
14John CorcoranHistory and Philosophy of Logic 42 (3): 201223. 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 ConsistencyIn Graham Priest, J. C. Beall & Bradley ArmourGarb (eds.), The Law of NonContradiction: New Philosophical Essays, Clarendon Press. 2006.

6Mereological Singularism and ParadoxErkenntnis 120. forthcoming.The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “setlike 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 nonatomic. The purpose of this paper is to defuse Schein’s argument, by noting thr…Read more

70Logic and science: science and logicSynthese 126. forthcoming.According to Ole Hjortland, Timothy Williamson, Graham Priest, and others, antiexceptionalism 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 antiexceptionalism about logic. Antiexceptionalists disagree with one another regarding what logic and, indeed, antiexceptionalis…Read more

17Group nouns and pseudo‐singularityThought: A Journal of Philosophy 10 (1): 6677. 2021.Thought: A Journal of Philosophy, EarlyView.

2The History of Continua: Philosophical and Mathematical Perspectives (edited book)Oxford University Press. 2020.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.

6Link’s Revenge: A Case Study in Natural Language MereologyIn Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium, De Gruyter. pp. 336. 2019.

2Mathematics in Philosophy, Philosophy in Mathematics: Three Case StudiesIn Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. Filmat Studies in the Philosophy of Mathematics, Springer Verlag. 2016.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.

9Inconsistency and Incompleteness, RevisitedIn Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 469479. 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 longstanding 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

18Foundations of mathematics: Metaphysics, epistemology, structurePhilosophical Quarterly 54 (214). 2004.

30Logical pluralism and normativityInquiry: An Interdisciplinary Journal of Philosophy 63 (34): 389410. 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

Link's Revenge: A Case Study in Natural Language MereologyIn Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics, De Gruyter. pp. 336. 2019.

14Introduction to Special Issue: The Emergence of StructuralismPhilosophia Mathematica 27 (3): 299302. 2019.

39Friedrich Waismann: The Open Texture of Analytic Philosophy (edited book)Palgrave Macmillan. 2019.This edited collection covers Friedrich Waismann's most influential contributions to twentiethcentury philosophy of language: his concepts of open texture and language strata, his early criticism of verificationism and the analyticsynthetic 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

211Set Theory, Type Theory, and Absolute GeneralityMind 123 (489): 157174. 2014.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 settheoretic universe is openended. 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

2An Introduction to Nonclassical Logic (review)Review of Metaphysics 56 (3): 670671. 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 OntologyOxford University Press USA. 1997.Moving beyond both realist and antirealist 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.

8Mathematics in philosophy, Selected essays, by Charles Parsons, Cornell University Press, Ithaca, N.Y., 1983, 365 pp (review)Journal of Symbolic Logic 53 (1): 320329. 1988.

36Stephen C. Kleene. Origins of recursive function theory. Annals of the history of computing, vol. 3 , pp. 52– 67.  Martin Davis. Why Gödel didn't have Church's thesis. Information and control, vol. 54 , pp. 3– 24.  Stephen C. Kleene. Reflections on Church's thesis. Notre Dame journal of formal logic, vol. 28 , pp. 490– 498 (review)Journal of Symbolic Logic 55 (1): 348350. 1990.

15Perspectives on the history of mathematical logic, edited by Thomas Drucker, Birkhäuser, Boston, Basel, and Berlin, 1991, xxiii + 195 pp.  John W. Dawson Jr. The reception of Gödel's incompleteness theorems. Pp. 84–100 (review)Journal of Symbolic Logic 57 (4): 14871489. 1992.

10Wilfried Sieg. Step by recursive step: Church's analysis of effective calculability. The bulletin of symbolic logic, vol. 3 , pp. 154–180 (review)Journal of Symbolic Logic 64 (1): 398399. 1999.

64Does logical pluralism imply, or suggest, truth pluralism, or vice versa?Synthese 198 (Suppl 20): 49254936. 2019.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.

27Ineffability within the limits of abstraction aloneIn 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 neologicist foundation for a set theory. We show how to reformulate a key aspect of our set theory as a neologicist abstraction principle. That puts the enterprise on the neologicist 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
Columbus, Ohio, United States of America
Areas of Specialization
Philosophy of Language 
Logic and Philosophy of Logic 
Philosophy of Mathematics 
Areas of Interest
Philosophy of Language 
Logic and Philosophy of Logic 
Philosophy of Mathematics 