‘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. (shrink)

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2 × 2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects in terms of those games. The (...) measure also allows for an easy comparison between different effects in terms of matrix robustness. Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984). The evolution of cooperation . New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling . Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice reduction (Grim et al. 2005. Public Affairs Quarterly, 19 , 95–125). (shrink)

It is widely accepted that the way information transfers across networks depends importantly on the structure of the network. Here, we show that the mechanism of information transfer is crucial: in many respects the effect of the specific transfer mechanism swamps network effects. Results are demonstrated in terms of three different types of transfer mechanism: germs, genes, and memes. With an emphasis on the specific case of transfer between sub-networks, we explore both the dynamics of each of these across networks (...) and a measure of their comparative fitness. Germ and meme transfer exhibit very different dynamics across linked networks. For germs, measured in terms of time to total infection, network type rather than degree of linkage between sub-networks is the primary factor. For memes or belief transfer, measured in terms of time to consensus, it is the opposite: degree of linkage trumps network type in importance. The dynamics of genetic information transfer is unlike either germs or memes. Transfer of genetic information is robust across network differences to which both germs and memes prove sensitive. We also consider function: how well germ, gene, and meme transfer mechanisms can meet their respective objectives of infecting the population, mixing and transferring genetic information, and spreading a message. A shared formal measure of fitness is introduced for purposes of comparison, again with an emphasis on linked sub-networks. Meme transfer proves superior to transfer by genetic reproduction on that measure, with both memes and genes superior to infection dynamics across all networks types. What kinds of network structure optimize fitness also differ among the three. Both germs and genes show fairly stable fitness with added links between sub-networks, but genes show greater sensitivity to the structure of sub-networks at issue. Belief transfer, in contrast to the other two, shows a clear decline in fitness with increasingly connected networks. When it comes to understanding how information moves on networks, our results indicate that questions of information dynamics on networks cannot be answered in terms of networks alone. A primary role is played by the specific mechanism of information transfer at issue. We must first ask about how a particular type of information moves. (shrink)

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. (shrink)

A glowing review of an outstanding collection, with critical points regarding counterfactuals and God's options.

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 Prisoner's 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, 1980b, 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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

Modeling and simulation clearly have an upside. My discussion here will deal with the inevitable downside of modeling — the sort of things that can go wrong. It will set out a taxonomy for the pathology of models — a catalogue of the various ways in which model contrivance can go awry. In the course of that discussion, I also call on some of my past experience with models and their vulnerabilities.

The Hong and Page ‘diversity trumps ability’ result has been used to argue for the more general claim that a diverse set of agents is epistemically superior to a comparable group of experts. Here we extend Hong and Page’s model to landscapes of different degrees of randomness and demonstrate the sensitivity of the ‘diversity trumps ability’ result. This analysis offers a more nuanced picture of how diversity, ability, and expertise may relate. Although models of this sort can indeed be suggestive (...) for diversity policies, we advise against interpreting such results overly broadly. (shrink)

This article aims to describe the last 10 years of the collaborative scientific endeavors on polarization in particular and collective problem-solving in general by our multidisciplinary research team. We describe the team’s disciplinary composition—social psychology, political science, social philosophy/epistemology, and complex systems science— highlighting the shared and unique skill sets of our group members and how each discipline contributes to studying polarization and collective problem-solving. With an eye to the literature on team dynamics, we describe team logistics and processes that (...) we believe make our multidisciplinary team persistent and productive. We emphasize challenges and difficulties caused by disciplinary differences in terms of terminology, units/levels of analysis, methodology, and theoretical assumptions. We then explain how work disambiguating the concepts of polarization and developing an integrative theoretical and methodological framework with complex systems perspectives has helped us overcome these challenges. We summarize the major findings that our research has produced over the past decade, and describe our current research and future directions. Last, we discuss lessons we have learned, including difficulties in a “three models” project and how we addressed them, with suggestions for effective multidisciplinary team research. (shrink)

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. (shrink)

Given certain standard assumptions-that particular sentences are meaningful, for example, and do genuinely self-attribute their own falsity-the paradoxes appear to show intriguing patterns of generally unstable semantic behavior. In what follows we want to concentrate on those patterns themselves: the pattern of the Liar, for example, which if assumed either true or false appears to oscillate endlessly between truth and falsehood.

A Cantorian argument that there is no set of all truths. There is, for the same reason, no possible world as a maximal set of propositions. And omniscience is logically impossible.

A scientific community can be modeled as a collection of epistemic agents attempting to answer questions, in part by communicating about their hypotheses and results. We can treat the pathways of scientific communication as a network. When we do, it becomes clear that the interaction between the structure of the network and the nature of the question under investigation affects epistemic desiderata, including accuracy and speed to community consensus. Here we build on previous work, both our own and others’, in (...) order to get a firmer grasp on precisely which features of scientific communities interact with which features of scientific questions in order to influence epistemic outcomes. (shrink)

An exchange between Patrick Grim and Alvin Plantinga regarding Cantorian arguments against the possibility of an omniscient being.

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. (shrink)

We model scientific theories as Bayesian networks. Nodes carry credences and function as abstract representations of propositions within the structure. Directed links carry conditional probabilities and represent connections between those propositions. Updating is Bayesian across the network as a whole. The impact of evidence at one point within a scientific theory can have a very different impact on the network than does evidence of the same strength at a different point. A Bayesian model allows us to envisage and analyze the (...) differential impact of evidence and credence change at different points within a single network and across different theoretical structures. (shrink)

Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?

The Law of Non-Contradiction holds that both sides of a contradiction cannot be true. Dialetheism is the view that there are contradictions both sides of which are true. Crucial to the dispute, then, is the central notion of contradiction. My first step here is to work toward clarification of that simple and central notion: Just what is a contradiction?

One set of neglected problems consists of paradoxes of omniscience clearly recognizable as forms of the Liar, and these I have never seen raised at all. Other neglected problems are difficulties for omniscience posed by recent work on belief de se and essential indexicals. These have not yet been given the attention they deserve.

The iterated Prisoner’s Dilemma has become the standard model for the evolution of cooperative behavior within a community of egoistic agents, frequently cited for implications in both sociology and biology. Due primarily to the work of Axelrod (1980a, 198Ob, 1984, 1985), a strategy of tit for tat (TFT) has established a reputation as being particularly robust. Nowak and Sigmund (1992) have shown, however, that in a world of stochastic error or imperfect communication, it is not TFT that finally triumphs in (...) an ecological model based on population percentages (Axelrod and Hamilton 1981), but ‘generous tit for tat’ (GTFT), which repays cooperation with a probability of cooperation approaching 1 but forgives defection with a probability of l/3. In this paper, we consider a spatialized instantiation of the stochastic Prisoner’s Dilemma, using two-dimensional cellular automata (Wolfram, 1984, 1986; Gutowitz, 1990) to model the spatial dynamics of populations of competing strategies. The surprising result is that in the spatial model it is not GIFT but still more generous strategies that are favored. The optimal strategy within this spatial ecology appears to be a form of ‘bending over backwards’, which returns cooperation for defection with a probability of 2/3 - a rate twice as generous as GTFT. (shrink)

This book is an introduction, entirely by example, to the possibilities of using computer models as tools in phosophical research in general and in philosophical logic in particular. Topics include chaos, fractals, and the semantics of paradox; epistemic dynamics; fractal images of formal systems; the evolution of generosity; real-valued game theory; and computation and undecidability in the spatialized Prisoner's Dilemma.

John Abbruzzese has recently attempted a defense of omniscience against a series of my attacks. This affords me a welcome occasion to clarify some of the arguments, to pursue some neglected subtleties, and to re-think some important complications. In the end, however, I must insist that at least three of four crucial arguments really do show an omniscient being to be impossible. Abbruzzese sometimes misunderstands the forms of the argument themselves, and quite generally misunderstands their force.

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. (shrink)

Among the most telling atheistic arguments are those to the effect that the existence of any being that meets standard divine specifications is impossible – that there not only is not but could not be any such being.

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. (shrink)

We apply spatialized game theory and multi-agent computational modeling as philosophical tools: (1) for assessing the primary social psychological hypothesis regarding prejudice reduction, and (2) for pursuing a deeper understanding of the basic mechanisms of prejudice reduction.

We work with a large spatialized array of individuals in an environment of drifting food sources and predators. The behavior of each individual is generated by its simple neural net; individuals are capable of making one of two sounds and are capable of responding to sounds from their immediate neighbors by opening their mouths or hiding. An individual whose mouth is open in the presence of food is “fed” and gains points; an individual who fails to hide when a predator (...) is present is “hurt” by losing points. Opening mouths, hiding, and making sounds each exact an energy cost. There is no direct evolutionary gain for acts of cooperation or “successful communication” per se. In such an environment we start with a spatialized array of neural nets with randomized weights. Using standard learning algorithms, our individuals “train up” on the behavior of successful neighbors at regular intervals. Given that simple setup, will a community of neural nets evolve a simple language for signaling the presence of food and predators? With important qualifications, the answer is “yes.” In a simple spatial environment, pursuing individualistic gains and using partial training on successful neighbors, randomized neural nets can learn to communicate. (shrink)

We are increasingly exposed to polarized media sources, with clear evidence that individuals choose those sources closest to their existing views. We also have a tradition of open face-to-face group discussion in town meetings, for example. There are a range of current proposals to revive the role of group meetings in democratic decision-making. Here, we build a simulation that instantiates aspects of reinforcement theory in a model of competing social influences. What can we expect in the interaction of polarized media (...) with group interaction along the lines of town meetings? Some surprises are evident from a computational model that includes both. Deliberative group discussion can be expected to produce opinion convergence. That convergence may not, however, be a cure for extreme views polarized at opposite ends of the opinion spectrum. In a large class of cases, we show that adding the influence of group meetings in an environment of self-selected media produces not a moderate central consensus but opinion convergence at one of the extremes defined by polarized media. (shrink)

Epistemic justifications for democracy have been offered in terms of two different aspects of decision-making: voting and deliberation, or ‘votes’ and ‘talk.’ The Condorcet Jury Theorem is appealed to as a justification in terms votes, and the Hong-Page “Diversity Trumps Ability” result is appealed to as a justification in terms of deliberation. Both of these, however, are most plausibly construed as models of direct democracy, with full and direct participation across the population. In this paper, we explore how these results (...) hold up if we vary the model so as to reflect the more familiar democratic structure of a representative hierarchy. We first recount extant analytic work that shows that representation inevitably weakens the voting results of the Condorcet Jury Theorem, but we question the ability of that result to shine light on real representative systems. We then show that, when we move from votes to talk, as modeled in Hong-Page, representation holds its own and even has a slight edge. (shrink)