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"

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.

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.

In Physical Causation, Phil Dowe proposes a Conserved Quality account of causation and offers criticisms of several alternatives, including Humean, counter-factual, and mark transmission accounts. Dowe eschews “conceptual analysis” and instead offers his theory as an “empirical account of causation at it is in the actual world.” Dowe takes this as absolving him of the responsibility of giving an account of the essence of causation, threatening to turn his metaphysical account into a watered-down version of more-or-less contemporary physical theory. Nonetheless, on the basis of the strength of many of the criticisms of alternatives, I can recommend this book to anyone interested in contemporary debate about causation.

The logical treatment of the nature of religious belief (here I will concentrate on belief in Christianity) has been distorted by the acceptance of a false dilemma. On the one hand, many (e.g., Braithwaite, Hare) have placed the significance of religious belief entirely outside the realm of intellectual cognition. According to this view, religious statements do not express factual propositions: they are not made true or false by the ways things are. Religious belief consists in a certain attitude toward the world, life, or other human beings, or in what sorts of things one values. On the other hand, others (such as Swinburne, 1981, Chapers 1 and 4) have taken religious belief to include (at least) being certain of the truth of particular factual religious propositions. The strength of a person's religious belief is identified with his degree of confidence in the truth of those propositions, measured by the "subjective probability" which those propositions have for that person. I propose a third alternative, according to which, (1) contrary to the first view, religious belief does involve a relation to factual religious propositions, such as that God exists, that Jesus was God and man, etc., -- propositions which are made true or false by the way things actually are -- but, (2) contrary to the second view, the strength of religious belief is measured, not by the degree of one's confidence1 in the truth of these propositions, but rather by the way in which the value or desirability to oneself of the various ways the world could be is affected by their including or not including the truth of these religious propositions. Thus, religious belief does consist in what one values or prizes, not in what..

Although the notion of common or mutual belief plays a crucial role in game theory, economics and social philosophy, no thoroughly representational account of it has yet been developed. In this paper, I propose two desiderata for such an account, namely, that it take into account the possibility of inconsistent data without portraying the human mind as logically and mathematically omniscient. I then propose a definition of mutual belief which meets these criteria. This account takes seriously the existence of computational limitations. Finally, I point out that the epistemic logic (or theory) needed to make the definition work is subject to the Kaplan/Montague Paradox of the Knower. I argue that this is not a defect of the account, and I discuss briefly the bearing of recent work on the paradox of the Liar upon this problem.

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.