•  1
    Book Reviews (review)
    with Desmond Paul Henry, A. Broadie, de Jong R. Willem, James Gasser, J. W. van Evra, Lewis C. Albert, J. Jay Zeman, Gabriel Nuchelmans, G. H. Bird, Jan Woleński, Barry Smith, and C. Cellucci
    History and Philosophy of Logic 9 (1): 107-129. 1988.
  • Book reviews (review)
    with Richard Shusterman, Rudolf Haller, L. Nathan Oaklander, L. E. Goodman, and George N. Schlesinger
    Peer Reviewed.
  •  14
    John Corcoran
    with José M. Sagüillo and Michael Scanlan
    History and Philosophy of Logic 42 (3): 201-223. 2021.
    We present a memorial summary of the professional life and contributions to logic of John Corcoran. We also provide a full list of his many publications.Courtesy of Lynn Corcoran.
  • Simple Truth, Contradiction, and Consistency
    In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Clarendon Press. 2006.
  •  7
    Mereological Singularism and Paradox
    Erkenntnis 1-20. forthcoming.
    The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “set-like entities”—is that it is ultimately incoherent. The most forceful form of this charge is due to Barry Schein, who argues that singularists must accept a certain comprehension principle which entails the existence of things having the contradictory property of being both atomic and non-atomic. The purpose of this paper is to defuse Schein’s argument, by noting thr…Read more
  •  70
    Logic and science: science and logic
    Synthese 1-26. forthcoming.
    According to Ole Hjortland, Timothy Williamson, Graham Priest, and others, anti-exceptionalism about logic is the view that logic “isn’t special”, but is continuous with the sciences. Logic is revisable, and its truths are neither analytic nor a priori. And logical theories are revised on the same grounds as scientific theories are. What isn’t special, we argue, is anti-exceptionalism about logic. Anti-exceptionalists disagree with one another regarding what logic and, indeed, anti-exceptionalis…Read more
  •  17
    Group nouns and pseudo‐singularity
    Thought: A Journal of Philosophy 10 (1): 66-77. 2021.
    Thought: A Journal of Philosophy, EarlyView.
  •  2
    Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.
  •  40
    A Note on Choice Principles in Second-order Logic
    with Benjamin Siskind and Paolo Mancosu
    Review of Symbolic Logic 1-12. forthcoming.
  •  2
    The interaction between philosophy and mathematics has a long and well articulated history. The purpose of this note is to sketch three historical case studies that highlight and further illustrate some details concerning the relationship between the two: the interplay between mathematical and philosophical methods in ancient Greek thought; vagueness and the relation between mathematical logic and ordinary language; and the study of the notion of continuity.
  •  9
    Inconsistency and Incompleteness, Revisited
    In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 469-479. 2019.
    Graham Priest introduces an informal but presumably rigorous and sharp ‘provability predicate’. He argues that this predicate yields inconsistencies, along the lines of the paradox of the Knower. One long-standing claim of Priest’s is that a dialetheist can have a complete, decidable, and yet sufficiently rich mathematical theory. After all, the incompleteness theorem is, in effect, that for any recursive theory A, if A is consistent, then A is incomplete. If the antecedent fails, as it might fo…Read more
  •  30
    Logical pluralism and normativity
    Inquiry: An Interdisciplinary Journal of Philosophy 63 (3-4): 389-410. 2020.
    We are logical pluralists who hold that the right logic is dependent on the domain of investigation; different logics for different mathematical theories. The purpose of this article is to explore the ramifications for our pluralism concerning normativity. Is there any normative role for logic, once we give up its universality? We discuss Florian Steingerger’s “Frege and Carnap on the Normativity of Logic” as a source for possible types of normativity, and then turn to our own proposal, which po…Read more
  •  15
    Mathematics in Philosophy, Selected Essays
    Journal of Symbolic Logic 53 (1): 320. 1983.
  •  9
    The Limits of Abstraction
    Philosophical Quarterly 54 (214): 166-174. 2004.
  • Link's Revenge: A Case Study in Natural Language Mereology
    In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics, De Gruyter. pp. 3-36. 2019.
  •  14
    Introduction to Special Issue: The Emergence of Structuralism
    with Prokop Sousedik and David Svoboda
    Philosophia Mathematica 27 (3): 299-302. 2019.
  •  39
    Friedrich Waismann: The Open Texture of Analytic Philosophy (edited book)
    Palgrave Macmillan. 2019.
    This edited collection covers Friedrich Waismann's most influential contributions to twentieth-century philosophy of language: his concepts of open texture and language strata, his early criticism of verificationism and the analytic-synthetic distinction, as well as their significance for experimental and legal philosophy. In addition, Waismann's original papers in ethics, metaphysics, epistemology and the philosophy of mathematics are here evaluated. They introduce Waismann's theory of action a…Read more
  •  211
    In light of the close connection between the ontological hierarchy of set theory and the ideological hierarchy of type theory, Øystein Linnebo and Agustín Rayo have recently offered an argument in favour of the view that the set-theoretic universe is open-ended. In this paper, we argue that, since the connection between the two hierarchies is indeed tight, any philosophical conclusions cut both ways. One should either hold that both the ontological hierarchy and the ideological hierarchy are ope…Read more
  •  2
    The Continuous (edited book)
    Oxford University Press. forthcoming.
  •  2
    An Introduction to Non-classical Logic (review)
    Review of Metaphysics 56 (3): 670-671. 2003.
    This book is just what its title says: an introduction to nonclassical logic. And it is a very good one. Given the extensive interest in nonclassical logics, in various parts of the philosophical scene, it is a welcome addition to the corpus. Typical courses in logic, at all levels and in both philosophy departments and mathematics departments, focus exclusively on classical logic. Most instructors, and some textbooks, give some mention to some nonclassical systems, but usually few details are p…Read more
  • Philosophy of Mathematics: Structure and Ontology
    Oxford University Press USA. 1997.
    Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
  •  64
    The answers to the questions in the title depend on the kind of pluralism one is talking about. We will focus here on our own views. The purpose of this article is to trace out some possible connections between these kinds of pluralism. We show how each of them might bear on the other, depending on how certain open questions are resolved.
  •  27
    Ineffability within the limits of abstraction alone
    In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics, Oxford University Press. 2016.
    The purpose of this article is to assess the prospects for a Scottish neo-logicist foundation for a set theory. We show how to reformulate a key aspect of our set theory as a neo-logicist abstraction principle. That puts the enterprise on the neo-logicist map, and allows us to assess its prospects, both as a mathematical theory in its own right and in terms of the foundational role that has been advertised for set theory. On the positive side, we show that our abstraction based theory can be mod…Read more