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Profile: John Burgess (Princeton University)
  1. 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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  2.  7
    Alexis G. Burgess & John P. Burgess (2011). Truth. Princeton University Press.
    This is a concise, advanced introduction to current philosophical debates about truth. A blend of philosophical and technical material, the book is organized around, but not limited to, the tendency known as deflationism, according to which there is not much to say about the nature of truth. In clear language, Burgess and Burgess cover a wide range of issues, including the nature of truth, the status of truth-value gaps, the relationship between truth and meaning, relativism and pluralism about truth, and (...)
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  3.  20
    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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  4. 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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  5.  31
    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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  6. John P. Burgess (forthcoming). Book Review: Text and Psyche: Experiencing Scripture Today. [REVIEW] Interpretation 53 (4):430-431.
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  7.  86
    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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  8.  44
    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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  9.  50
    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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  10.  96
    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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  11.  42
    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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  12.  86
    John P. Burgess (2005). Being Explained Away. The Harvard Review of Philosophy 13 (2):41-56.
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  13.  79
    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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  14. 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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  15. 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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  16.  37
    John P. Burgess (2014). New Foundations for Physical Geometry: The Theory of Linear Structures, by Tim Maudlin. Australasian Journal of Philosophy 93 (1):187-190.
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  17. John P. Burgess (2013). Saul Kripke: Puzzles and Mysteries. Polity.
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  18.  34
    John P. Burgess (1981). Quick Completeness Proofs for Some Logics of Conditionals. Notre Dame Journal of Formal Logic 22 (1):76-84.
  19.  74
    John P. Burgess (2013). On a Derivation of the Necessity of Identity. Synthese 191 (7):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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  20.  24
    John P. Burgess (2013). Quinus Ab Omni Nævo Vindicatus. Canadian Journal of Philosophy 27 (sup1):25-65.
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  21.  54
    John P. Burgess (1983). Why I Am Not a Nominalist. Notre Dame Journal of Formal Logic 24 (1):93-105.
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  22.  57
    John P. Burgess (forthcoming). Book Review: The Ten Commandments: A Preaching Commentary. [REVIEW] Interpretation 57 (4):452-452.
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  23.  10
    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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  24. John P. Burgess & Gideon Rosen (1999). A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. Oxford University Press Uk.
    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 abstract entities, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. A Subject With No Object cuts through a host of technicalities that (...)
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  25.  40
    John P. Burgess (1978). The Unreal Future. Theoria 44 (3):157-179.
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  26.  44
    John P. Burgess (1979). Logic and Time. Journal of Symbolic Logic 44 (4):566-582.
  27.  24
    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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  28.  94
    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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  29.  44
    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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  30.  17
    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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  31.  11
    John P. Burgess (2004). Deflating Existential Consequence: A Case for Nominalism. Bulletin of Symbolic Logic 10 (4):573-577.
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  32. 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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  33.  1
    John P. Burgess (2003). Is There a Problem About the Deflationary Theory of Truth? In Leon Horsten & Volker Halbach (eds.), Principles of Truth. De Gruyter 37-56.
  34.  64
    John P. Burgess (2005). Translating Names. Analysis 65 (287):196–205.
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  35.  15
    John P. Burgess (2014). Kevin Scharp, Replacing Truth. Studia Logica 102 (5):1087-1089.
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  36.  93
    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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  37.  5
    John P. Burgess (2004). A Philosophical Guide to Conditionals. Bulletin of Symbolic Logic 10 (4):565-570.
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  38.  22
    John P. Burgess (1984). Synthetic Mechanics. Journal of Philosophical Logic 13 (4):379 - 395.
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  39.  21
    John P. Burgess (1981). Relevance: A Fallacy? Notre Dame Journal of Formal Logic 22 (2):97-104.
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  40. John P. Burgess (2008). Mathematics, Models, and Modality: Selected Philosophical Essays. Cambridge University Press.
    John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy (...)
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  41.  10
    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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  42.  27
    John P. Burgess (2008). Thomas McKay. Plural Predication. Philosophia Mathematica 16 (1):133-140.
    This work, the first book-length study of its topic, is an important contribution to the literature of philosophical logic and philosophy of language, with implications for other branches of philosophy, including philosophy of mathematics. However, five of the book's ten chapters , including many of the author's most original contributions, are devoted to issues about natural language, and lie pretty well outside the scope of this journal, not to mention that of the reviewer's competence. For this reason I will here (...)
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  43. 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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  44.  64
    John P. Burgess (2000). Critical Studies / Book Reviews. Philosophia Mathematica 8 (1):84-91.
  45.  69
    John P. Burgess (2008). Charles Parsons. Mathematical Thought and its Objects. Philosophia Mathematica 16 (3):402-409.
    This long-awaited volume is a must-read for anyone with a serious interest in philosophy of mathematics. The book falls into two parts, with the primary focus of the first on ontology and structuralism, and the second on intuition and epistemology, though with many links between them. The style throughout involves unhurried examination from several points of view of each issue addressed, before reaching a guarded conclusion. A wealth of material is set before the reader along the way, but a reviewer (...)
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  46.  14
    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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  47.  35
    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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  48.  8
    John P. Burgess (2012). Frege’s Theorem by Richard G. Heck, Jr. Journal of Philosophy 109 (12):728-732.
  49. 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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  50.  22
    John P. Burgess (1969). Probability Logic. Journal of Symbolic Logic 34 (2):264-274.
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