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Roy T. Cook [68]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.  38
    The Yablo Paradox: An Essay on Circularity.Roy T. Cook - 2014 - 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.  61
    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. 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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  7.  53
    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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  8. 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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  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.  97
    There Are Non-Circular Paradoxes (but Yablo's Isn't One of Them!).Roy T. Cook - 2006 - The Monist 89 (1):118-149.
  11.  80
    Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures.Roy T. Cook - 2004 - Mind 113 (449):154-157.
  12. 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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  13. The Foundations of Mathematics in the Theory of Sets.Roy T. Cook - 2003 - British Journal for the Philosophy of Science 54 (2):347-352.
  14. 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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  15.  5
    There Are Non-Circular Paradoxes.Roy T. Cook - 2006 - The Monist 89 (1):118-149.
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  16.  6
    An Intensional Theory of Truth: An Informal Report.Roy T. Cook - forthcoming - Philosophical Forum.
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  17.  31
    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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  18. Knights, Knaves and Unknowable Truths.Roy T. Cook - 2006 - Analysis 66 (1):10-16.
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  19.  87
    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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  20. Paradoxes.Roy T. Cook - 2013 - 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. 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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  22.  34
    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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  23. 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.
     
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  24. 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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  25.  88
    The State of the Economy: Neo-Logicism and Inflationt.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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  26. A Dictionary of Philosophical Logic.Roy T. Cook - 2009 - Edinburgh University Press.
     
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  27. What Negation is Not: Intuitionism and ‘0=1’.Roy T. Cook & Jon Cogburn - 2000 - Analysis 60 (1):5–12.
  28. 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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  29.  84
    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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  30.  31
    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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  31.  50
    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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  32.  74
    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.
  33.  98
    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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  34. Comics, Prints, and Multiplicity.Roy T. Cook & Aaron Meskin - 2015 - Journal of Aesthetics and Art Criticism 73 (1):57-67.
    Comics comprise a hybrid art form descended from printmaking and mostly made using print technologies. But comics are an art form in their own right and do not belong to the art form of printmaking. We explore some features art comics and fine art prints do and do not have in common. Although most fine art prints and comics are multiple artworks, it is not obvious whether the multiple instances of comics and prints are artworks in their own right. The (...)
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  35. 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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  36.  8
    Embracing Intensionality: Paradoxicality and Semi-Truth Operators in Fixed Point Models.Nicholas Tourville & Roy T. Cook - forthcoming - Logic Journal of the IGPL.
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  37. 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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  38.  28
    Paolo Mancosu.*Abstraction and Infinity. [REVIEW]Roy T. Cook & Michael Calasso - 2019 - Philosophia Mathematica 27 (1):125-152.
    MancosuPaolo.* *ion and Infinity. Oxford University Press, 2016. ISBN: 978-0-19-872462-9. Pp. viii + 222.
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  39.  21
    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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  40. 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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  41. 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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  42.  86
    The No-No Paradox Is a Paradox.Roy T. Cook - 2011 - Australasian Journal of Philosophy 89 (3):467-482.
    The No-No Paradox consists of a pair of statements, each of which ?says? the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the ?paradox? must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's view (...)
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  43.  85
    The Paradox of Adverbs.Roy T. Cook & Namjoong Kim - 2015 - Analysis 75 (4):559-561.
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  44.  60
    Drawings of Photographs in Comics.Roy T. Cook - 2012 - Journal of Aesthetics and Art Criticism 70 (1):129-138.
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  45.  34
    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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  46.  99
    If A Then B: How the World Discovered Logic.Roy T. Cook - 2014 - History and Philosophy of Logic 35 (3):301-303.
  47.  54
    Aristotelian Logic, Axioms, and Abstraction.Roy T. Cook - 2003 - Philosophia Mathematica 11 (2):195-202.
    Stewart Shapiro and Alan Weir have argued that a crucial part of the demonstration of Frege's Theorem (specifically, that Hume's Principle implies that there are infinitely many objects) fails if the Neo-logicist cannot assume the existence of the empty property, i.e., is restricted to so-called Aristotelian Logic. Nevertheless, even in the context of Aristotelian Logic, Hume's Principle implies much of the content of Peano Arithmetic. In addition, their results do not constitute an objection to Neo-logicism so much as a clarification (...)
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  48.  27
    Robert Lorne Victor Hale FRSE May 4, 1945 – December 12, 2017.Roy T. Cook & Stewart Shapiro - 2018 - Philosophia Mathematica 26 (2):266-274.
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  49.  17
    Critical Notice: Humberstone, Lloyd, the Connectives, Cambridge, Ma: MIT Press, 2011, Pp. XVII + 1492, $Us65.00, £44.95. [REVIEW]Roy T. Cook - 2013 - Australasian Journal of Philosophy 91 (2):395-405.
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  50.  24
    Vagueness and Meaning.Roy T. Cook - 2011 - In Giuseppina Ronzitti (ed.), Vagueness: A Guide. Springer Verlag. pp. 83--106.
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