Browse Papers

Using an axiomatization of second-order arithmetic (essentially second-order Peano Arithmetic without the Successor Axiom), arithmetic's basic operations are defined and its fundamental laws, up to unique prime factorization, are proven. Two manners of expressing a system's consistency are presented - the "Godel" consistency, where a wff is represented by a natural number, and the "real" consistency, where a wff is represented as a second-order sequence, which is a stronger notion. It is shown that the system can prove at least its Godel consistency and that closely allied systems can prove their real consistency.

What are philosophical intuitions? There is a tension between two intuitive criteria. On the one hand, many of our ordinary beliefs do not seem intuitively to be intuitions; this suggests a relatively restrictionist approach to intuitions. (A few attempts to restrict: intuitions must be noninferential, or have modal force, or abstract contents.) On the other hand, it is counterintuitive to deny a great many of our beliefs—including some that are inferential, transparently contingent, and about concrete things. This suggests a liberal conception of intuitions. I defend the liberal view from the objection that it faces intuitive counterexamples; central to the defense is a treatment of the pragmatics of ‘intuition’ language.

This paper seeks to explain how we can be a priori justified in believing that we are not in a "sceptical scenario" (e.g. that we are not currently being deceived by the machinations of an evil demon). The upshot is that explaining our justification for this belief is less fundamental than explaining our justification for our fundamental belief-forming practices -- including (most notably) the practice that is here called "taking one's experience at face value". If this is indeed a "primitively rational" belief-forming practice, then it is not hard to explain why (in the absence of defeating evidence of various kinds) we are also a priori justified in believing it to be reliable.

Suppose that it is necessary that if one believes that the F is F if any unique thing is, one believes of the F, if there is one, that it is F if any unique thing is. I argue that it follows (in all but a few cases) that it is also necessary that if one knows a priori that the F is F if any unique thing is, one knows a priori of the F, if there is one, that it is F if any unique thing is. I claim that because of this, a priori knowledge of de re propositions, including contingent de re propositions, is a relatively common phenomenon. However, because attributions of belief and knowledge are context-sensitive, the question whether it possible to know a priori of a given object that it is F if anything is will typically have different answers in different contexts.

In my dissertation (UCLA 2002), I argue that, by appropriating Fregean resources, Millians can solve the problems that empty names pose. As a result, the debate between Millians and Fregeans should be understood, not as a debate about whether there are senses, but rather as a debate about where there are senses.

Those who subscribe to a prudential conception of practical reason do not believe that there is a conflict between other-regarding and self-regarding norms as the former are held to be founded on the latter. Moral conduct, they maintain, is always rationally justifiable. The reasons we should fulfil the demands of other-regarding norms are the same as those we have for fulfilling self-regarding norms. David Brink has put forth an interesting and novel account of this approach to practical reason which he calls ‘metaphysical egoism’. Metaphysical egoism requires that we modify our pre-theoretical understandings of self-interest on metaphysical grounds. I critically assess Brink’s argument and claim that metaphysical egoism does not adequately function as a motive or guide for action. It is susceptible to many of the same problems which strategic egoism faces.