167 found
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  1. A subject with no object: strategies for nominalistic interpretation of mathematics.John P. Burgess & Gideon Rosen - 1997 - New York: Oxford University Press. Edited by Gideon A. Rosen.
    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 (...)
  2.  39
    Rigor and Structure.John P. Burgess - 2015 - Oxford, England: Oxford University Press UK.
    While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics (...)
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  3.  75
    Fixing Frege.John P. Burgess - 2005 - 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 ...
  4. Truth.Alexis G. Burgess & John P. Burgess - 2011 - 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 (...)
  5.  78
    A Subject with no Object.Zoltan Gendler Szabo, John P. Burgess & Gideon Rosen - 1999 - Philosophical Review 108 (1):106.
    This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...)
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  6. Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 2003 - Bulletin of Symbolic Logic 9 (4):520-521.
     
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  7.  35
    Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 1974 - Cambridge, England: Cambridge University Press. Edited by John P. Burgess & Richard C. Jeffrey.
    This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book 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, (...)
  8. Philosophical Logic.John P. Burgess - 2009 - Princeton, NJ, USA: Princeton University Press.
    Philosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic, focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances the (...)
  9.  11
    Fixing Frege.John P. Burgess - 2005 - Princeton University Press.
    The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been (...)
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  10.  46
    Abstract Objects.John P. Burgess - 1992 - Philosophical Review 101 (2):414.
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  11. Why I am not a nominalist.John P. Burgess - 1983 - Notre Dame Journal of Formal Logic 24 (1):93-105.
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  12. Truth.Alexis G. Burgess & John P. Burgess - 2011 - Bulletin of Symbolic Logic 18 (2):271-272.
  13. On a derivation of the necessity of identity.John P. Burgess - 2014 - 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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  14.  70
    Truth and the Absence of Fact.John P. Burgess - 2002 - Philosophical Review 111 (4):602-604.
    This volume reprints a dozen of the author’s papers, most with substantial postscripts, and adds one new one. The bulk of the material is on topics in philosophy of language, but there are also two papers on philosophy of mathematics written after the appearance of the author’s collected papers on that subject, and one on epistemology. As to the substance of Field’s contributions, limitations of space preclude doing much more below than indicating the range of issues addressed, and the general (...)
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  15. The truth is never simple.John P. Burgess - 1986 - 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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  16.  73
    Platonism and Anti-Platonism in Mathematics.John P. Burgess - 2001 - Philosophical Review 110 (1):79.
    Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and Quine, tells us there exist no numbers at all, and so no prime numbers. Nominalists are aware that the assertion of the existence of prime numbers is warranted by the standards of mathematical science; they simply reject scientific standards of warrant.
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  17. A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics.John P. Burgess & Gideon Rosen - 2001 - Studia Logica 67 (1):146-149.
     
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  18. Quick completeness proofs for some logics of conditionals.John P. Burgess - 1981 - Notre Dame Journal of Formal Logic 22 (1):76-84.
  19. Mathematics and bleak house.John P. Burgess - 2004 - 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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  20. E pluribus unum: Plural logic and set theory.John P. Burgess - 2004 - 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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  21. A Subject with No Object. Strategies for Nominalistic Interpretations of Mathematics.John P. Burgess & Gideon Rosen - 1999 - Noûs 33 (3):505-516.
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  22. Logic and time.John P. Burgess - 1979 - Journal of Symbolic Logic 44 (4):566-582.
  23. Philosophical logic.John P. Burgess - 2010 - Bulletin of Symbolic Logic 16 (3):411-413.
     
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  24. Which Modal Logic Is the Right One?John P. Burgess - 1999 - 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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  25.  79
    Decidability for branching time.John P. Burgess - 1980 - 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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  26.  2
    Nominalism Reconsidered.John P. Burgess & Gideon Rosen - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: Oxford University Press.
    Nominalism is the view that mathematical objects do not exist. This chapter delimits several types of nominalistic projects: revolutionary programs that attempt to change mathematics and hermeneutic programs that attempt to interpret mathematics. Some programs accord with naturalism, and some oppose naturalism. Steven Yablo’s fictionalism is brought into the fold and discussed at some length.
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  27. Occam's razor and scientific method.John P. Burgess - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 195--214.
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  28. The unreal future.John P. Burgess - 1978 - Theoria 44 (3):157-179.
    Perhaps if the future existed, concretely and individually, as something that could be discerned by a better brain, the past would not be so seductive: its demands would he balanced by those of the future. Persons might then straddle the middle stretch of the seesaw when considering this or that object. It might be fun. But the future has no such reality (as the pictured past and the perceived present possess); the future is but a figure of speech, a specter (...)
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  29.  71
    Synthetic mechanics.John P. Burgess - 1984 - Journal of Philosophical Logic 13 (4):379 - 395.
  30. Madagascar revisited.John P. Burgess - 2014 - Analysis 74 (2):195-201.
    The history behind the ‘Madagascar’ example of Gareth Evans is traced, suggesting that the decisive reference-shift occurred in the 16th, not the 17, century. The difference between this example and the ‘Gödel’ example of Saul Kripke is explained in terms of the distinction between de re and de dicto beliefs and intentions.
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  31.  88
    Quinus ab Omni Nævo Vindicatus.John P. Burgess - 1997 - Canadian Journal of Philosophy 27 (sup1):25-65.
    Today there appears to be a widespread impression that W. V. Quine's notorious critique of modal logic, based on certain ideas about reference, has been successfully answered. As one writer put it some years ago: “His objections have been dead for a while, even though they have not yet been completely buried.” What is supposed to have killed off the critique? Some would cite the development of a new ‘possible-worlds’ model theory for modal logics in the 1960s; others, the development (...)
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  32. Quine, analyticity and philosophy of mathematics.John P. Burgess - 2004 - 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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  33.  72
    Relevance: a fallacy?John P. Burgess - 1981 - Notre Dame Journal of Formal Logic 22 (2):97-104.
  34. Being Explained Away.John P. Burgess - 2005 - The Harvard Review of Philosophy 13 (2):41-56.
    When I first began to take an interest in the debate over nominalism in philosophy of mathematics, some twenty-odd years ago, the issue had already been under discussion for about a half-century. The terms of the debate had been set: W. V. Quine and others had given “abstract,” “nominalism,” “ontology,” and “Platonism” their modern meanings. Nelson Goodman had launched the project of the nominalistic reconstruction of science, or of the mathematics used in science, in which Quine for a time had (...)
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  35. Quinus ab omni naevo vindicatus.John P. Burgess - 1998 - In Ali A. Kazmi (ed.), Meaning and Reference. University of Calgary Press. pp. 25--66.
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  36. Against Ethics.John P. Burgess - 2007 - 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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  37.  35
    Axioms for tense logic. I. "Since" and "until".John P. Burgess - 1982 - Notre Dame Journal of Formal Logic 23 (4):367-374.
  38.  23
    From Mathematics to Philosophy.John P. Burgess - 1977 - Journal of Symbolic Logic 42 (4):579-580.
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  39.  39
    No requirement of relevance.John P. Burgess - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: Oxford University Press. pp. 727--750.
    There are schools of logicians who claim that an argument is not valid unless the conclusion is relevant to the premises. In particular, relevance logicians reject the classical theses that anything follows from a contradiction and that a logical truth follows from everything. This chapter critically evaluates several different motivations for relevance logic, and several systems of relevance logic, finding them all wanting.
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  40.  28
    Lewis on Mereology and Set Theory.John P. Burgess - 2015 - In Barry Loewer & Jonathan Schaffer (eds.), A companion to David Lewis. Chichester, West Sussex ;: Wiley-Blackwell. pp. 459–469.
    David Lewis in the short monograph Parts of Classes (PC) undertakes a fundamental re‐examination of the relationship between mereology, the general theory of parts, and set theory, the general theory of collections. Given Lewis's theses, to be an element of a set or member of class is just to have a singleton that is a part thereof. Lewis in PC adds a claim of kind of ontological innocence, comparable to that of first‐order logic, for mereology. The only substantive assumption of (...)
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  41. Dummett's case for intuitionism.John P. Burgess - 1984 - 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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  42.  65
    Deflating Existential Consequence: A Case for Nominalism.John P. Burgess - 2004 - Bulletin of Symbolic Logic 10 (4):573-577.
  43. Mathematics, Models, and Modality: Selected Philosophical Essays.John P. Burgess - 2008 - 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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  44. Friedman and the axiomatization of Kripke's theory of truth.John P. Burgess - unknown
    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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  45.  43
    Kripke.John P. Burgess - 2012 - Malden, MA: Polity.
    Saul Kripke has been a major influence on analytic philosophy and allied fields for a half-century and more. His early masterpiece, _Naming and Necessity_, reversed the pattern of two centuries of philosophizing about the necessary and the contingent. Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection _Philosophical Troubles_. In this book Kripke’s long-time colleague, the logician and philosopher John P. Burgess, offers a thorough and self-contained guide to (...)
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  46.  52
    On a Consistent Subsystem of Frege's Grundgesetze.John P. Burgess - 1998 - 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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  47.  34
    Common sense and "relevance".John P. Burgess - 1983 - Notre Dame Journal of Formal Logic 24 (1):41-53.
  48.  37
    The decision problem for linear temporal logic.John P. Burgess & Yuri Gurevich - 1985 - Notre Dame Journal of Formal Logic 26 (2):115-128.
  49.  78
    Probability logic.John P. Burgess - 1969 - Journal of Symbolic Logic 34 (2):264-274.
    In this paper we introduce a system S5U, formed by adding to the modal system S5 a new connective U, Up being read “probably”. A few theorems are derived in S5U, and the system is provided with a decision procedure. Several decidable extensions of S5U are discussed, and probability logic is related to plurality quantification.
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  50. Putting structuralism in its place.John P. Burgess - unknown
    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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