My research is primarily in logic, metaphysics, and the philosophy of language. I am interested in intensional paradoxes—paradoxes of mental and linguistic content—and the constraints they place on our ability to theorize about attitudes like hope and fear. I'm also interested in the challenges we face when we try to ascribe too much structure to the objects of propositional attitudes—when we make propositions too fine-grained. Beyond propositions and the problems surrounding them, I am interested in practical reasoning, and in particular in nonmonotonic logics of planning with conflicting beliefs and desires.
Break the Weakest Rules
I have the details typed up, but this isn't a full paper yet. Please email me if you'd like to see the draft.
As theories of reasoning, traditional logical systems are highly idealized and impractical. I propose a theory of defeasible rules of inference called defaults to represent more realistic, everyday reasoning, both about beliefs and about actions and planning. The primary benefit of the system I develop over previous versions of default logic is the ability to capture reasoning about the potential consequences of our actions, and this sort of hypothetical reasoning makes my proposal more general than those of John Horty and Richmond Thomason, whom I follow in using default logic to analyze practical reasons. I then turn to two more general lessons about reasons arising from default logic. First, I argue that at least from a technical standpoint, we can replace conditional normative reasons—normative reasons that we have only under certain conditions—with unconditional ones. Second, I argue that while default logic can account for a great deal of the reasoning we do, decision theory may still be better equipped to address certain cases in which something like wishful thinking is acceptable.
Paradoxes and Theorizing about Attitudes
I am in the process of revising this paper. Please email me for a current draft.
Propositions are more than the bearers of truth and the meanings of sentences: we also use them in our theorizing about an array of attitudes including belief, desire, hope, fear, knowledge, and understanding. This variety of roles leads to a variety of paradoxes, most of which have been sorely neglected. I introduce a new member of a family of paradoxes first studied by Arthur Prior, arguing that it presents a serious—indeed, I think fatal—problem for most familiar resolutions of paradoxes. In particular, I argue that truth-value gap, contextualist, situation theoretic, revision theoretic, ramified, and dialetheist approaches to the paradox must deny us the conceptual resources that they themselves make use of. The remaining strategies, one due to Hartry Field and one due to Prior himself, avoid these issues, but only by insisting that certain goals, which we might have thought were central to theorizing about attitudes, turn out to be impossible to achieve.
Outline of a Theory of Quantification / final draft
Principia Mathematica: The Centenary Volume, Nicholas Griffin and Bernard Linsky, eds., forthcoming
Historically, Russell's ramified theory of types has been largely neglected. As a foundation of mathematics, it required the axiom of reducibility, which was unpopular at the time. As a solution to paradoxes, it seemed unnecessary in light of Ramsey's distinction between semantical and set-theoretical paradoxes. As a general theory, Russell motivated it with the vicious circle principle, which Gödel attacked. But several authors, including Alonzo Church, David Kaplan, and Rich Thomason, have suggested ramification as a resolution of a family of paradoxes that fall through the cracks of Ramsey's division. These paradoxes have been largely neglected as well, and what little existing work there is often leaves much to be desired. But so does ramification. Like Tarski's hierarchy of languages, it is much too heavy-handed to do justice to the paradoxes. I provide a refinement of ramification's restrictions on propositional quantification, analogous to Kripke's refinement of Tarski's truth predicates. I end with a brief sketch of some alternative resolutions of the paradoxes, all of which can be carried out within the intensional logic I develop.
Paradoxes of Intensionality with Richmond H. Thomason
Review of Symbolic Logic, 4, pp. 394–411, 2011 (©ASL)
We identify a class of paradoxes that is neither set-theoretical nor semantical, but that seems to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly accepted methods for dealing with the logical paradoxes.
Intensionality and Paradoxes in Ramsey's 'The Foundations of Mathematics'
Review of Symbolic Logic, 3, pp. 1–25, 2010 (©ASL)
In 'The Foundations of Mathematics', Frank Ramsey separates paradoxes into two groups, now taken to be the logical and the semantical. But he also revises the logical system developed in Whitehead and Russell's Principia Mathematica, and in particular attempts to provide an alternate resolution of the semantical paradoxes. I reconstruct the logic that he develops for this purpose, and argue that it falls well short of his goals. I then argue that the two groups of paradoxes that Ramsey identifies are not properly thought of as the logical and semantical, and that in particular, the group normally taken to be the semantical paradoxes includes other paradoxes—the intensional paradoxes—which are not resolved by the standard metalinguistic approaches to the semantical paradoxes. It thus seems that if we are to take Ramsey's interest in these problems seriously, then the intensional paradoxes deserve more widespread attention than they have historically received.
Please email me for syllabi.
Texas Tech University
Descartes and Hume (Fall 2012)
Epistemology (Fall 2011, Spring 2013)
Philosophy of Religion (Fall 2011)
Introduction to Philosophy (Spring 2013)
Introduction to Formal Logic (Fall 2011, Spring 2012, Fall 2012)
Advanced Logic (Spring 2012)
Graduate Seminar on Logic (Spring 2012)
University of Michigan
Critical Thinking and Introduction to Logic (Spring 2011)
Introduction to Philosophy (Winter 2011, Fall 2010, Winter 2009)
Introduction to Formal Logic (Spring 2008)