Robert Charles Koons

The ancient puzzle of the Liar was shown by Tarski to be a genuine paradox or antinomy. I show, analogously, that certain puzzles of contemporary game theory are genuinely paradoxical, i.e., certain very plausible principles of rationality, which are in fact presupposed by game theorists, are inconsistent as naively formulated. ;I use Godel theory to construct three versions of this new paradox, in which the role of 'true' in the Liar paradox is played, respectively, by 'provable', 'self-evident', and 'justifiable'. I also construct in modal operator logic a paradox involving reflexive empirical reasoning. Unlike the paradox of the Liar, the paradox of reflexive reasoning does not depend on self-reference. ;I consider various solutions to the Liar paradox and evaluate how well these solutions cope with the paradox of reflexive reasoning. I then formalize the solution to the paradoxes which I favor: the indexical-hierarchical approach, first sketched out by Charles Parsons and Tyler Burge. In this solution, occurrences of the predicate 'true' in sentence-tokens are contextually relativized to levels of a hierarchy. Drawing also on some brief remarks of Bertrand Russell and Charles Parsons, I develop an account of the kind of schematic generality needed for this theory to be statable. ;Finally, I demonstrate that the principles shown to be paradoxical are in fact presupposed by contemporary game theorists in their reliance on the notion of common knowledge or, more precisely, mutual belief. I create novel analyses of and corresponding solutions to several recalcitrant puzzles within game theory, including the "chain-store paradox"

A staunch hylomorphism involves a commitment to a sparse theory of universals and a sparse theory of composite material objects, as well as to an ontology of fundamental causal powers. Faint-hearted hylomorphism, in contrast, lacks one or more of these elements. On the staunch version of HM, a substantial form is not merely some structural property of a set of elements—it is rather a power conferred on those elements by that structure, a power that is the cause of the generation (by fusion) and persistence of a composite whole through time. Bernard Williams discussed (and rejected) a faint-hearted version of HM in 1986, and faint-hearted HM has been defended more recently by Mark Johnston (2006) and Kathrin Koslicki (2008). I defend the superiority of the staunch version, in spite of its heavier ontological commitments, as a way of accounting for a real distinction between living organisms and heaps of matter, without recourse to dualism or vitalism, and as a way of combining a powers ontology with the possibility of gunk.

Materialism—the view that all of reality is wholly determined by the very, very small—and extreme nominalism—the view that properties, kinds, and qualities do not really exist—have been the dominant view in analytic philosophy for the last 100 years or so. Both views, however, have failed to provide adequate accounts for the possibility of intentionality and of knowledge. We must therefore look to alternatives. One well-tested alternative, the hylomorphism of Aristotle and the medieval scholastics, was rejected without being refuted and so deserves further examination. I will argue that Aristotelian hylomorphic provides a markedly superior account of knowledge, cognitive normativity, and intentionality.