John Burgess Princeton University
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  1. John Burgess, Logicism: A New Look.
    Adapated from talks at the UCLA Logic Center and the Pitt Philosophy of Science Series. Exposition of material from Fixing Frege, Chapter 2 (on predicative versions of Frege’s system) and from “Protocol Sentences for Lite Logicism” (on a form of mathematical instrumentalism), suggesting a connection. Provisional version: references remain to be added. To appear in Mathematics, Modality, and Models: Selected Philosophical Papers, coming from Cambridge University Press.
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  2. John P. Burgess (unknown). . New Foundations for Physical Geometry: The Theory of Linear Structures, by Tim Maudlin:1-3.
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  3. John P. Burgess (forthcoming). Book Review: Reading the Bible with the Dead: What You Can Learn From the History of Exegesis That You Can't Learn From Exegesis Alone. [REVIEW] Interpretation 62 (3):332-332.
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  4. John P. Burgess (forthcoming). Book Review: The Ten Commandments: A Preaching Commentary. [REVIEW] Interpretation 57 (4):452-452.
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  5. John P. Burgess (forthcoming). Book Review: The Word of God for the People of God: An Entryway to the Theological Interpretation of Scripture. [REVIEW] Interpretation 65 (3):328-329.
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  6. John P. Burgess (forthcoming). Book Review: Text and Psyche: Experiencing Scripture Today. [REVIEW] Interpretation 53 (4):430-431.
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  7. John P. Burgess (forthcoming). New Foundations for Physical Geometry: The Theory of Linear Structures, by Tim Maudlin. Australasian Journal of Philosophy:1-3.
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  8. John P. Burgess (forthcoming). Philosophy of Mathematics in the Twentieth Century: Selected Essays. History and Philosophy of Logic:1-2.
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  9. John P. Burgess (2014). Kevin Scharp, Replacing Truth. Studia Logica 102 (5):1087-1089.
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  10. John Burgess (2013). Reflections on" Wang's Paradox". Teorema: Revista Internacional de Filosofía 32 (1):125-139.
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  11. John P. Burgess (2013). Kripke. Polity.
    In this book Kripke’s long-time colleague, the logician and philosopher John P. Burgess, offers a thorough and self-contained guide to all of Kripke’s published books and his most important philosophical papers, old and new.
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  12. John P. Burgess (2013). On a Derivation of the Necessity of Identity. Synthese:1-19.
    The source, status, and significance of the derivation of the necessity of identity at the beginning of Kripke’s lecture “Identity and Necessity” is discussed from a logical, philosophical, and historical point of view.
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  13. John P. Burgess (2013). Quinus Ab Omni Nævo Vindicatus. Canadian Journal of Philosophy 27 (sup1):25-65.
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  14. John P. Burgess (2013). Saul Kripke: Puzzles and Mysteries. Polity.
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  15. John P. Burgess (2012). Richard G. Heck, Jr.: Frege’s Theorem. [REVIEW] Journal of Philosophy 109 (12):728-733.
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  16. Alexis G. Burgess & John P. Burgess (2011). Truth. Princeton University Press.
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  17. John P. Burgess (2011). Kripke Models. In Alan Berger (ed.), Saul Kripke. Cambridge University Press.
    Saul Kripke has made fundamental contributions to a variety of areas of logic, and his name is attached to a corresponding variety of objects and results. 1 For philosophers, by far the most important examples are ‘Kripke models’, which have been adopted as the standard type of models for modal and related non-classical logics. What follows is an elementary introduction to Kripke’s contributions in this area, intended to prepare the reader to tackle more formal treatments elsewhere.2 2. WHAT IS A (...)
     
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  18. John P. Burgess (2011). The Development of Modern Logic. History and Philosophy of Logic 32 (2):187 - 191.
    History and Philosophy of Logic, Volume 32, Issue 2, Page 187-191, May 2011.
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  19. John Burgess (2010). On the Outside Looking in : A Caution About Conservativeness. In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
    My contribution to the symposium on Goedel’s philosophy of mathematics at the spring 2006 Association for Symbolic Logic meeting in Montreal. Provisional version: references remain to be added. To appear in an ASL volume of proceedings of the Goedel sessions at that meeting.
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  20. John P. Burgess (2010). Axiomatizing the Logic of Comparative Probability. Notre Dame Journal of Formal Logic 51 (1):119-126.
    1 Choice conjecture In axiomatizing nonclassical extensions of classical sentential logic one tries to make do, if one can, with adding to classical sentential logic a finite number of axiom schemes of the simplest kind and a finite number of inference rules of the simplest kind. The simplest kind of axiom scheme in effect states of a particular formula P that for any substitution of formulas for atoms the result of its application to P is to count (...)
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  21. John P. Burgess (2010). Review of B. Hale and A. Hoffmann (Eds.), Modality: Metaphysics, Logic, and Epistemology. [REVIEW] Notre Dame Philosophical Reviews 2010 (10).
  22. John P. Burgess (2009). Philosophical Logic. Princeton University Press.
    Classical logic -- Temporal logic -- Modal logic -- Conditional logic -- Relevantistic logic -- Intuitionistic logic.
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  23. John P. Burgess (2009). Review of Paul A. Gregory, Quine's Naturalism: Language, Theory, and the Knowing Subject. [REVIEW] Notre Dame Philosophical Reviews 2009 (5).
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  24. John P. Burgess (2008). 3. Cats, Dogs, and so On. In Dean W. Zimmerman (ed.), Oxford Studies in Metaphysics. Oxford University Press. 4--56.
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  25. John P. Burgess (2008). Charles Parsons. Mathematical Thought and its Objects. Philosophia Mathematica 16 (3):402-409.
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  26. John P. Burgess (2008). Thomas McKay. Plural Predication. Philosophia Mathematica 16 (1):133-140.
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  27. George Boolos, John Burgess, Richard P. & C. Jeffrey (2007). Computability and Logic. Cambridge University Press.
    Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel’s incompleteness theorems, but also a large number of optional topics, from Turing’s theory of computability to Ramsey’s theorem. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a (...)
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  28. John P. Burgess (2007). Against Ethics. Ethical Theory and Moral Practice 10 (5):427 - 439.
    This is the verbatim manuscript of a paper which has circulated underground for close to thirty years, reaching a metethical conclusion close to J. L. Mackie’s by a somewhat different route.
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  29. John P. Burgess (2007). Charles Parsons:Mathematics in Philosophy: Selected Essays,:Mathematics in Philosophy: Selected Essays. Philosophy of Science 74 (4):549-552.
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  30. John P. Burgess (2006). Discussion: Soames on Empiricism. [REVIEW] Philosophical Studies 129 (3):619 - 626.
    Philosophical Analysis in the Twentieth Century by Scott Soames reminds me of nothing so much as Lectures on Literature by Vladimir Nabokov. Both are works that arose immediately out of the needs of undergraduate teaching, yet each manages to say much of significance to knowledgeable professionals. Each indirectly provides an outline of the history of its field, through a presentation of selected major works, taken in chronological order and including items that are generally recognized as marking decisive turning points. Yet (...)
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  31. John P. Burgess (2006). Review: Discussion: Soames on Empiricism. [REVIEW] Philosophical Studies 129 (3):619 - 626.
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  32. John Burgess (2005). On Anti-Anti-Realism. Facta Philosophica 7 (2):145-165.
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  33. John P. Burgess (2005). Being Explained Away. The Harvard Review of Philosophy 13 (2):41-56.
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  34. John P. Burgess (2005). Charles S. Chihara. A Structural Account of Mathematics. Oxford: Oxford University Press, 2004. Pp. XIV + 380. ISBN 0-19-926753-. [REVIEW] Philosophia Mathematica 13 (1):78-90.
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  35. John P. Burgess (2005). Fixing Frege. Princeton University Press.
    This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in ...
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  36. John P. Burgess (2005). No Requirement of Relevance. In Stewart Shapiro (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. 727--750.
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  37. John P. Burgess (2005). Translating Names. Analysis 65 (287):196–205.
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  38. John P. Burgess (2004). A Philosophical Guide to Conditionals. Bulletin of Symbolic Logic 10 (4):565-570.
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  39. John P. Burgess (2004). Deflating Existential Consequence: A Case for Nominalism. Bulletin of Symbolic Logic 10 (4):573-577.
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  40. John P. Burgess (2004). E Pluribus Unum: Plural Logic and Set Theory. Philosophia Mathematica 12 (3):193-221.
    A new axiomatization of set theory, to be called Bernays-Boolos set theory, is introduced. Its background logic is the plural logic of Boolos, and its only positive set-theoretic existence axiom is a reflection principle of Bernays. It is a very simple system of axioms sufficient to obtain the usual axioms of ZFC, plus some large cardinals, and to reduce every question of plural logic to a question of set theory.
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  41. John P. Burgess (2004). Mathematics and Bleak House. Philosophia Mathematica 12 (1):18-36.
    The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.
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  42. John P. Burgess (2004). Quine, Analyticity and Philosophy of Mathematics. Philosophical Quarterly 54 (214):38–55.
    Quine correctly argues that Carnap's distinction between internal and external questions rests on a distinction between analytic and synthetic, which Quine rejects. I argue that Quine needs something like Carnap's distinction to enable him to explain the obviousness of elementary mathematics, while at the same time continuing to maintain as he does that the ultimate ground for holding mathematics to be a body of truths lies in the contribution that mathematics makes to our overall scientific theory of the world. Quine's (...)
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  43. John P. Burgess (2003). Review: The Limits of Abstraction by Kit Fine. [REVIEW] Notre Dame Journal Fo Formal Logic 44:227-251.
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  44. John P. Burgess (2003). Which Modal Models Are the Right Ones (for Logical Necessity)? Theoria 18 (2):145-158.
    Recently it has become almost the received wisdom in certain quarters that Kripke models are appropriate only for something like metaphysical modalities, and not for logical modalities. Here the line of thought leading to Kripke models, and reasons why they are no less appropriate for logical than for other modalities, are explained. It is also indicated where the fallacy in the argument leading to the contrary conclusion lies. The lessons learned are then applied to the question of the status of (...)
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  45. John P. Burgess (2003). A Remark on Henkin Sentences and Their Contraries. Notre Dame Journal of Formal Logic 44 (3):185-188.
    That the result of flipping quantifiers and negating what comes after, applied to branching-quantifier sentences, is not equivalent to the negation of the original has been known for as long as such sentences have been studied. It is here pointed out that this syntactic operation fails in the strongest possible sense to correspond to any operation on classes of models.
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  46. John P. Burgess (2003). Book Review: Kit Fine. The Limits of Abstraction. [REVIEW] Notre Dame Journal of Formal Logic 44 (4):227-251.
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  47. J. Burgess (2001). Set Theory. In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell Publishers. 55.
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  48. J. Burgess (1999). Review of ¸iteShapiro:PM. [REVIEW] Notre Dame Journal of Formal Logic 40 (2):283--91.
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  49. John P. Burgess (1999). Book Review: Stewart Shapiro. Philosophy of Mathematics: Structure and Ontology. [REVIEW] Notre Dame Journal of Formal Logic 40 (2):283-291.
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  50. John P. Burgess (1999). Which Modal Logic Is the Right One? Notre Dame Journal of Formal Logic 40 (1):81-93.
    The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of Supecki and Bryll, is presented for the claim that the right demonstrability logic must be contained in S5, (...)
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  51. John Burgess (1998). Occam's Razor and Scientific Method. In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press. 195--214.
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  52. John P. Burgess (1998). Quinus Ab Omni Naevo Vindicatus. In Ali A. Kazmi (ed.), Meaning and Reference. University of Calgary Press. 25--66.
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  53. John P. Burgess (1998). On a Consistent Subsystem of Frege's Grundgesetze. Notre Dame Journal of Formal Logic 39 (2):274-278.
    Parsons has given a (nonconstructive) proof that the first-order fragment of the system of Frege's Grundgesetze is consistent. Here a constructive proof of the same result is presented.
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  54. John P. Burgess & A. P. Hazen (1998). Predicative Logic and Formal Arithmetic. Notre Dame Journal of Formal Logic 39 (1):1-17.
    After a summary of earlier work it is shown that elementary or Kalmar arithmetic can be interpreted within the system of Russell's Principia Mathematica with the axiom of infinity but without the axiom of reducibility.
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  55. John P. Burgess (1997). Review: Theodore Hailperin, Sentential Probability Logic. Origins, Development, Current Status, and Technical Applications. [REVIEW] Journal of Symbolic Logic 62 (3):1040-1041.
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  56. John P. Burgess & Gideon A. Rosen (1997). A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. Oxford University Press.
    Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...)
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  57. John P. Burgess (1996). Marcus, Kripke, and Names. Philosophical Studies 84 (1):1 - 47.
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  58. John P. Burgess (1995). Frege and Arbitrary Functions. In William Demopoulos (ed.), Frege's Philosophy of Mathematics. Harvard University Press. 89--107.
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  59. John Burgess (1993). Review: Stewart Shapiro, Foundations Without Foundationalism. A Case for Second-Order Logic. [REVIEW] Journal of Symbolic Logic 58 (1):363-365.
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  60. John P. Burgess (1993). Hintikka Et Sandu Versus Frege in Re Arbitrary Functions. Philosophia Mathematica 1 (1):50-65.
    Hintikka and Sandu have recently claimed that Frege's notion of function was substantially narrower than that prevailing in real analysis today. In the present note, their textual evidence for this claim is examined in the light of relevant historical and biographical background and judged insufficient.
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  61. John P. Burgess (1992). How Foundational Work in Mathematics Can Be Relevant to Philosophy of Science. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:433 - 441.
    Foundational work in mathematics by some of the other participants in the symposium helps towards answering the question whether a heterodox mathematics could in principle be used as successfully as is orthodox mathematics in scientific applications. This question is turn, it will be argued, is relevant to the question how far current science is the way it is because the world is the way it is, and how far because we are the way we are, which is a central question, (...)
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  62. John P. Burgess (1992). Proofs About Proofs: A Defense of Classical Logic. Part I: The Aims of Classical Logic. In Michael Detlefsen (ed.), Proof, Logic, and Formalization. Routledge. 1--23.
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  63. John P. Burgess (1992). Review: Constructibility and Mathematical Existence by Charles S. Chihara. [REVIEW] Philosophical Review 101:916-918.
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  64. John P. Burgess (1991). Synthetic Mechanics Revisited. Journal of Philosophical Logic 20 (2):121 - 130.
    Earlier results on eliminating numerical objects from physical theories are extended to results on eliminating geometrical objects.
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  65. John P. Burgess (1989). Boolos George. To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables). The Journal of Philosophy, Vol. 81 (1984), Pp. 430–449. Boolos George. Nominalist Platonism, The Philosophical Review, Vol. 94 (1985), Pp. 327–344. [REVIEW] Journal of Symbolic Logic 54 (2):616-617.
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  66. John P. Burgess (1989). Review: George Boolos, To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables); George Boolos, Nominalist Platonism. [REVIEW] Journal of Symbolic Logic 54 (2):616-617.
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  67. John P. Burgess (1988). Addendum to "the Truth is Never Simple". Journal of Symbolic Logic 53 (2):390-392.
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  68. John P. Burgess (1988). Sets and Point-Sets: Five Grades of Set-Theoretic Involvement in Geometry. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:456 - 463.
    The consequences for the theory of sets of points of the assumption of sets of sets of points, sets of sets of sets of points, and so on, are surveyed, as more generally are the differences among the geometric theories of points, of finite point-sets, of point-sets, of point-set-sets, and of sets of all ranks.
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  69. John P. Burgess (1986). The Truth is Never Simple. Journal of Symbolic Logic 51 (3):663-681.
    The complexity of the set of truths of arithmetic is determined for various theories of truth deriving from Kripke and from Gupta and Herzberger.
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  70. John P. Burgess (1985). [Omnibus Review]. Journal of Symbolic Logic 50 (2):544-547.
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  71. John P. Burgess (1985). From Preference to Utility: A Problem of Descriptive Set Theory. Notre Dame Journal of Formal Logic 26 (2):106-114.
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  72. John P. Burgess & Yuri Gurevich (1985). The Decision Problem for Linear Temporal Logic. Notre Dame Journal of Formal Logic 26 (2):115-128.
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  73. John P. Burgess (1984). Beyond Tense Logic. [REVIEW] Journal of Philosophical Logic 13 (3):235-248.
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  74. John P. Burgess (1984). Review: Beyond Tense Logic. [REVIEW] Journal of Philosophical Logic 13 (3):235 - 248.
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  75. John P. Burgess (1984). Synthetic Mechanics. Journal of Philosophical Logic 13 (4):379 - 395.
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  76. John P. Burgess (1984). Dummett's Case for Intuitionism. History and Philosophy of Logic 5 (2):177-194.
    Dummett's case against platonism rests on arguments concerning the acquisition and manifestation of knowledge of meaning. Dummett's arguments are here criticized from a viewpoint less Davidsonian than Chomskian. Dummett's case against formalism is obscure because in its prescriptive considerations are not clearly separated from descriptive. Dummett's implicit value judgments are here made explicit and questioned. ?Combat Revisionism!? Chairman Mao.
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  77. John P. Burgess (1984). Read on Relevance: A Rejoinder. Notre Dame Journal of Formal Logic 25 (3):217-223.
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  78. John P. Burgess (1983). Common Sense and ``Relevance''. Notre Dame Journal of Formal Logic 24 (1):41-53.
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  79. John P. Burgess (1983). Why I Am Not a Nominalist. Notre Dame Journal of Formal Logic 24 (1):93-105.
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  80. John P. Burgess (1982). Review: Robert Vaught, A. R. D. Mathias, H. Rogers, Descriptive Set Theory in $L{Omega1omega}$; Robert Vaught, Invariant Sets in Topology and Logic. [REVIEW] Journal of Symbolic Logic 47 (1):217-218.
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  81. John P. Burgess (1982). Axioms for Tense Logic. I. ``Since'' and ``Until''. Notre Dame Journal of Formal Logic 23 (4):367-374.
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  82. John P. Burgess (1982). Axioms for Tense Logic. II. Time Periods. Notre Dame Journal of Formal Logic 23 (4):375-383.
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  83. John P. Burgess (1981). Careful Choices---A Last Word on Borel Selectors. Notre Dame Journal of Formal Logic 22 (3):219-226.
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  84. John P. Burgess (1981). Quick Completeness Proofs for Some Logics of Conditionals. Notre Dame Journal of Formal Logic 22 (1):76-84.
  85. John P. Burgess (1981). Relevance: A Fallacy? Notre Dame Journal of Formal Logic 22 (2):97-104.
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  86. John P. Burgess (1981). The Completeness of Intuitionistic Propositional Calculus for its Intended Interpretation. Notre Dame Journal of Formal Logic 22 (1):17-28.
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  87. John P. Burgess (1980). Brouwer and Souslin on Transfinite Cardinals. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (14-18):209-214.
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  88. John P. Burgess (1980). Decidability for Branching Time. Studia Logica 39 (2-3):203 - 218.
    The species of indeterminist tense logic called Peircean by A. N. Prior is proved to be recursively decidable.
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  89. John P. Burgess (1979). Logic and Time. Journal of Symbolic Logic 44 (4):566-582.
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  90. John P. Burgess (1978). Consistency Proofs in Model Theory: A Contribution to Jensenlehre. Annals of Mathematical Logic 14 (1):1-12.
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  91. John P. Burgess (1978). On the Hanf Number of Souslin Logic. Journal of Symbolic Logic 43 (3):568-571.
    We show it is consistent with ZFC that the Hanf number of Ellentuck's Souslin logic should be exactly $\beth_{\omega_2}$.
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  92. John P. Burgess (1978). The Unreal Future. Theoria 44 (3):157-179.
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  93. John P. Burgess (1977). Review: Hao Wang, From Mathematics to Philosophy. [REVIEW] Journal of Symbolic Logic 42 (4):579-580.
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  94. John P. Burgess (1970). Review: C. L. Hamblin, The Modal "Probably.". [REVIEW] Journal of Symbolic Logic 35 (4):582-583.
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  95. John P. Burgess (1970). Review: Nicholas Rescher, A Probabilistic Approach to Modal Logic. [REVIEW] Journal of Symbolic Logic 35 (4):583-583.
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  96. John P. Burgess (1969). Probability Logic. Journal of Symbolic Logic 34 (2):264-274.
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  97. John Burgess, Review of Charles Parsons: Mathematical Thought and its Objects. [REVIEW]
    This long-awaited volume is a must-read for anyone with a serious interest in\nphilosophy of mathematics. The book falls into two parts, with the primary focus of\nthe first on ontology and structuralism, and the second on intuition and\nepistemology, though with many links between them. The style throughout involves\nunhurried examination from several points of view of each issue addressed, before\nreaching a guarded conclusion. A wealth of material is set before the reader along\nthe way, but a reviewer wishing to summarize the author’s views (...)
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  98. John Burgess, Tarski's Tort.
    A revision of a sermon on the evils of calling model theory “semantics”, preached at Notre Dame on Saint Patrick’s Day, 2005. Provisional version: references remain to be added. To appear in Mathematics, Modality, and Models: Selected Philosophical Papers, coming from Cambridge University Press.
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  99. John P. Burgess, Friedman and the Axiomatization of Kripke's Theory of Truth.
    What is the simplest and most natural axiomatic replacement for the set-theoretic definition of the minimal fixed point on the Kleene scheme in Kripke’s theory of truth? What is the simplest and most natural set of axioms and rules for truth whose adoption by a subject who had never heard the word "true" before would give that subject an understanding of truth for which the minimal fixed point on the Kleene scheme would be a good model? Several axiomatic systems, old (...)
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  100. John P. Burgess, Putting Structuralism in its Place.
    One textbook may introduce the real numbers in Cantor’s way, and another in Dedekind’s, and the mathematical community as a whole will be completely indifferent to the choice between the two. This sort of phenomenon was famously called to the attention of philosophers by Paul Benacerraf. It will be argued that structuralism in philosophy of mathematics is a mistake, a generalization of Benacerraf’s observation in the wrong direction, resulting from philosophers’ preoccupation with ontology.
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  101. John P. Burgess, Reviewed By.
    In this era when results of empirical scientific research are being appealed to all across philosophy, when we even find moral philosophers invoking the results of brain scans, many profess to practice "naturalized epistemology," or to be "epistemological naturalists." Such phrases derive from the title of a well-known essay by Quine,[1] but Paul Gregory's thesis in the work under review is that there is less connection than is usually assumed between Quine's variety of naturalized epistemology and what is today taken, (...)
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  102. John P. Burgess, Two Undecidable Questions About Group Actions.
    It is shown that for invariance under the action of special groups the statements "Every invariant PCA is decomposable into (1 invariant Borel sets" and "Every pair of invariant PCA is reducible by a pair of invariant PCA sets" are independent of the axioms of set theory.
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