•  45
    Translating Logical Terms
    Topoi 38 (2): 291-303. 2019.
    The is an old question over whether there is a substantial disagreement between advocates of different logics, as they simply attach different meanings to the crucial logical terminology. The purpose of this article is to revisit this old question in light a pluralism/relativism that regards the various logics as equally legitimate, in their own contexts. We thereby address the vexed notion of translation, as it occurs between mathematical theories. We articulate and defend a thesis that the not…Read more
  •  45
    Intentional Mathematics (edited book)
    Elsevier. 1985.
    Among the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.
  • Philosophy of Mathematics: Structure and Ontology
    Philosophical Quarterly 50 (198): 120-123. 2000.
  •  24
    Comparing implicit and explicit memory for brand names from advertisements
    with H. Shanker Krishnan
    Journal of Experimental Psychology: Applied 2 (2): 147. 1996.
  •  36
    The Company Kept by Cut Abstraction (and its Relatives)
    Philosophia Mathematica 19 (2): 107-138. 2011.
    This article concerns the ongoing neo-logicist program in the philosophy of mathematics. The enterprise began life, in something close to its present form, with Crispin Wright’s seminal [1983]. It was bolstered when Bob Hale [1987] joined the fray on Wright’s behalf and it continues through many extensions, objections, and replies to objections . The overall plan is to develop branches of established mathematics using abstraction principles in the form: Formula where a and b are variables of a g…Read more
  •  159
    Higher-Order Logic or Set Theory: A False Dilemma
    Philosophia Mathematica 20 (3): 305-323. 2012.
    The purpose of this article is show that second-order logic, as understood through standard semantics, is intimately bound up with set theory, or some other general theory of interpretations, structures, or whatever. Contra Quine, this does not disqualify second-order logic from its role in foundational studies. To wax Quinean, why should there be a sharp border separating mathematics from logic, especially the logic of mathematics?
  •  41
    Remarks on the development of computability
    History and Philosophy of Logic 4 (1-2): 203-220. 1983.
    The purpose of this article is to examine aspects of the development of the concept and theory of computability through the theory of recursive functions. Following a brief introduction, Section 2 is devoted to the presuppositions of computability. It focuses on certain concepts, beliefs and theorems necessary for a general property of computability to be formulated and developed into a mathematical theory. The following two sections concern situations in which the presuppositions were realized …Read more
  •  137
    Mathematical structuralism
    Philosophia Mathematica 4 (2): 81-82. 1996.
  •  585
    What is mathematical logic?
    Philosophia 8 (1): 79-94. 1978.
    This review concludes that if the authors know what mathematical logic is they have not shared their knowledge with the readers. This highly praised book is replete with errors and incoherency.
  •  60
    Space, number and structure: A tale of two debates
    Philosophia Mathematica 4 (2): 148-173. 1996.
    Around the turn of the century, Poincare and Hilbert each published an account of geometry that took the discipline to be an implicit definition of its concepts. The terms ‘point’, ‘line’, and ‘plane’ can be applied to any system of objects that satisfies the axioms. Each mathematician found spirited opposition from a different logicist—Russell against Poincare' and Frege against Hilbert— who maintained the dying view that geometry essentially concerns space or spatial intuition. The debates ill…Read more
  •  53
    Effectiveness
    In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics, Springer. pp. 37--49. 2006.
  •  46
    Structure and ontology
    Philosophical Topics 17 (2): 145-171. 1989.
  •  20
    Consumer memory for intentions: A prospective memory perspective
    with H. Shanker Krishnan
    Journal of Experimental Psychology: Applied 5 (2): 169. 1999.
  •  1
    Vagueness, Metaphysics, and Objectivity
    In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds: Vaguenesss, its Nature and its Logic, Oxford University Press. 2010.
  •  1
  •  23
    The Work of John Corcoran: An Appreciation
    with Stewart Shapiro and Michael Scanlan
    History and Philosophy of Logic 20 (3-4): 149-158. 1999.
  •  43
    Turing projectability
    with Timothy McCarthy
    Notre Dame Journal of Formal Logic 28 (4): 520-535. 1987.
  •  72
    Prolegomenon To Any Future Neo‐Logicist Set Theory: Abstraction And Indefinite Extensibility
    British Journal for the Philosophy of Science 54 (1): 59-91. 2003.
    The purpose of this paper is to assess the prospects for a neo-logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): PQ[Ext(P) = Ext(Q) [(BAD(P) & BAD(Q)) x(Px Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’. 1 Background: what and why? 2 Framew…Read more
  •  40
    Book reviews (review)
    with Ben-Ami Scharfstein, Gary Jason, John Blackmore, R. A. Naulty, and F. Bradford Wallack
    Philosophia 17 (4): 551-570. 1987.
  •  19
    The governance of identity
    In Fraser MacBride (ed.), Identity and Modality, Oxford University Press. pp. 164--173. 2006.
  •  6
    Intentional forgetting as a facilitator for recalling new product attributes
    with Charles Lindsey and H. Shanker Krishnan
    Journal of Experimental Psychology: Applied 12 (4): 251-263. 2006.