Robert C. Koons

Dynamics of argumentation systems: A division-based method

The changing of arguments and their attack relation is an intrinsic property of a variety of argumentation systems. So, it is very important to efficiently figure out how the status of arguments in a system evolves when the system is updated. However, unlike other areas of argumentation that have been deeply explored, such as argumentation semantics, proof theories, and algorithms, etc., dynamics of argumentation systems has been comparatively neglected. In this paper, we formulate a general theory (called a division-based method) to cope with this problem based on a new concept: the division of an argumentation framework. When an argumentation framework is updated, it is divided into three parts: an unaffected, an affected, and a conditioning part. The status of arguments in the unaffected sub-framework remains unchanged, while the status of the affected arguments is computed in a special argumentation framework (called a conditioned argumentation framework, or briefly CAF) that is composed of an affected part and a conditioning part. We have proved that under a certain semantics that satisfies the directionality criterion (complete, preferred, ideal, or grounded semantics), the extensions of the updated framework are equal to the result of a combination of the extensions of an unaffected sub-framework and sets of the extensions of a set of assigned CAFs. Due to the efficiency of the division-based method, it is expected to be very useful in various kinds of argumentation systems where arguments and attacks are dynamics.

Teleology as Higher-Order Causation: A Situation-Theoretic Account

Situation theory, as developed by Barwise and his collaborators, is used to demonstrate the possibility of defining teleology (and related notions, like that of proper or biological function) in terms of higher order causation, along the lines suggested by Taylor and Wright. This definition avoids the excessive narrowness that results from trying to define teleology in terms of evolutionary history or the effects of natural selection. By legitimating the concept of teleology, this definition also provides promising new avenues for solving long standing problems in the philosophy of mind, such as the problems of intentionality and mental causation.

The Logic of Causal Explanation An Axiomatization

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.

Defeasible Reasoning and Moral Dilemmas

Since Aristotle, ethical theory has been tied to what we call the Classical Deductivist Model. Classical deductivism consists of two tenets: (1) ethical truth is consistent and completely determinate, (2) all particular ethical truths are deducible from a set of exceptionless general principles. Ethical theorists as diverse as Aristotelian naturalists, ethical hedonists, utilitarians, Moorean intuitionists, Kantians, relativists and subjectivists share this common logical framework. The only exceptions are those, like emotivists and prescriptivists, who deny that ethical statements have any truth-values. Yet even these theorists have typically embraced tenets analogous to those of the Classical Deductivist Model. For example, the prescriptivist Hare insists that our moral prescriptions consist of a set of logically consistent, fully general principles.

Belief revision in a changing world

Several authors (Keller and Winslett 1985, Winslett 1988, Katsuno and Mendelzon 1989, Morreau and Rott 1991) have recently argued for a distinction in the way beliefs are updated with new information. They distinguish between information that tells the agent that the world has changed over time and information that fills in or corrects the agents picture of the world at a particular time. We provide an explicit representation of this distinction by means of a modal logic that combines epistemic and dynamic features. Furthermore, we develop a completely declarative semantics for belief revision. This semantics enables us to deduce the result of revising a given body of beliefs in the light of new information, given simply the semantic content of the prior beliefs and of the new data. No purely procedural assumptions about the agents epistemic policies or values (no information about priorities of defaults or degrees of entrenchment) are needed, beyond what is explicitly represented in the objects of the agents beliefs. We accomplish this by distinguishing hard (incorrigible, unrevisable) belief and soft belief; further, the soft attitudes supervene on the hard level. We use a specific theory of nonmonotonic inference to generate soft attitudes from hard ones. This last point is especially important in attempting to deal with belief change, because when an agent acquires new beliefs there is the question: what beliefs about the world persist? We think that only a nonmonotonic logic can adequately deal with this question in a sufficiently rich framework for belief revision like the one we propose.

A representational account of mutual belief

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.

The Modest College and the Imperial University

To understand the ethos of a people, examine their system of education. Educating the young is an essential human act, and in the institutions of a society we can see most clearly the people’s aspirations, their conception of our ultimate end, and their fundamental beliefs about human nature and our place in the cosmos.

From the logical point of view: the chain store paradox revisited

The standard approach to a rational action paradox in game theory (namely, the chain store paradox) has presupposed that the players beliefs are probabilities represented by functions with values between 0 and 1. However, a general solution must include the possibility that the subjective probabilities take only the values 1 and 0, requiring a non-Bayesian account of belief revision. In this paper, we propose a situation-theoretic diagnosis and solution to the paradox, based on the conception of Austinian propositions relativized to particular situations, as developed by Barwise and Etchemendy.

Bob and Carol and Tess and Ali

Conflicting religious experiences in different traditions do not necessarily defeat the rationality of conflicting beliefs sustained by those experiences in those traditions. The circularity that protects religious beliefs from such mutual defeat is not vicious. Moreover, the lack of ‘epistemological humility’ exhibited by such believers poses no threat to world peace. In fact, a campaign for compulsory humility would itself constitute a much greater threat.