Undecidability in the Spatialized Prisoner's Dilemma

n 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 configurationns of Prisoner’s Dilemma strategies will take the form of such cellular automata

Against a Deontic Argument for God's Existence

Against an argument by Carl Kordig

What Kind of Science is Simulation?

Is simulation some new kind of science? We argue that instead simulation fits smoothly into existing scientific practice, but does so in several importantly different ways. Simulations in general, and computer simulations in particular, ought to be understood as techniques which, like many scientific techniques, can be employed in the service of various and diverse epistemic goals. We focus our attentions on the way in which simulations can function as (i) explanatory and (ii) predictive tools. We argue that a wide variety of simulations, both computational and physical, are best conceived in terms of a set of common features: initial or input conditions, a mechanism or set of rules, and a set of results or output conditions. Studying simulations in these terms yields a new understanding of their character as well as a body of normative recommendations for the care and feeding of scientific simulations

Modeling Information

The topics of modeling and information come together in at least two ways. Computational modeling and simulation play an increasingly important role in science, across disciplines from mathematics through physics to economics and political science. The philosophical questions at issue are questions as to what modeling and simulation are adding, altering, or amplifying in terms of scientific information. What changes with regard to information acquisition, theoretical development, or empirical confirmation with contemporary tools of computational modeling? In this sense the title of this article is read in the following way: What kind of information is modeling information? What kind of information does modeling give us

Plantinga's God and Other Monstrosities

Variations on the ontological argument for most minimal and most mediocre beings