
45Translating Logical TermsTopoi 38 (2): 291303. 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

45Intentional 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.

24Comparing implicit and explicit memory for brand names from advertisementsJournal of Experimental Psychology: Applied 2 (2): 147. 1996.

36The Company Kept by Cut Abstraction (and its Relatives)Philosophia Mathematica 19 (2): 107138. 2011.This article concerns the ongoing neologicist 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

159HigherOrder Logic or Set Theory: A False DilemmaPhilosophia Mathematica 20 (3): 305323. 2012.The purpose of this article is show that secondorder 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 secondorder 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?

41Remarks on the development of computabilityHistory and Philosophy of Logic 4 (12): 203220. 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

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585What is mathematical logic?Philosophia 8 (1): 7994. 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.

60Space, number and structure: A tale of two debatesPhilosophia Mathematica 4 (2): 148173. 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

53EffectivenessIn Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics, Springer. pp. 3749. 2006.

6Foundations without Foundationalism: A Case for SecondOrder LogicPhilosophical Review 103 (1): 150. 1994.

20Consumer memory for intentions: A prospective memory perspectiveJournal of Experimental Psychology: Applied 5 (2): 169. 1999.

1Vagueness, Metaphysics, and ObjectivityIn Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds: Vaguenesss, its Nature and its Logic, Oxford University Press. 2010.

12Review: Stephen C. Kleene, Origins of Recursive Function Theory; Martin Davis, Why Godel Didn't have Church's Thesis; Stephen C. Kleene, Reflections on Church's Thesis (review)Journal of Symbolic Logic 55 (1): 348350. 1990.

1BuraliForti's revengeIn J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox, Oxford University Press. 2007.

23The Work of John Corcoran: An AppreciationHistory and Philosophy of Logic 20 (34): 149158. 1999.

72Prolegomenon To Any Future Neo‐Logicist Set Theory: Abstraction And Indefinite ExtensibilityBritish Journal for the Philosophy of Science 54 (1): 5991. 2003.The purpose of this paper is to assess the prospects for a neologicist 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

19The governance of identityIn Fraser MacBride (ed.), Identity and Modality, Oxford University Press. pp. 164173. 2006.

6Intentional forgetting as a facilitator for recalling new product attributesJournal of Experimental Psychology: Applied 12 (4): 251263. 2006.
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 