•  29
    The Yablo Paradox: An Essay on Circularity (review)
    History and Philosophy of Logic 36 (2): 188-190. 2015.
  •  199
    Abstraction Relations Need Not Be Reflexive
    Thought: A Journal of Philosophy 2 (2): 137-147. 2013.
    Neo-Fregeans 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 non-reflexive abstraction relations to restricted abstraction principles
  •  169
    Extensionalizing Intensional Second-Order Logic
    Notre Dame Journal of Formal Logic 56 (1): 243-261. 2015.
    Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities. This paper considers two interpretations of second-order logic—as being either extens…Read more
  •  129
    Natural Deduction for Modal Logic with a Backtracking Operator
    Journal of Philosophical Logic 44 (3): 237-258. 2015.
    Harold Hodes in [1] introduces an extension of first-order 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