Patrick Grim

The philosophical computer: exploratory essays in philosophical computer modeling

Philosophical modeling is as old as philosophy itself; examples range from Platos Cave and the Divided Line to Rawlss original position. What is new are the astounding computational resources now available for philosophical modeling. Although the computer cannot offer a substitute for philosophical research, it can offer an important new environment for philosophical research. – The authors present a series of exploratory examples of computer modeling, using a range of computational techniques to illuminate a variety of questions in philosophy and philosophical logic. Topics include self-reference and paradox in fuzzy logics, varieties of epistemic chaos, fractal images of formal systems, and cellular automata models in game theory. Examples in the last category include models for the evolution of generosity, possible causes and cures for discrimination, and the formal undecidability of patterns of social and biological interaction. The cross-platform CD-ROM provided with the book contains a variety of working examples, in color and often operating dynamically, embedded in a text that parallels that of the book. Source code of all major programs is included to facilitate further research. – Contents : Preface. Introduction. – 1. Chaos, Fractals, and the Semantics of Paradox; – 2. Notes on Epistemic Dynamics; – 3. Fractal Images of Formal Systems; – 4. The This Evolution of Generosity n a Hobbesian Model; – 5. Real-Valued Game Theory: Real Life, Cooperative Chaos, and Discrimination; – 6. Computation and Undecidability in the Spatialized Prisoners Dilemma. – Appendix A: Competitive Strategies Adequate for a Minsky Register Machine; – Appendix B: An Algebraic Treatment for Competitive Strategies. Afterword. Notes; Index.

Self-reference and chaos in fuzzy logic

Investigates a range of phenomena from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the

How simulations fail

Abstract‘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.

The undecidability of the spatialized prisoner's dilemma

In the spatialized Prisoners Dilemma, players compete against their immediate neighbors and adopt a neighbors 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 Prisoners 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 Prisoners Dilemma strategies will take the form of such cellular automata.

Making Meaning Happen

What is it for a sound or gesture to have a meaning, and how does it come to have one? In this paper, a range of simulations are used to extend the tradition of theories of meaning as use. The authors work throughout with large spatialized arrays of sessile individuals in an environment of wandering food sources and predators. Individuals gain points by feeding and lose points when they are hit by a predator and are not hiding. They can also make sounds heard by immediate neighbours in the array, and can respond to sounds from immediate neighbours. No inherent meaning for these sounds is built into the simulation; under what circumstances they are sent, if any, and what the response to them is, if any, vary initially with the strategies randomized across the array. These sounds do take on a specific function for communities of individuals, however, with any of three forms of strategy change: direct imitation of strategies of successful neighbours, a localized genetic algorithm in which strategies are ‘crossed’ with those of successful neighbours, and neural net training on the behaviour of successful neighbours. Starting from an array randomized across a large number of strategies, and using any of these modes of strategy change, communities of ‘communicators’ emerge. Within these evolving communities the sounds heard from immediate neighbours, initially arbitrary across the array, come to be used for very specific communicative functions. ‘Communicators’ make a particular sound on feeding and respond to that same sound from neighbours by opening their mouths; they make a different sound when hit with a predator and respond to that sound by hiding. Robustly and persistently, even in simple computer models of communities of self-interested agents, something suggestively like signalling emerges and spreads.

Operators in the paradox of the knower

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montagues 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.

Evolution of communication in perfect and imperfect worlds

We extend previous work on cooperation to some related questions regarding the evolution of simple forms of communication. The evolution of cooperation within the iterated Prisoners Dilemma has been shown to follow different patterns, with significantly different outcomes, depending on whether the features of the model are classically perfect or stochastically imperfect (Axelrod, 1980a,b, 1984, 1985; Axelrod and Hamilton, 1981; Nowak and Sigmund, 1990, 1992; Sigmund, 1993). Our results here show that the same holds for communication. Within a simple model, the evolution of communication seems to require a stochastically imperfect world.

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.

Disambiguation of social polarization concepts and measures

ABSTRACT This article distinguishes nine senses of polarization and provides formal measures for each one to refine the methodology used to describe polarization in distributions of attitudes. Each distinct concept is explained through a definition, formal measures, examples, and references. We then apply these measures to GSS data regarding political views, opinions on abortion, and religiosity—topics described as revealing social polarization. Previous breakdowns of polarization include domain-specific assumptions and focus on a subset of the distribution’s features. This has conflated multiple, independent features of attitude distributions. The current work aims to extract the distinct senses of polarization and demonstrate that by becoming clearer on these distinctions we can better focus our efforts on substantive issues in social phenomena.

Fractal images of formal systems

Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex ‘value spaces’, with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic.\looseness=-1