Robert Charles Koons

This chapter argues that materialism is vulnerable to two kinds of epistemological objections: transcendental arguments, that show that materialism is incompatible with the very possibility of knowledge; and defeater arguments, that show that belief in materialism provides an effective defeaters to claims to knowledge. It constructs objections of these two kinds in three areas of epistemology: our knowledge of the laws of nature (and of scientific essences), our knowledge of the ontology of material objects, mathematical and logical knowledge. The chapter argues that these epistemological weaknesses place the materialist in a dialectically weak position in respect of ontological identity claims, since the materialist cannot know the causal powers or persistence conditions of material objects. It also argues that the materialist can provide no non-circular account of epistemic normativity. Anti-realist accounts of normativity are unavailable because normativity is already implicated in all intentionality. Moreover, materialists face a fatal dilemma in attempting to carry out an etiological reduction of teleological norms, since neither Humean nor anti-Humean accounts of causation yield defensible results.

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"

Three-valued (strong-Kleene) modal logic provides the foundation for a new approach to formalizing causal explanation as a relation between partial situations. The approach makes fine-grained distinctions between aspects of events, even between aspects that are equivalent in classical logic. The framework can accommodate a variety of ontologies concerning the relata of causal explanation. I argue, however, for a tripartite ontology of objects corresponding to sentential nominals: facts, tropes (or facta or states of affairs), and situations (or events). I axiomatize the relations and use canonical models to demonstrate completeness.

In "The Compatibility of Naturalism and Scientific Realism" (Dec. 2003) , Brian Holtz offers two objections to my argument in "The Incompatibility of Naturalism and Scientific Realism" (in Naturalism: A Critical Appraisal , edited by William Lane Craig and J. P. Moreland, Routledge, 2000). His responses are: (1) my argument can be deflected by adopting a pragmatic or empiricist "definition" of "truth", and (2) the extra-spatiotemporal cause of the simplicity of the laws need not be God, or any other personal being.