
640Abstraction Relations Need Not Be ReflexiveThought: A Journal of Philosophy 2 (2): 137147. 2013.NeoFregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of nonreflexive abstraction relations to restricted abstraction principles

578Extensionalizing Intensional SecondOrder LogicNotre Dame Journal of Formal Logic 56 (1): 243261. 2015.NeoFregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of secondorder variables. The idea is that, given a secondorder entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between secondorder logic and set theory, where sets arise from pluralities. This paper considers two interpretations of secondorder logic—as being either extens…Read more

518Natural Deduction for Modal Logic with a Backtracking OperatorJournal of Philosophical Logic 44 (3): 237258. 2015.Harold Hodes in [1] introduces an extension of firstorder modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. I prove soundn…Read more

25Abstract Objects and the Semantics of Natural Language, by Friederike Moltmann: Oxford: Oxford University Press, 2013, pp. x + 244, £40 (review)Australasian Journal of Philosophy 92 (1): 209209. 2014.No abstract

23The Yablo Paradox: An Essay on Circularity (review)History and Philosophy of Logic 36 (2): 188190. 2015.As the title of this book suggests, the main focal point is the socalled Yablo Paradox,11First formulated by Stephen Yablo. an infinitary, apparently noncircular paradox involving truth, w...
Areas of Specialization
Logic and Philosophy of Logic 
Philosophy of Mathematics 
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Epistemology 
Metaphilosophy 
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Philosophy of Language 
Logic and Philosophy of Logic 
Philosophy of Mathematics 