Two players bargain to select a utility allocation in some set X⊂R+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\subset {\mathbb {R}}_+^2$$\end{document}. Bargaining takes place in infinite discrete time, where each period t is divided into two sub-periods. In the first sub-period, the players play a simultaneous-move game to determine that period’s proposer, and bargaining takes place in the second sub-period. Rejection triggers a one-period delay and move to t+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t+1$$\end{document}. For (...) every x∈X∩R++2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x\in X\cap {\mathbb {R}}^2_{++}$$\end{document}, there exists a cutoff δ<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta <1$$\end{document}, such that if at least one player has a discount factor above δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}, then for every y∈X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y\in X$$\end{document} that satisfies y≥x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y\ge x$$\end{document} there exists a subgame perfect equilibrium with immediate agreement on y. The equilibrium is supported by “dictatorial threats.” These threats can be dispensed with if X is the unit simplex and the target-vector is Pareto efficient. The results can be modified in a way that allows for arbitrarily long delays in equilibrium. (shrink)

A Dutch 'folk theorem' holds that 'from exchange it comes to tears'. This seems to contradict the basic idea found in economics that exchange and trade can make both sides better off. We show that the 'folk theorem' has a better theoretical foundation than sometimes thought, as it is vindicated by the equilibrium of an exchange game with two-sided asymmetric information. We, then, explain the practical value of such 'folk wisdom' in the real world by (...) showing why players might be unlikely to learn such an equilibrium strategy. (shrink)

I review the classic skeptical challenges of Foole in Leviathan and the Lydian Shepherd in Republic against the prudential rationality of justice. Attempts to meet these challenges contribute to the reconciliation project (Kavka in Hobbesian moral and political theory , 1986 ) that tries to establish that morality is compatible with rational prudence. I present a new Invisible Foole challenge against the prudential rationality of justice. Like the Lydian Shepherd, the Invisible Foole can violate justice offensively (Kavka, Hobbesian moral and (...) political theory , 1986 ; Law and Philosophy , 14:5–34, 1995 ) without harming his reputation for justice. And like the Foole, the Invisible Foole dismisses the possibility that being just preserves goods intrinsic to justice, and will be just only if he fears that others will punish his injustice by withholding the external goods like labor and material goods that he would otherwise receive for their performance in covenants. I argue that given a plausible folk-theorem interpretation , Hobbes’ response to the Foole’s challenge is inconclusive, and depends crucially upon common knowledge assumptions that may or may not obtain in actual societies. I present two analogous folk-theorem arguments in response to the Invisible Foole’s challenge, one using the idea that the Invisible Foole’s power of concealment might be transitory, and the other using the idea that members of society might stop performing in covenants with anyone, thus punishing the Invisible Foole indirectly, if the Invisible Foole commits sufficiently many injustices. (shrink)

If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly certain preliminary goal, and the choice is only the mean, by which it can be achieved or not by the one who determines the goal. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. Consequently, and paradoxically, the (...) determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. The choice is usually linked to very complicated systems such as human brain or society and even often associated with consciousness. In its background, the material world is deterministic and absolutely devoid of choice. However, quantum mechanics introduces the choice in the fundament of physical world, in the only way, in which it can exist: All exists in the “phase transition” of the present between the uncertain future and the well-ordered past. Thus the present is forced to choose in order to be able to transform the coherent state of future into the well-ordering of past. The concept of choice as if suggests that there is one who chooses. However quantum mechanics involves a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors, Conway and Kochen, and according to them: “Do we really have free will, or, as a few determined folk maintain, is it all an illusion? We don’t know, but will prove in this paper that if indeed there exist any experimenters with a modicum of free will, then elementary particles must have their own share of this valuable commodity” “The import of the free will theorem is that it is not only current quantum theory, but the world itself that is non-deterministic, so that no future theory can return us to a clockwork universe”. Those theorems can be considered as a continuation of the so-called theorems about the absence of “hidden variables” in quantum mechanics. (shrink)

In their classic analyses, Hobbes and Hume argue that offensively violating a covenant is irrational because the offense ruins one’s reputation. This paper explores conditions under which reputation alone can enforce covenants. The members of a community are modeled as interacting in a Covenant Game repeated over time. Folk theorems are presented that give conditions under which the Humean strategy of performing in covenants only with those who have never offensively violated or performed with an offensive violator characterizes an (...) equilibrium of the repeated Covenant Game. These folk theorems establish that for certain ideal settings Hobbes’ and Hume’s arguments against offensively violating covenants are compelling. However, these ideal settings presuppose that the community has certain mechanisms that generate common knowledge of the identities of those with whom one should perform. I analyze the results of computer simulations of the interactions in a community whose members must rely upon private communication alone. The computer simulation data show that in this community, reputation effects cannot effectively deter members from offensively violating covenants. I conclude that Hobbes’ and Hume’s warnings against offensive violation are compelling only on condition that the community is sufficiently structured to generate common knowledge among its members. I also conclude that even in such structured communities, the Humean strategy is not the uniquely “correct” policy. (shrink)

We introduce the notion of an outcome space, in which strategic interactions are embedded. This allows us to investigate the idea that one strategic interaction might be an expanded version of another interaction. We then characterize the Nash equilibria arising in such extensions and demonstrate a folk-type theorem stating that any individually rational element of the outcome space is a Nash equilibrium.

We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use (...) the concept to highlight a potential danger of intellectual enculturation. (shrink)

Personalized and continuing relationships play a central role in any society. Economists have built upon the theories of repeated games and reputations to make important advances in understanding such relationships. Repeated Games and Reputations begins with a careful development of the fundamental concepts in these theories, including the notions of a repeated game, strategy, and equilibrium. Mailath and Samuelson then present the classic folk theorem and reputation results for games of perfect and imperfect public monitoring, with the benefit (...) of the modern analytical tools of decomposability and self-generation. They also present more recent developments, including results beyond folk theorems and recent work in games of private monitoring and alternative approaches to reputations. Repeated Games and Reputations synthesizes and unifies the vast body of work in this area, bringing the reader to the research frontier. Detailed arguments and proofs are given throughout, interwoven with examples, discussions of how the theory is to be used in the study of relationships, and economic applications. The book will be useful to those doing basic research in the theory of repeated games and reputations as well as those using these tools in more applied research. (shrink)

offers an evolutionary approach to morality, in which moral rules form a cultural system that is robust and evolutionarily stable. The folk theorem is the analytical basis for his theory of justice. I argue that this is a mistake, as the equilibria described by the folk theorem lack dynamic stability in games with several players. While the dependence of Binmore's argument on the folk theorem is more tactical than strategic, this choice does have policy (...) implications. I do not believe that moral rules are solutions to the Nash bargaining problem. Rather, I believe that human beings are emotionally constituted, by virtue of their evolutionary history, to embrace prosocial and altruistic notions of in-group–out-group identification and reciprocity. These aspects of human nature are incompatible with Binmore's notion that humans are self-regarding creatures. I present empirical evidence supporting a specific form of human, other-regarding preferences known as strong reciprocity. Key Words: justice • ethics • folk theorem • evolutionary game theory. (shrink)

According to the so-called “Folk Theorem” for repeated games, stable cooperative relations can be sustained in a Prisoner’s Dilemma if the game is repeated an indefinite number of times. This result depends on the possibility of applying strategies that are based on reciprocity, i.e., strategies that reward cooperation with subsequent cooperation and punish defectionwith subsequent defection. If future interactions are sufficiently important, i.e., if the discount rate is relatively small, each agent may be motivated to cooperate by fear (...) of retaliation in the future. For finite games, however, where the number of plays is known beforehand, there is a backward induction argument showing that rational agents will not be able to achieve cooperation. On behalf of the Hobbesian “Foole”, who cannot see any advantage in cooperation, Gregory Kavka (1983, 1986) has presented an argument that significantly extends the range of the backward induction argument. He shows that, for the backward induction argument to be effective, it is not necessary that the precise number of future interactions be known. It is sufficient that there is a known definite upper bound on the number of interactions. A similar argument is developed by John W. Carroll (1987). We will here question the assumption of a known upper bound. When the assumption is made precise in the way needed for the argument to go through, its apparent plausibility evaporates. We then offer a reformulation of the argument, based on weaker, and more plausible, assumptions. (shrink)

This commentary on Philip Kitcher’s Ethical Project compares his theory of the evolution of morality with my less ambitious theory of the evolution of fairness norms that seeks to flesh out John Mackie’s insight that one should use game theory as a framework within which to assess anthropological data. It lays particular stress on the importance of the folk theorem of repeated game theory, which provides a template for the set of stable social contracts that were available to (...) ancestral hunter-gatherer communities. It continues by drawing attention to the relevance of Harsanyi’s theory of empathetic preferences in structuring the fairness criteria that evolved as one response to the equilibrium selection problem that the folk theorem demonstrates is endemic in our species. (shrink)

For fifty years, Bolivia’s political party system was a surprisingly robust component of an otherwise fragile democracy, withstanding coups, hyperinflation, guerrilla insurgencies, and economic chaos. Why did it suddenly collapse around 2002? This article offers a theoretical lens combining cleavage theory with Schattschneider’s concept of competitive dimensions for an empirical analysis of the structural and ideological characteristics of Bolivia’s party system from 1952 to 2010. Politics shifted from a conventional left-right axis of competition, unsuited to Bolivian society, to an ethnic/rural–cosmopolitan/urban (...) axis closely aligned with its major social cleavage. That shift fatally undermined elite parties and facilitated the rise of structurally and ideologically distinct organizations, as well as a new indigenous political class, that transformed the country’s politics. Decentralization and political liberalization were the triggers that politicized Bolivia’s latent cleavage, sparking revolution from below. The article suggests a folk theorem of identitarian cleavage and outlines a mechanism linking deep social cleavage to sudden political change. (shrink)

This article is extracted from a forthcoming book, ‘Natural Justice’. It is a nontechnical introduction to the part of game theory immediately relevant to social contract theory. The latter part of the article reviews how concepts such as trust, responsibility, and authority can be seen as emergent phenomena in models that take formal account only of equilibria in indefinitely repeated games. Key Words: game theory • equilibrium • evolutionary stability • reciprocity • folk theorem • trust • altruism (...) • responsibility • authority. (shrink)

Ordered social life requires rules of conduct that help generate and preserve peaceful and cooperative interactions among individuals. The problem is that these social rules impose costs. They prohibit us from doing some things we might see as important and they require us to do other things that we might otherwise not do. The question for the contractarian is whether the costs of these social rules can be rationally justified. I argue that traditional contract theories have tended to underestimate the (...) importance of evaluating the cost of enforcement and compliance in the contract procedure. In addition, the social contract has been understood narrowly as a method of justifying specifically moral or political rules. I defend a broader version of contractarianism as a justificatory model that can be used to evaluate any set of social rules or institutions that impose costson agents. In so doing, I argue that contractarianism is a general method of evaluating and justifying the rules that order the structure of social life. (shrink)

The primary objective of this study was to propose a functional discrete mathematical model for analyzing folklore fairy tales. Within this model, characters are denoted as vertices, and explicit instances of communication – both verbal and non-verbal – within the text are depicted as edges. Upon examining a corpus of Eastern Slavic fairy tales in comparison to Chukchi fairy tales, unforeseen outcomes emerged. Notably, the constructed models seem to evade establishing certain connections between characters. Consequently, instances where the interactions among (...) fairy tale characters would result in a non-planar graph structure are notably absent. To put it differently, the models refrain from incorporating sub-graphs delineated by the Kuratowski theorem governing planar graphs, specifically the minimal non-planar graphs Κ5 and Κ3,3. Remarkably, even in more extensive texts featuring a larger cast of characters, connections that would yield a non-planar graph pattern are consistently avoided. This leads to the formulation of a hypothesis positing that traditional folk tales adhere to a “planar narrative” design – an identifiable narrative variant characterized by inherent limitations in complexity. This design, in turn, appears deeply entrenched within the societal framework of the cultures that produced these folk narratives. (shrink)

Can experimental philosophy help us answer central questions about the nature of moral responsibility, such as the question of whether moral responsibility is compatible with determinism? Specifically, can folk judgments in line with a particular answer to that question provide support for that answer. Based on reasoning familiar from Condorcet’s Jury Theorem, such support could be had if individual judges track the truth of the matter independently and with some modest reliability: such reliability quickly aggregates as the number (...) of judges goes up. In this chapter, however, I argue, partly based on empirical evidence, that although non-specialist judgments might on average be more likely than not to get things right, their individual likelihoods fail to aggregate because they do not track truth with sufficient independence. (shrink)

In various theories of truth, people have set forth many definitions to clarify in what sense a set of sentences is paradoxical. But what, exactly, is _a_ paradox per se? It has not yet been realized that there is a gap between ‘being paradoxical’ and ‘being a paradox’. This paper proposes that a paradox is a minimally paradoxical set meeting some closure property. Along this line of thought, we give five tentative definitions based upon the folk notion of paradoxicality (...) implied in Tarski’s undefinability theorem of truth and the dependence relation proposed by Leitgeb (J Philos Log 34(2):155–192, 2005). A definition of ‘being a paradox’ is acceptable if its extension must be sufficiently comprehensive to include all known paradoxes on the one hand, and its standard must also be high enough to exclude those that are evidently not paradoxes on the other hand. It turns out that only the last attempt is acceptable: a set of sentences is a paradox if it is paradoxical and self-dependent, and at the same time, it and any of its paradoxical and self-dependent subsets bisimulate each other. In this way, we articulate in what sense a set of sentences is a paradox, and so establish a connection between the notion of a paradox and the notion of paradoxicality. (shrink)

The paper undertakes three interdisciplinary tasks. The first one consists in constructing a formal model of the basic arithmetic competence, that is, the competence sufficient for solving simple arithmetic story-tasks which do not require any mathematical mastery knowledge about laws, definitions and theorems. The second task is to present a generalized arithmetic theory, called the arithmetic of indexed numbers (INA). All models of the development of counting abilities presuppose the common assumption that our simple, folk arithmetic encoded linguistically in (...) the mind is based on the linear number representation. This classical conception is rejected and a competitive hypothesis is formulated according to which the basic mature representational system of cognitive arithmetic is a structure composed of many numerical axes which possess a common constituent, namely, the numeral zero. Arithmetic of indexed numbers is just a formal tool for modelling the basic mature arithmetic competence. The third task is to develop a standpoint called temporal pluralism, which is motivated by neo-Kantian philosophy of arithmetic. (shrink)

Folke Tersman explores what we can learn about the nature of moral thinking by examining moral disagreement. He explains how diversity of opinion on moral issues undermines the idea that moral convictions can be objectively valued. Arguments on moral thinking are often criticized for not being able to explain why there is a contrast between ethics and other areas in which there is disagreement, but where one does not give up the idea of an objective truth, as in the natural (...) sciences. Tersman shows that the contrast has to do with facts about when, and on what basis, moral convictions can be correctly attributed to an agent or speaker. (shrink)

The idea of reflective equilibrium remains the most popular approach to questions about method in ethics, despite the masses of criticism it has been faced with over the years. Is this due to the availability of compelling responses to the criticisms or rather to factors that are independent of its reasonableness? The aim of this paper is to provide support for the first answer. I particularly focus on the recent discussion. Some recent objections are related to general arguments against the (...) possibility of moral knowledge, such as so-called “evolutionary debunking arguments.” I argue that nothing that has come to light in that debate, or in the recent discussion about IRE more generally, decisively strengthens the case against it. If anything, the recent developments show that IRE deserves its present status. (shrink)

The fact that debunkers can turn to the argument from disagreement for help is ofcourse not a surprise. After all, both types of challenge basically pursue the same,skeptical conclusion. What I have tried to show, however, is that they are related in amore intimate way.

A recent study of moral intuitions, performed by Joshua Greene and a group of researchers at Princeton University, has recently received a lot of attention. Greene and his collaborators designed a set of experiments in which subjects were undergoing brain scanning as they were asked to respond to various practical dilemmas. They found that contemplation of some of these cases (cases where the subjects had to imagine that they must use some direct form of violence) elicited greater activity in certain (...) areas of the brain associated with emotions compared with the other cases. It has been argued (e.g., by Peter Singer) that these results undermine the reliability of our moral intuitions, and therefore provide an objection to methods of moral reasoning that presuppose that they carry an evidential weight (such as the idea of reflective equilibrium). I distinguish between two ways in which Greene's findings lend support for a sceptical attitude towards intuitions. I argue that, given the first version of the challenge, the method of reflective equilibrium can easily accommodate the findings. As for the second version of the challenge, I argue that it does not so much pose a threat specifically to the method of reflective equilibrium but to the idea that moral claims can be justified through rational argumentation in general. (shrink)

Crispin Wright holds that moral realism is implausible since it is not a priori that every moral disagreement involves cognitive shortcomings. I develop two responses to this argument. First, a realist may argue that it holds for at least one of the parties to any disagreement that he holds false background beliefs (moral or otherwise) or that his verdict to the disputed judgment fails to cohere with his system. Second, he may argue that if none of the verdicts involves shortcomings, (...) the appropriate conclusion is that the disagreement is not genuine, since we must otherwise attribute an inexplicable error. (shrink)

A common anti-realist strategy is to argue that moral realism (or at least the non-naturalist form of it) should be abandoned because it cannot adequately make room for moral knowledge and justified moral belief, for example in view of an evolutionary account of the origins of moral beliefs or of the existence of radical moral disagreement. Why is that (alleged) fact supposed to undermine realism? I examine and discuss three possible answers to this question. According to the answer that I (...) think holds most promise, it undermines realism because it renders realism “epistemically incoherent” (in a sense explicated in the paper), and a central aim of the paper is to elaborate and defend that suggestion against certain objections. I end by briefly commenting on the more general significance of the discussion, by considering some other areas (epistemology and vagueness) where similar questions might be raised. (shrink)

An increasingly popular strategy among critics of ethical anti-realism is to stress that the traditional arguments for that position work just as well in the case of other areas. For example, on the basis of that claim, it has recently been claimed that ethical expressivists are committed to being expressivists also about epistemic judgments (including the judgment that it is rational to believe in ethical expressivism). This in turn is supposed to seriously undermine their position. The purpose of my paper (...) is to examine this challenge. I argue that, in spite of the many similarities between the discourses, there are also crucial differences and that those differences justify a mixed verdict about them. (shrink)

Some think that recent empirical research has shown that peoples' moral intuitions vary in a way that is hard to reconcile with the supposition that they are even modestly reliable. This is in turn supposed to generate skeptical conclusions regarding the claims and theories advanced by ethicists because of the crucial role intuitions have in the arguments offered in support of those claims. I begin by trying to articulate the most compelling version of this challenge. On that version, the main (...) problem is the absence of a believable positive account of the reliability of the intuitions . I then consider the response to this challenge that, in my view, holds most promise. It differs from others by invoking substantive moral assumptions. Such a strategy may appear problematically circular, in that the justification of those assumptions seems to presuppose the very thesis that is challenged . However, although I think that objection can be met, I argue that there are other problems with the strategy. On the basis of a set of conditions that a successful defense of the pertinent kind plausibly must satisfy, I argue that the prospects of developing such an account are bleak. (shrink)

According to a traditional argument against moral realism, the existence of objective moral facts is hard to reconcile with the existence of radical disagreement over moral issues. An increasingly popular response to this argument is to insist that it generalizes too easily. Thus, it has been argued that if one rejects moral realism on the basis of disagreement then one is committed to similar views about epistemology and meta-ethics itself, since the disagreements that arise in those areas are just as (...) deep as the moral ones. This in turn is taken to show that a moral anti-realist should seek another basis for her position. For, if she extends her anti-realism also to epistemology and meta-ethics, then she is no longer in a position to say that her meta-ethical position is (objectively) true or that it is a fact that we have reason to accept it. She therefore seems left with a position that hardly even seems to be a position. The purpose of the paper is to challenge this response and in particular the claim that the argument from disagreement applies equally well to epistemology and meta-ethics as it does to ethics. It is argued that, despite contrary appearances, there are crucial differences between the disagreements that occur in ethics compared to those that arise in the other areas. Moreover, even granted that the disagreements are just as deep, there are other differences between the areas that nevertheless justify drawing different conclusions about their status from the existence of those disagreements. (shrink)

Facts about moral disagreement and human evolution have both been said to exclude the possibility of moral knowledge, but the question of how these challenges interact has largely gone unaddressed. The paper aims to present and defend a novel version of the evolutionary “debunking” argument for moral skepticism that appeals to both types of considerations. This argument has several advantages compared to more familiar versions. The standard debunking strategy is to argue that evolutionary accounts of moral beliefs generate skeptical implications (...) because they attribute those beliefs to factors that are unrelated to their truth. That strategy is vulnerable to “third-factor” responses, which invoke first-order moral claims to challenge the assumption that Darwinian factors and the moral truths are really unrelated in that way. In contrast, our version is immune to those responses, as it does not proceed via assumptions about how Darwinian factors relate to the moral facts. Instead, it focuses on what evolutionary accounts of moral beliefs have to say about the fact that people often reach divergent moral beliefs. The argument thereby illustrates how the debunking strategy can join forces with the argument from moral disagreement. The combination of those strategies presents, we think, a challenge that is more formidable than when they are considered separately. (shrink)

A traditional objection to coherentism is that there may be incompatible though equally coherent sets of beliefs. The purpose of the paper is to assess this objection. It is argued that the better a belief "p" coheres with the system of a person, the less likely it is that the negation of the belief coheres equally well with someone else's system, or even that there is someone else who believes the negation of "p". The arguments are based on two plausible (...) assumptions about coherence, and some more controversial assumptions concerning meaning and interpretation. (shrink)