Patrick Grim

Talk of ‘robustness’ remains vague, despite the fact that it is clearly an important parameter in evaluating models in general and game-theoretic results in particular. Here we want to make it a bit less vague by offering a graphic measure for a particular kind of robustness— ‘matrix robustness’— using a three dimensional display of the universe of 2 x 2 game theory. In a display of this form, familiar games such as the Prisoner’s Dilemma, Stag Hunt, Chicken and Deadlock appear as volumes, making comparison easy regarding the extent of different game-theoretic effects. We illustrate such a comparison in robustness between the triumph of Tit for Tat in a spatialized environment (Grim 1995, Grim, Mar, and St. Denis 1998) and a spatialized modeling of the Contact Hypothesis regarding prejudice reduction (Grim, et. al 2005a, 2005b). The geometrical representation of relative robustness also offers a possibility for links between geometrical theorems and results regarding robustness in game theory.

What the Sorites has to tell us is a simple truth regarding our categories. It appears to saddle us with something other than a simple truth—something worse, a contradiction or a problem or a paradox—only when we insist on viewing it through a discrete logic of categories. Discrete categories and discrete logic are for robots. We aren’t robots, and the simple truth is that we don’t handle categories in the way any discrete logic would demand. For us non-robots, what the Sorites has to offer is a straightforward truth regarding how incapable robots and their logic are of handling categories like ours.

In this paper we make a simple theoretical point using a practical issue as an example. The simple theoretical point is that robustness is not 'all or nothing': in asking whether a system is robust one has to ask 'robust with respect to what property?' and 'robust over what set of changes in the system?' The practical issue used to illustrate the point is an examination of degrees of linkage between sub-networks and a pointed contrast in robustness and fragility between the dynamics of (1) contact infection and (2) information transfer or belief change. Time to infection across linked sub-networks, it turns out, is fairly robust with regard to the degree of linkage between them. Time to infection is fragile and sensitive, however, with regard to the type of sub-network involved: total, ring, small world, random, or scale-free. Aspects of robustness and fragility are reversed where it is belief updating with reinforcement rather than infection that is at issue. In information dynamics, the pattern of time to consensus is robust across changes in network type but remarkably fragile with respect to degree of linkage between sub-networks. These results have important implications for public health interventions in realistic social networks, particularly with an eye to ethnic and socio-economic sub-communities, and in social networks with sub-communities changing in structure or linkage.

A small consortium of philosophers has begun work on the implications of epistemic networks (Zollman 2008 and forthcoming; Grim 2006, 2007; Weisberg and Muldoon forthcoming), building on theoretical work in economics, computer science, and engineering (Bala and Goyal 1998, Kleinberg 2001; Amaral et. al., 2004) and on some experimental work in social psychology (Mason, Jones, and Goldstone, 2008). This paper outlines core philosophical results and extends those results to the specific question of thresholds. Epistemic maximization of certain types does show clear threshold effects. Intriguingly, however, those effects appear to be importantly independent from more familiar threshold effects in networks.

In order to understand the transmission of a disease across a population we will have to understand not only the dynamics of contact infection but the transfer of health-care beliefs and resulting health-care behaviors across that population. This paper is a first step in that direction, focusing on the contrasting role of linkage or isolation between sub-networks in (a) contact infection and (b) belief transfer. Using both analytical tools and agent-based simulations we show that it is the structure of a network that is primary for predicting contact infection—whether the networks or sub-networks at issue are distributed ring networks or total networks (hubs, wheels, small world, random, or scale-free for example). Measured in terms of time to total infection, degree of linkage between sub-networks plays a minor role. The case of belief is importantly different. Using a simplified model of belief reinforcement, and measuring belief transfer in terms of time to community consensus, we show that degree of linkage between sub-networks plays a major role in social communication of beliefs. Here, in contrast to the case of contract infection, network type turns out to be of relatively minor importance. What you believe travels differently. In a final section we show that the pattern of belief transfer exhibits a classic power law regardless of the type of network involved.

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?

Philosophical work on free will, contemporary as well as historical, is inevitably framed by the problem of free will and determinism. One of my goals in what follows is to give a feel for the main lines of that debate in philosophy today. I will also be outlining a particular perspective on free will. Many working philosophers consider themselves Compatibilists; the perspective outlined, building on a number of arguments in the recent literature, is a contemporary form of such a view. It cannot, however, claim to be the contemporary philosophical perspective. There is no such thing. Against a background of the perennial problem of free will and determinism, through ongoing argument and debate, philosophers continue to try to work toward an understanding of precisely what it means for an action to be free.

Beyond belief change and meme adoption, both genetics and infection have been spoken of in terms of information transfer. What we examine here, concentrating on the specific case of transfer between sub-networks, are the differences in network dynamics in these cases: the different network dynamics of germs, genes, and memes. Germs and memes, it turns out, exhibit a very different dynamics across networks. For infection, measured in terms of time to total infection, it is network type rather than degree of linkage between sub-networks that is of primary importance. For belief transfer, measured in terms of time to consensus, it is degree of linkage rather than network type that is crucial. Genes model each of these other dynamics in part, but match neither in full. For genetics, like belief transfer and unlike infection, network type makes little difference. Like infection and unlike belief, on the other hand, the dynamics of genetic information transfer within single and between linked networks are much the same. In ways both surprising and intriguing, transfer of genetic information seems to be robust across network differences crucial for the other two.

Polarization is a topic of intense interest among social scientists, but there is significant disagreement regarding the character of the phenomenon and little understanding of underlying mechanics. A first problem, we argue, is that polarization appears in the literature as not one concept but many. In the first part of the article, we distinguish nine phenomena that may be considered polarization, with suggestions of appropriate measures for each. In the second part of the article, we apply this analysis to evaluate the types of polarization generated by the three major families of computational models proposing specific mechanisms of opinion polarization.

Environmental variability has been proposed as an important mechanism in behavioral psychology, in ecology and evolution, and in cultural anthropology. Here we demonstrate its importance in simulational studies as well. In earlier work we have shown the emergence of communication in a spatialized environment of wandering food sources and predators, using a variety of mechanisms for strategy change: imitation (Grim, Kokalis, Tafti & Kilb 2000), localized genetic algorithm (Grim, Kokalis, Tafti & Kilb 2001), and partial training of neural nets on the behavior of successful neighbors (Grim, St. Denis & Kokalis 2002). Here we focus on environmental variability, comparing results for all of these mechanisms in a range of different environments: (a) environments with constant resources, (b) environments with random resources around the same mean, and (c) sine-wave variable environments with cycles of ‘boom and bust’. Communication, it turns out, is strongly favored by environmental variability on the pattern of ‘boom and bust.'

We motivate a picture of social epistemology that sees forgetting as subject to epistemic evaluation. Using computer simulations of a simple agent-based model, we show that how agents forget can have as large an impact on group epistemic outcomes as how they share information. But, how we forget, unlike how we form beliefs, isn’t typically taken to be the sort of thing that can be epistemically rational or justified. We consider what we take to be the most promising argument for this claim and find it lacking. We conclude that understanding how agents forget should be as central to social epistemology as understanding how agents form beliefs and share information with others.

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

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.

Understanding the dynamics of information is crucial to many areas of research, both inside and outside of philosophy. Using computer simulations of three kinds of information, germs, genes, and memes, we show that the mechanism of information transfer often swamps network structure in terms of its effects on both the dynamics and the fitness of the information. This insight has both obvious and subtle implications for a number of questions in philosophy, including questions about the nature of information, whether there is genetic information, and how to arrange scientific communities.

The goal of philosophy of information is to understand what information is, how it operates, and how to put it to work. But unlike ‘information’ in the technical sense of information theory, what we are interested in is meaningful information. To understand the nature and dynamics of information in this sense we have to understand meaning. What we offer here are simple computational models that show emergence of meaning and information transfer in randomized arrays of neural nets. These we take to be formal instantiations of a tradition of theories of meaning as use. What they offer, we propose, is a glimpse into the origin and dynamics of at least simple forms of meaning and information transfer as properties inherent in behavioral coordination across a community.

Our scientific theories, like our cognitive structures in general, consist of propositions linked by evidential, explanatory, probabilistic, and logical connections. Those theoretical webs ‘impinge on the world at their edges,’ subject to a continuing barrage of incoming evidence. Our credences in the various elements of those structures change in response to that continuing barrage of evidence, as do the perceived connections between them. Here we model scientific theories as Bayesian nets, with credences at nodes and conditional links between them modelled as conditional probabilities. We update those networks, in terms of both credences at nodes and conditional probabilities at links, through a temporal barrage of random incoming evidence. Robust patterns of punctuated equilibrium, suggestive of ‘normal science’ alternating with ‘paradigm shifts,’ emerge prominently in that change dynamics. The suggestion is that at least some of the phenomena at the core of the Kuhnian tradition are predictable in the typical dynamics of scientific theory change captured as Bayesian nets under even a random evidence barrage.

Eliseo Vivas's intellectual life started at the political left and within the tradition of American naturalism, and has ended up somewhere to the political right and with some form of anti-naturalism. Vivas also started "with a great deal of cocksure confidence about his knowledge of the ills of society and the nature of the universe" and ended up recognizing that "he knew very little besides the fact that he did not know, because genuine knowledge about these matters does not exist". This book, written in the form of a biography of one Alonzo Quijano, is an intimate intellectual memoir of the changes in political attitude and philosophical conviction that went between. A flirtation with communism in the thirties and various political squabbles within academia are presented as stages on life's way, and serve as background for freely rambling discussions of naturalism, liberalism, the origin of man, ethical and aesthetic values, ultimate mysteries, and the nature and limits of philosophy.

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