•  19
    Chapter Four. Conditional Logic
    In J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 71-98. 1969.
  •  25
    Is There a Problem about the Deflationary Theory of Truth?
    In Leon Horsten & Volker Halbach (eds.), Principles of Truth, De Gruyter. pp. 37-56. 2003.
  •  20
    Modal Logic in the Modal Sense of Modality (review)
    In Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics, De Gruyter. pp. 51-72. 2015.
  •  43
    Kevin Scharp, Replacing Truth
    Studia Logica 102 (5): 1087-1089. 2014.
  • Frege and arbitrary functions
    In William Demopoulos (ed.), Frege's philosophy of mathematics, Harvard University Press. pp. 89--107. 1995.
  •  13
    Two Soviet Studies on Frege
    Telos: Critical Theory of the Contemporary 1969 (4): 248-254. 1969.
  •  26
    Brouwer and Souslin on Transfinite Cardinals
    Mathematical Logic Quarterly 26 (14-18): 209-214. 1980.
  •  6
    [Omnibus Review]
    Journal of Symbolic Logic 50 (2): 544-547. 1985.
  •  281
    Being Explained Away
    The Harvard Review of Philosophy 13 (2): 41-56. 2005.
    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 …Read more
  •  41
    Kripke Models
    In Alan Berger (ed.), Saul Kripke, Cambridge University Press. 2011.
    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 …Read more
  •  135
    The unreal future
    Theoria 44 (3): 157-179. 1978.
    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 of thought.
  •  43
    Predicative Logic and Formal Arithmetic
    with A. P. Hazen
    Notre Dame Journal of Formal Logic 39 (1): 1-17. 1998.
    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
  •  34
    A Remark on Henkin Sentences and Their Contraries
    Notre Dame Journal of Formal Logic 44 (3): 185-188. 2003.
    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
  •  125
    Which Modal Logic Is the Right One?
    Notre Dame Journal of Formal Logic 40 (1): 81-93. 1999.
    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 logi…Read more
  •  46
    Book Review: Kit Fine. The Limits of Abstraction (review)
    Notre Dame Journal of Formal Logic 44 (4): 227-251. 2003.
  •  35
    On a Consistent Subsystem of Frege's Grundgesetze
    Notre Dame Journal of Formal Logic 39 (2): 274-278. 1998.
    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
  •  61
    Axiomatizing the Logic of Comparative Probability
    Notre Dame Journal of Formal Logic 51 (1): 119-126. 2010.
    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 as an axiom. The simplest kind of onepremise in…Read more
  • Review: The limits of abstraction by Kit fine (review)
    Notre Dame Journal Fo Formal Logic 44 227-251. 2003.
  •  118
    Quinus ab omni naevo vindicatus
    In Ali A. Kazmi (ed.), Meaning and Reference, University of Calgary Press. pp. 25--66. 1998.
  •  211
    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 o…Read more
  •  77
    3. Cats, Dogs, and so on
    In Dean W. Zimmerman (ed.), Oxford Studies in Metaphysics, Oxford University Press. pp. 4--56. 2008.
  •  168
    The truth is never simple
    Journal of Symbolic Logic 51 (3): 663-681. 1986.
    The complexity of the set of truths of arithmetic is determined for various theories of truth deriving from Kripke and from Gupta and Herzberger.
  • Index
    In J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 149-153. 1969.
  •  62
    Synthetic mechanics
    Journal of Philosophical Logic 13 (4). 1984.