José Benardete developed a famous paradox involving a beginningless set of items each member of which satisfies some predicate just in case no earlier member satisfies it. The Grim Reaper version of this paradox has recently been employed in favor of various finitist metaphysical theses, ranging from temporal finitism to causal finitism to the discrete nature of time. Here, I examine a new challenge to these finitist arguments—namely, the challenge of implying that the future cannot be (...) endless. In particular, I develop future-oriented Benardete paradoxes and examine their epistemic symmetry with past-oriented paradoxes. (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.

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. (shrink)

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.

Let us sum up. The paradox of the Knower poses a direct and formal challenge to the coherence of common notions of knowledge and truth. We've considered a number of ways one might try to meet that challenge: propositional views of truth and knowledge, redundancy or operator views, and appeal to hierarchy of various sorts. Mere appeal to propositions or operators, however, seems to be inadequate to the task of the Knower, at least if unsupplemented by an auxiliary recourse (...) to hierarchy. But the cost of hierarchy appears to be an abandonment of any notion of all truth or of omniscience. What the contradictions of the Knower seem to demand, then, is at least an abandonment of these. As noted in the introduction, the argument is complicated enough that one must be wary of dogmatic and precipitate conclusions. One may legitimately wonder whether some new response, or some variation on an old one, will yet offer a way out.Far too often, however, it is asked what has gone wrong with paradox rather than what paradox may have to teach us. What the Knower may have to teach us, I think, is that there really can be no coherent notion of all truth and really can be no coherent notion of omniscience. In its own way that conclusion is perhaps as humbling as is any traditional notion of God. (shrink)

Problems for 'precise replacements' as a way out of sorites paradoxes.

On swizzle sticks, sorites paradoxes, and precise replacements.

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. (shrink)

What I hope to show here is that the costs of taking sorites arguments seriously, in particular the costs with respect to hopes for precise replacement are significantly greater than proponents of sorites arguments have estimated.

An eternal society with the abilities of ordinary humans in each year of its existence would have had the ability to actualize a logical contradiction. This fact casts doubt on the metaphysical possibility of an infinite past. In addition to using this paradox in an argument against an infinite past, one can also use the paradox mutatis mutandis as a decisive argument against the sempiternality of God.

Causal finitism, the view that the causal history of any event must be finite, has garnered much philosophical interest recently—especially because of its applicability to the Kalām cosmological argument. The most prominent argument for causal finitism is the Grim Reaper argument, which attempts to show that, if infinite causal histories are possible, then other paradoxical states of affairs must also be possible. However, this style of argument has been criticized on the grounds of (i) relying on controversial modal (...) principles, and (ii) providing a false diagnosis of the paradoxes involved. In this paper, I develop a new kind of Grim Reaper argument immune to these criticisms. I show that, by using insights from the literature on time travel, causal finitists should instead argue that infinite causal histories are problematically inexplicable, as they entail the possibility of unexplained foiling mechanisms. The fruits of this paper are that (i) a novel supporting argument for the Kalām is developed, and (ii) along the way of building this argument, it is shown that the literatures on time travel and causal finitism are deeply and intimately connected. (shrink)

Patrick Grim advances arguments meant to show that the doctrine of divine omniscience—the classical doctrine according to which God knows all truths—is false. In particular, we here have in mind to focus on two such arguments: the set theoretic argument and the semantic argument. These arguments due to Grim run parallel to, respectively, familiar paradoxes in set theory and naive truth theory. It is beyond the purview of this article to adjudicate whether or not these are successful arguments (...) against the classical doctrine of omniscience. What we are here interested in is a way in which these arguments can be generalized. In particular, we show how generalizations of those arguments can target, explicitly, alternatives to the classical doctrine of omniscience, including what we here call 'restricted omniscience' and 'open future open theism'. As a corollary, considerations of Grim-style arguments do not support these alternatives to the classical doctrine of omniscience over the classical doctrine. We conclude that what is paradoxical is not the classical doctrine of omniscience just as such; rather, what is paradoxical is a core commitment shared by the classical doctrine and its more modest alternatives, namely, the thesis that God is a perfectly logical reasoner. (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)

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)

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)

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

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume 30, Number 2, November 2004, pp. 213-236 Pleased and Afflicted: Hume on the Paradox of Tragic Pleasure E. M. DADLEZ How fast can you run? As fast as a leopard. How fast are you going to run? A whistle sounds the order that sends Archie Hamilton and his comrades over the top of the trench to certain death. Racing to circumvent that order and arriving (...) seconds too late, Archie's friend Frank screams in rage and despair. Archie is cut down before he has run twenty yards. Peter Weir's film Gallipoli is a chronicle of the disastrous Dardanelles campaign of the first World War, but it is also a film about racing. Archie is trained by his uncle Jack to run "as fast as a leopard." The film begins as it ends, with Archie sprinting in response to a whistle. Frank is first shown racing after a train, along with friends who are on their way to enlist. Archie and Frank meet while competing in a race, they race in Cairo once they have enlisted, and they finally race death. From the beginning, Archie has been faster; even at the end he is the first to die. And from the beginning he has swept Frank along in his wake, encouraging him, pushing him, inspiring him, and helping him to positions for which he is inadequately qualified. In the end, Archie's compassion and kindness prompt a decision which has grim consequences both for himself and for hundreds of others. Knowing that his friend fears death in the trenches, Archie recommends Frank as a substitute for himself, a designated message runner. But Frank is not fast enough, and falls short by mere seconds which Archie would not have lost. This is what leads to the failure of the one real effort to countermand the fatal charge. E. M. Dadlez is Professor of Humanities and Philosophy, University of Central Oklahoma, Edmond, OK 73034, USA. e-mail: [email protected] 214 E. M. Dadlez I am an emotional wreck by the time the movie is over, though I should admit that most of my tears are the result of sheer rage. Both my dogs exited the room in some haste once I began to shout at the television and the unpardonably dimwitted British officers who sat sipping tea at a comfortable distance as they gave the order for soldiers to commit suicide. But it isn't just the scope of the real human disaster, or the enormity of the blunder, or the pointlessness of the entire enterprise, or even my renewed conviction that stupidity is, in fact, evil, that is so unsettling. The film unnerves with respect to personal as well as global concerns, focusing attention on the chance of vanity's leading one to undertake responsibilities beyond one's competence, the possibility of advancement or security being achievable only at the expense of another, and the realization of how easy it might be to let those things happen. Gallipoli is a sad, disturbing film, and the spectator is grieved and disturbed in the course of watching it. Yet, having said that, I must own to having a copy in my possession, and to having watched it more than once. I recommend it to friends, offering to lend them my videotape. In fact, I press it on them. I say that it is a terrific, rewarding work which they should take the time to see. How is it that I can describe my experience of the film in such glowing terms and at the same time acknowledge the extreme distress I felt in the course of watching it? How can I reconcile the discordant aspects of my experience? David Hume explores some possible answers in his essay "Of Tragedy."1 He begins by calling attention to the paradox of tragic pleasure: It seems an unaccountable pleasure, which the spectators of a well written tragedy receive from sorrow, terror... and other passions, which are in themselves disagreeable and uneasy. The more they are touched and affected, the more are they delighted with the spectacle.... The whole art of the poet is employed in rousing and supporting the compassion and... (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)

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)

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)

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)

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)

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?

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?

Plena are large-scale macro-totalities appropriate to the realms of all facts, all truths, and all things. Our attempt here is to take some first technical steps toward an adequate conception of plena.

‘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)

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)

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.

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.

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)

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)

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

What structure of scientific communication and cooperation, between what kinds of investigators, is best positioned to lead us to the truth? Against an outline of standard philosophical characteristics and a recent turn to social epistemology, this paper surveys highlights within two strands of computational philosophy of science that attempt to work toward an answer to this question. Both strands emerge from abstract rational choice theory and the analytic tradition in philosophy of science rather than postmodern sociology of science. The first (...) strand of computational research models the effect of communicative networks within groups, with conclusions regarding the potential benefit of limited communication. The second strand models the potential benefits of cognitive diversity within groups. Examples from each strand of research are used in analyzing what makes modeling of this sort both promising and distinctly philosophical, but are also used to emphasize possibilities for failure and inherent limitations as well. (shrink)

How do conventions of communication emerge? How do sounds or gestures take on a semantic meaning, and how do pragmatic conventions emerge regarding the passing of adequate, reliable, and relevant information? My colleagues and I have attempted in earlier work to extend spatialized game theory to questions of semantics. Agent-based simulations indicate that simple signaling systems emerge fairly naturally on the basis of individual information maximization in environments of wandering food sources and predators. Simple signaling emerges by means of any (...) of various forms of updating on the behavior of immediate neighbors: imitation, localized genetic algorithms, and partial training in neural nets. Here the goal is to apply similar techniques to questions of pragmatics. The motivating idea is the same: the idea that important aspects of pragmatics, like important aspects of semantics, may fall out as a natural results of information maximization in informational networks. The attempt below is to simulate fundamental elements of the Gricean picture: in particular, to show within networks of very simple agents the emergence of behavior in accord with the Gricean maxims. What these simulations suggest is that important features of pragmatics, like important aspects of semantics, don't have to be added in a theory of informational networks. They come for free. (shrink)

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)

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.

A survey of logical problems for the concept of omniscience.

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. (shrink)

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. Keywords: meaning, communication, genetic algorithms, neural networks. (shrink)

There are many social psychological theories regarding the nature of prejudice, but only one major theory of prejudice reduction: under the right circumstances, prejudice between groups will be reduced with increased contact. On the one hand, the contact hypothesis has a range of empirical support and has been a major force in social change. On the other hand, there are practical and ethical obstacles to any large-scale controlled test of the hypothesis in which relevant variables can be manipulated. Here we (...) construct a spatialized model that tests the core hypothesis in a large array of game-theoretic agents. Robust results offer a new kind of support for the contact hypothesis: results in simulation do accord with a hypothesis of reduced prejudice with increased contact. The spatialized game-theoretic model also suggests a deeper explanation for at least some of the social psychological phenomena at issue. (shrink)

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. (shrink)

Allen s has proposed a new approach to possible worlds, designed explicitly to overcome Cantorian difficulties for possible worlds construed as maximal consistent set of propositions. I emphasize some of the distinctive features of Hazenworlds, some of their weaknesses, and some further Cantorian problems for worlds against which they seem powerless.