Patrick Grim

Most current modeling for evolution of communication still underplays or ignores the role of local action in spatialized environments: the fact that it is immediate neighbors with which one tends to communicate, and from whom one learns strategies or conventions of communication. Only now are the lessons of spatialization being learned in a related field: game-theoretic models for cooperation. In work on altruism, on the other hand, the role of spatial organization has long been recognized under the term ‘viscosity’.Here we offer some simple simulations that dramatize the importance of spatialization for studies of both cooperation and communication, in each case contrasting a model dynamics in which strategy change proceeds globally, and a spatialized model dynamics in which interaction and strategy change both operate purely locally. Local action in a spatialized model clearly favors the emergence of cooperation. In the case of communication, spatialized models allow communication to arise and flourish where the global dynamics more typical in the literature make it impossible.Simulations make a dramatic case for spatialized modeling, but analysis proves difficult. In a final section we outline some of the surprises of spatial dynamics but also some of the complexity facing attempts at deeper analysis.

‘The problem with simulations is that they are doomed to succeed.’ So runs a common criticism of simulations—that they can be used to ‘prove’ anything and are thus of little or no scientific value. While this particular objection represents a minority view, especially among those who work with simulations in a scientific context, it raises a difficult question: what standards should we use to differentiate a simulation that fails from one that succeeds? In this paper we build on a structural analysis of simulation developed in previous work to provide an evaluative account of the variety of ways in which simulations do fail. We expand the structural analysis in terms of the relationship between a simulation and its real-world target emphasizing the important role of aspects intended to correspond and also those specifically intended not to correspond to reality. The result is an outline both of the ways in which simulations can fail and the scientific importance of those various forms of failure.

This is an exploration of a cluster of related logical results. Taken together these seem to have something philosophically important to teach us: something about knowledge and truth and something about the logical impossibility of totalities of knowledge and truth. The book includes explorations of new forms of the ancient and venerable paradox of the :Liar, applications and extensions of Kaplan and Montague's paradox of the Knower, generalizations of Godel's work on incompleteness, and new uses of Cantorian diagonalization. Throughout, the concern is with metaphysical and epistemological implications of these results: what such results may have to teach us about knowledge, truth, and possibility.

Since the sixties, computational modeling has become increasingly important in both the physical and the social sciences, particularly in physics, theoretical biology, sociology, and economics. Sine the eighties, philosophers too have begun to apply computational modeling to questions in logic, epistemology, philosophy of science, philosophy of mind, philosophy of language, philosophy of biology, ethics, and social and political philosophy. This chapter analyzes a selection of interesting examples in some of those areas.

R l purtill has claimed that the ontological argument that plantinga presents in "the nature of necessity" is basically the same as that offered in hartshorne's "the logic of perfection" and that it falls victim to the same criticisms. i argue that plantinga's ontological argument is different enough "not" to fall victim to purtill's criticisms. what makes plantinga's argument different, however, also makes it vulnerable to a different criticism: the god of plantinga's conclusion is not a being greater than which none can be conceived

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense.

In the spatialized Prisoner's Dilemma, players compete against their immediate neighbors and adopt a neighbor's strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without opposition, or will an equilibrium of some small number of strategies emerge? Here it is shown, for finite configurations of Prisoner's Dilemma strategies embedded in a given infinite background, that such questions are formally undecidable: there is no algorithm or effective procedure which, given a specification of a finite configuration, will in all cases tell us whether that configuration will or will not result in progressive conquest by a single strategy when embedded in the given field. The proof introduces undecidability into decision theory in three steps: by (1) outlining a class of abstract machines with familiar undecidability results, by (2) modelling these machines within a particular family of cellular automata, carrying over undecidability results for these, and finally by (3) showing that spatial configurations of Prisoner's Dilemma strategies will take the form of such cellular automata