semantic values is indefinitely extensible, with each successive Revenge sentence introducing a new ‘pathological’ semantic value into the discourse. (...)
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  26. What negation is not: Intuitionism and ‘0=1’.Roy T. Cook & Jon Cogburn - 2000 - Analysis 60 (1):5–12.
  27. New waves on an old beach: Fregean philosophy of mathematics today.Roy T. Cook - 2009 - In Ø. Linnebo O. Bueno (ed.), New Waves in Philosophy of Mathematics.
  28.  95
    Should Anti-Realists be Anti-Realists About Anti-Realism?Roy T. Cook - 2014 - Erkenntnis 79 (S2):233-258.
    On the Dummettian understanding, anti-realism regarding a particular discourse amounts to (or at the very least, involves) a refusal to accept the determinacy of the subject matter of that discourse and a corresponding refusal to assert at least some instances of excluded middle (which can be understood as expressing this determinacy of subject matter). In short: one is an anti-realist about a discourse if and only if one accepts intuitionistic logic as correct for that discourse. On careful examination, the strongest (...)
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  29. Appendix: How to read Grundgesetze.Roy T. Cook - 2013 - In Philip A. Ebert & Marcus Rossberg (eds.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford: Oxford University Press. pp. A1-A42.
    This appendix is intended to assist the reader in becoming comfortable with the notations, rules, and definitions of Frege's Grundgesetze.
     
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  30. Hume’s Big Brother: counting concepts and the bad company objection.Roy T. Cook - 2009 - Synthese 170 (3):349 - 369.
    A number of formal constraints on acceptable abstraction principles have been proposed, including conservativeness and irenicity. Hume’s Principle, of course, satisfies these constraints. Here, variants of Hume’s Principle that allow us to count concepts instead of objects are examined. It is argued that, prima facie, these principles ought to be no more problematic than HP itself. But, as is shown here, these principles only enjoy the formal properties that have been suggested as indicative of acceptability if certain constraints on the (...)
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  31.  49
    Necessity, Necessitism, and Numbers.Roy T. Cook - 2016 - Philosophical Forum 47 (3-4):385-414.
    Timothy Williamson’s Modal Logic as Metaphysics is a book-length defense of necessitism about objects—roughly put, the view that, necessarily, any object that exists, exists necessarily. In more formal terms, Williamson argues for the validity of necessitism for objects (NO: ◻︎∀x◻︎∃y(x=y)). NO entails both the (first-order) Barcan formula (BF: ◇∃xΦ → ∃x◇Φ, for any formula Φ) and the (first-order) converse Barcan formula (CBF: ∃x◇Φ → ◇∃xΦ, for any formula Φ). The purpose of this essay is not to assess Williamson’s arguments either (...)
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  32. Impure Sets Are Not Located: A Fregean Argument.Roy T. Cook - 2012 - Thought: A Journal of Philosophy 1 (3):219-229.
    It is sometimes suggested that impure sets are spatially co-located with their members (and hence are located in space). Sets, however, are in important respects like numbers. In particular, sets are connected to concepts in much the same manner as numbers are connected to concepts—in both cases, they are fundamentally abstracts of (or corresponding to) concepts. This parallel between the structure of sets and the structure of numbers suggests that the metaphysics of sets and the metaphysics of numbers should parallel (...)
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  33.  48
    Canonicity and Normativity in Massive, Serialized, Collaborative Fiction.Roy T. Cook - 2013 - Journal of Aesthetics and Art Criticism 71 (3):271-276.
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  34.  24
    The Arché Papers on the Mathematics of Abstraction.Roy T. Cook (ed.) - 2007 - Springer.
    Unique in presenting a thoroughgoing examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns).
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  35. Do Comics Require Pictures? Or Why Batman #663 Is a Comic.Roy T. Cook - 2011 - Journal of Aesthetics and Art Criticism 69 (3):285-296.
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  36.  67
    Drawings of Photographs in Comics.Roy T. Cook - 2012 - Journal of Aesthetics and Art Criticism 70 (1):129-138.
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  37. Response to my critics.Roy T. Cook - 2012 - Análisis Filosófico 32 (1):69-97.
    During the Winter of 2011 I visited SADAF and gave a series of talks based on the central chapters of my manuscript on the Yablo paradox. The following year, I visited again, and was pleased and honored to find out that Eduardo Barrio and six of his students had written ‘responses’ that addressed the claims and arguments found in the manuscript, as well as explored new directions in which to take the ideas and themes found there. These comments reflect my (...)
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  38.  8
    Perspectival Logical Pluralism.Roy T. Cook - 2023 - Res Philosophica 100 (2):171-202.
    Logical pluralism is the view that there is more than one formal logic that correctly (or best, or legitimately) codifies the logical consequence relation in natural language. This essay provides a taxonomy of different variations on the logical pluralist theme based on a five-part structure, and then identifies an unoccupied position in this taxonomy: perspectival logical pluralism. Perspectival pluralism provides an attractive position from which to formulate a philosophy of logic from a feminist perspective (and from other, identity-based perspectives, such (...)
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  39.  19
    Joan Weiner.*Taking Frege at His Word.Roy T. Cook - 2023 - Philosophia Mathematica 31 (1):120-124.
    In Taking Frege at his Word, Joan Weiner proposes a wide-ranging re-thinking of Frege’s philosophical and mathematical projects. She begins by outlining what sh.
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  40.  10
    Conditionals, curry, and consequence: embracing deduction.Roy T. Cook & Nicholas Tourville - 2023 - Synthese 201 (2):1-27.
    We extend the Embracing Revenge account of the semantic paradoxes by constructing two distinct consequence relations that reflect, in different ways, the transfinitely-many-valued semantics developed in earlier work. In particular, we adapt the underlying ideas of “gappy” approaches based on K3, and “glutty” approaches based on LP, to the Embracing Revenge framework, by treating the infinitely many non-classical truth values as infinitely many ways that a sentence might fail to receive a classical truth value in the former case, and as (...)
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  41.  87
    Patricia A. Blanchette. Frege's Conception of Logic. Oxford University Press, 2012. ISBN 978-0-19-926925-9 (hbk). Pp. xv + 256. [REVIEW]Roy T. Cook - 2013 - Philosophia Mathematica (1):nkt029.
  42.  34
    PATRICIA A. BLANCHETTE. Frege's Conception of Logic. Oxford University Press, 2012. ISBN 978-0-19-926925-9 . Pp. xv + 256. [REVIEW]Roy T. Cook - 2014 - Philosophia Mathematica 22 (1):108-120.
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  43.  6
    Philosophy of Comics: An Introduction.Roy T. Cook - 2023 - Journal of Aesthetics and Art Criticism 81 (1):105-109.
    Philosophical work on comics from within the “analytic” tradition is a relatively new phenomenon, and still somewhat of a niche subfield in the philosophy of ar.
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  44. The Art of Comics: A Philosophical Approach.Aaron Meskin, Roy T. Cook & Warren Ellis (eds.) - 2011 - Wiley-Blackwell.
    _The Art of Comics_ is the first-ever collection of essays published in English devoted to the philosophical topics raised by comics and graphic novels. In an area of growing philosophical interest, this volume constitutes a great leap forward in the development of this fast expanding field, and makes a powerful contribution to the philosophy of art. The first-ever anthology to address the philosophical issues raised by the art of comics Provides an extensive and thorough introduction to the field, and to (...)
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  45. Curry, Yablo and duality.Roy T. Cook - 2009 - Analysis 69 (4):612-620.
    The Liar paradox is the directly self-referential Liar statement: This statement is false.or : " Λ: ∼ T 1" The argument that proceeds from the Liar statement and the relevant instance of the T-schema: " T ↔ Λ" to a contradiction is familiar. In recent years, a number of variations on the Liar paradox have arisen in the literature on semantic paradox. The two that will concern us here are the Curry paradox, 2 and the Yablo paradox. 3The Curry paradox (...)
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  46.  75
    Frege's Recipe.Roy T. Cook & Philip A. Ebert - 2016 - Journal of Philosophy 113 (7):309-345.
    In this paper, we present a formal recipe that Frege followed in his magnum opus “Grundgesetze der Arithmetik” when formulating his definitions. This recipe is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied it in developing the formal material of Grundgesetze. We then show that a version of Basic Law V plays a fundamental role in Frege’s recipe and, in what follows, we will explicate what exactly this role is and (...)
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  47.  22
    Strong Homomorphisms, Category Theory, and Semantic Paradox.Jonathan Wolfgram & Roy T. Cook - 2022 - Review of Symbolic Logic 15 (4):1070-1093.
    In this essay we introduce a new tool for studying the patterns of sentential reference within the framework introduced in [2] and known as the language of paradox $\mathcal {L}_{\mathsf {P}}$ : strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms. In particular, we show that (i) strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms between $\mathcal {L}_{\mathsf {P}}$ constructions preserve paradoxicality, (ii) many (but not all) earlier results regarding the paradoxicality of $\mathcal {L}_{\mathsf {P}}$ constructions can be recast as special cases of our central result regarding (...)
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  48.  23
    Frege's Concept-Script (Grundgesetze der Arithmetik).Roy T. Cook, Philip A. Ebert & Marcus Rossberg - 2022 - In Bruno Woltzenlogel Paleo & Giselle Reis (eds.), Encyclopedia of Proof Systems. London: College Publications. pp. 5–7.
  49. The Foundations of Mathematics in the Theory of Sets. [REVIEW]Roy T. Cook - 2003 - British Journal for the Philosophy of Science 54 (2):347-352.
  50. Still counterintuitive: A reply to Kremer.Roy T. Cook - 2003 - Analysis 63 (3):257–261.
    In (2002) I argued that Gupta and Belnap’s Revision Theory of Truth (1993) has counterintuitive consequences. In particular, the pair of sentences: (S1) At least one of S1 and S2 is false. (S2) Both of S1 and S2 are false.1 is pathological on the Revision account. There is one, and only one, assignment of truth values to {(S1), (S2)} that make the corresponding Tarski..
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