Many pioneers of the Scientific Revolution such as Galileo, Kepler, Stevin, Descartes, Mersenne, and others, wrote extensively about musical theory. This was not a chance interest of a few individual scientists. Rather, it reflects a continuing concern of scientists from Pythagorean times onwards to solve certain quantifiable problems in musical theory. One of the issues involved was technically known as ‘the division of the octave’, the problem, that is, of which notes to make music with. Simon Stevin's contribution to (...) this issue, in his treatise Vande Spiegheling der Singconst , is usually conceived of as a remarkably early plea for equal temperament, which is the tuning system we nowadays all take for granted. In this paper I show that, even though it is true that Stevin calculated the figures for what is now known as equal temperament, in fact the subject of temperament has almost nothing to do with his accompanying considerations, and that, therefore, his calculations served another purpose. A careful analysis of the problem situation in the science of music around 1600, reveals that Stevin's treatise highlights a particular stage in the history of what has always been the core issue of the science of music, namely, the problem of consonance. This is the search for an explanation, on scientific principles, of Pythagoras' law: ‘Why is it that those few musical intervals which affect our ear in a sweet and pleasing manner, correspond to the ratios of the first few integers?’ Through an analysis of the source material available we find that Stevin's theory, which makes no sense if interpreted as an early stage in the ‘evolution’ of equal temperament, was meant as a solution—as freshly original as it was wrongheaded—to this perennial problem of consonance, which has continued to baffle some of the best scientific minds from the very beginning of science to the present day. (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of (...) solutions on variable and fixed player set. Specifications of several properties characterize specific solutions in this class. (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of (...) solutions on variable and fixed player set. Specifications of several properties characterize specific solutions in this class. (shrink)

A solution for cooperative games with transferable utility, or simply TU-games, assigns a payoff vector to every TU-game. In this paper we discuss two classes of equal surplus sharing solutions. The first class consists of all convex combinations of the equal division solution and the center-of-gravity of the imputation-set value. The second class is the dual class consisting of all convex combinations of the equal division solution and the egalitarian non-separable contribution value. (...) We provide characterizations of the two classes of solutions using either population solidarity or a reduced game consistency in addition to other standard properties. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume XX, Number 2, November 1994, pp. 219-240 Infinite Divisibility in Hume's First Enquiry DALE JACQUETTE The Limitations of Reason The arguments against infinite divisibility in the notes to Sections 124 and 125 of David Hume's Enquiry Concerning Human Understanding are presented as "sceptical" results about the limitations of reason. The metaphysics of infinite divisibility is introduced merely as a particular, though especially representative problem, among several (...) that Hume discusses. Hume first writes: The chief objection against all abstract reasonings is derived from the ideas of space and time; ideas, which, in common life and to a careless view, are very clear and intelligible, but when they pass through the scrutiny of the profound sciences (and they are the chief object of these sciences) afford principles, which seem full of absurdity and contradiction.1 There follows an intuitive appeal to the apparent incoherence of the consequences of infinite divisibility in the geometry of space and measurement of time. Hume enlists natural belief against the infinite divisibility thesis in the mathematics of extension: But what renders the matter more extraordinary, is, that these seemingly absurd opinions are supported by a chain of reasoning, the Dale Jacquette is at the Department of Philosophy, The Pennsylvania State University, 246 Sparks Building, University Park PA 16802 USA. e-mail: [email protected] 220 Dale Jacquette clearest and most natural; nor is it possible for us to allow the premises without admitting the consequences. Nothing can be more convincing and satisfactory than all the conclusions concerning the properties of circles and triangles; and yet, when these are once received, how can we deny, that the angle of contact between a circle and its tangent is infinitely less than any rectilinear angle, that as you may increase the diameter of the circle in infinitum, this angle of contact becomes still less, even in infinitum, and that the angle of contact between other curves and their tangents may be infinitely less than those between any circle and its tangent, and so on, in infinitum? The demonstration of these principles seems as unexceptionable as that which proves the three angles of a triangle to be equal to two right ones, though the latter opinion be natural and easy, and the former big with contradiction and absurdity. (EHU 156-157) The implied sense of contradiction is then extended by Hume to the problem of infinite divisibility in time. The absurdity of these bold determinations of the abstract sciences seems to become, if possible, still more palpable with regard to time than extension. An infinite number of real parts of time, passing in succession, and exhausted one after another, appears so evident a contradiction, that no man, one should think, whose judgment is not corrupted, instead of being improved, by the sciences, would ever be able to admit of it. (EHU 157) The contradictions involved in traditional concepts of extension and time demarcate the limits of which reason is capable. But Hume's answer is more complex than merely surrendering to skepticism over the prospects of reason achieving understanding in the metaphysics of space and time. He tries to show that what he calls "Pyrrhonian" skepticism is ultimately self-defeating in its application of reason against reason. In place of a negative conclusion, he offers another solution to the paradoxes of infinite divisibility. What is remarkable about Hume's pronouncements against the infinite divisibility of extension and time, that may signal a change in his methodology if not his overall position on divisibility in the Enquiry from that of A Treatise of Human Nature, is his straightforward claim that natural belief rebels against the concept of infinite divisibility as its consequences apply to the metric of space and time.2 As in the Treatise, Hume pits natural disbelief in infinite divisibility against abstract metaphysical reason. But in the Enquiry, he does not invoke reason merely to correct the excesses of natural belief for the skeptical deflation of natural belief, say, in the necessity of causal connection, or the existence of mind-independent continuants. On the contrary, Hume Studies Infinite Divisibility in Hume's First Enquiry 221 Hume here appears instead to invoke natural disbelief in... (shrink)

In this paper, I argue that the asymmetrical mediated communication of the broad democratic public sphere can profitably be understood through the lens of deliberative democracy only if we adopt a system approach to deliberation. A system approach, however, often introduces a division of labor between ordinary citizens and experts. Although this division of labor is unavoidable and I believe compatible with a deliberative principle of legitimacy, it flirts with elitist theories of democracy: epistemic elites come up with (...) the agendas, ideas, and policy positions and democratic publics ratify or repudiate the agendas but do not generate or really engage with them. This I argue would violate an essential defining feature of deliberative democracy, namely that epistemic quality and equal participation are tightly linked. I turn to Habermas and his idea of a feedback loop as a possible solution to this dilemma. (shrink)

This chapter rejects Equal Division, focusing on Hillel Steiner’s formulation of the view. First, further explanation of why one might take Equal Division to follow from Equal Original Claims is provided. Then, David Miller’s objection is introduced, according to which there is no defensible metric by which resource shares can be made commensurate, given the fact of reasonable value pluralism. The chapter argues that what the metric problem really shows, is that Equal Division (...) possesses insufficient impartiality to satisfy the equal original claims that motivate the view in the first place. This case is made by critiquing the three principal metrics proposed to amalgamate individual valuations of natural resources and thereby render Equal Division both coherent and defensible; namely, economic value, opportunity cost, and ecological space. The chapter concludes that to respect Equal Original Claims, the better approach will be to formulate a Common Ownership conception of justice for natural resources. (shrink)

We modify the payment rule of the standard divide the dollar (DD) game by introducing a second stage and thereby resolve the multiplicity problem and implement equal division of the dollar in equilibrium. In the standard DD game, if the sum of players’ demands is less than or equal to a dollar, each player receives what he demanded; if the sum of demands is greater than a dollar, all players receive zero. We modify this second part, which (...) involves a harsh punishment. In the modified game $(D\!D^{\prime })$ , if the demands are incompatible, then players have one more chance. In particular, they play an ultimatum game to avoid the excess. In the two-player version of this game, there is a unique subgame perfect Nash equilibrium in which players demand (and receive) an equal share of the dollar. We also provide an $n$ -player extension of our mechanism. Finally, the mechanism we propose eliminates not only all pure strategy equilibria involving unequal divisions of the dollar, but also all equilibria where players mix over different demands in the first stage. (shrink)

New and recent axioms for cooperative games with transferable utilities are introduced. The non-negative player axiom requires to assign a non-negative payoff to a player that belongs to coalitions with non-negative worth only. The axiom of addition invariance on bi-partitions requires that the payoff vector recommended by a value should not be affected by an identical change in worth of both a coalition and the complementary coalition. The nullified solidarity axiom requires that if a player who becomes null weakly loses (...) from such a change, then every other player should weakly lose too. We study the consequence of imposing some of these axioms in addition to some classical axioms. It turns out that the resulting values or set of values have all in common to split efficiently the worth achieved by the grand coalition according to an exogenously given weight vector. As a result, we also obtain new characterizations of the equal division value. (shrink)

We introduce three natural collective variants of the well-known axiom of desirability, which require that if the contributions of a first coalition are at least as large as the contributions of a second coalition, then the payoff in the first coalition should be as large as the payoff in the second coalition. These axioms are called coalitional desirability and average coalitional desirability. The third variant, called uniform coalitional desirability, applies only to coalitions with the same size. We show that coalitional (...) desirability is very strong: no value satisfies simultaneously this axiom and efficiency. To the contrary, the combination of either average coalitional desirability or uniform coalitional desirability with efficiency and additivity characterizes the equal division value. (shrink)

This article considers whether any interpretation of the idea of equal claims to the natural world can resolve the Canyon Dilemma (i.e. can justify protecting the Grand Canyon but not a small canyon from mining by a poor generation). It first considers and ultimately rejects the idea of subjecting natural resource rights to an intergenerational equal division. It then demonstrates that a pluralist theory of environmental justice committed to both respect for the separateness of persons and to (...) the collective good can justify a type of intergenerational non-absolute equal division of natural resource rights that can navigate the Canyon Dilemma. (shrink)

We provide characterizations of the equal division values and their convex mixtures, using a new axiom on a fixed player set based on player nullification which requires that if a player becomes null, then any two other players are equally affected. Two economic applications are also introduced concerning bargaining under risk and common-pool resource appropriation.

We start by considering the Alternate Strike (AS) scheme, a real-life arbitration scheme where two parties select an arbitrator by alternately crossing off at each round one name from a given panel of arbitrators. We find out that the AS scheme is not invariant to “bad” alternatives. We then consider another alternating-move scheme, the Voting by Alternating Offers and Vetoes (VAOV) scheme, which is invariant to bad alternatives. We fully characterize the subgame perfect equilibrium outcome sets of these above two (...) schemes in terms of the rankings of the parties over the alternatives only. We also identify some of the typical equilibria of these above two schemes. We then analyze two additional alternating-move schemes in which players’ current proposals have to either honor or enhance their previous proposals. We show that the first scheme’s equilibrium outcome set coincides with that of the AS scheme, and the equilibrium outcome set of the second scheme coincides with that of the VAOV scheme. Finally, it turns out that all schemes’ equilibrium outcome sets converge to the Equal Area solution’s outcome of cooperative bargaining problem, if the alternatives are distributed uniformly over the comprehensive utility possibility set and as the number of alternatives tends to infinity. Journal of Economic Literature Classification Number: C72. (shrink)

This chapter contains section titled: A radical proposal Some history Why our conception of equal opportunity changes Racism and the costs of unequal opportunity The social context of political philosophy Contributive justice Race and opportunity.

ABSTRACT Many of our common-sense moral judgments seemingly imply the existence of moral luck. I attempt to avoid moral luck while retaining most of these judgments. I defend a view on which agents have moral equality of opportunity. This allows us to account for our anti-moral-luck intuitions at less cost than has been previously recognized.

Are there distinctively political values? Certain egalitarians seem to think that equality is one such value. Scheffler 's contribution to the symposium seeks to articulate a division of moral labour between norms of personal morality and the principles of justice that regulate social institutions, and using this suggests that the egalitarian critique of Rawls can be deflected. In this paper, instead, I question the status of equality as an intrinsic value. I argue that an egalitarianism which focuses on the (...) status of equality as valuable in itself embraces a theory of value with the worst elements of utilitarianism while leaving behind any of the intuitive appeal that utilitarianism has. In its place I press that we need a political conception of egalitarianism which stresses the role of equality as a political ideal without presupposing any values with which we engage beyond those found in the norms of personal morality. (shrink)

In this paper, we study the role of fairness motivation in bargaining. We show that bargaining between two strongly fairness motivated individuals who have different views about what represents a fair division may end in disagreement. Further, by applying the Nash bargaining solution, we study the influence of fairness motivation on the bargaining outcome when an agreement is reached. In particular, we show that the bargaining outcome is sensitive to the fairness motivation of the two individuals, unless they (...) both consider an equal division fair. We argue that our results accommodate existing experimental and field data on bargaining. (shrink)

A community faces the obligation of providing an indivisible public good that each of its members is able to provide at a certain cost. The solution is to rely on the member who can provide the public good at the lowest cost, with a due compensation from the other members. This problem has been studied in a non-cooperative setting by Kleindorfer and Sertel. They propose an auction mechanism that results in an interval of possible individual contributions whose lower bound (...) is the equal division. Here, instead we take a cooperative stand point by modelling this problem as a cost sharing game that turns out to be a ‘reverse’ airport game whose core is shown to have a regular structure. This enables an easy calculation of the nucleolus that happens to define the upper bound of the Kleindorfer–Sertel interval. The Shapley value instead is not an appropriate solution in this context because it may imply compensations to non-providers. (shrink)

We study how to partition a set of agents in a stable way when each coalition in the partition has to share a unit of a perfectly divisible good, and each agent has symmetric single-peaked preferences on the unit interval of his potential shares. A rule on the set of preference profiles consists of a partition function and a solution. Given a preference profile, a partition is selected and as many units of the good as the number of coalitions (...) in the partition are allocated, where each unit is shared among all agents belonging to the same coalition according to the solution. A rule is stable at a preference profile if no agent strictly prefers to leave his coalition to join another coalition and all members of the receiving coalition want to admit him. We show that the proportional solution and all sequential dictator solutions admit stable partition functions. We also show that stability is a strong requirement that becomes easily incompatible with other desirable properties like efficiency, strategy-proofness, anonymity, and non-envyness. (shrink)

We introduce a new allocation rule, called the sequential equal surplus division for rooted forest TU-games. We provide two axiomatic characterizations for this allocation rule. The first one uses the classical property of component efficiency plus an edge deletion property. The second characterization uses standardness, an edge deletion property applied to specific rooted trees, a consistency property, and an amalgamation property. We also provide an extension of the sequential equal surplus division applied to the problem of (...) sharing a river with bifurcations. (shrink)

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

Making adaptive choices between solution strategies is a central element of contemporary mathematics education. However, previous studies signal that students make suboptimal choices between mental and written strategies to solve division problems. In particular, some students of a lower math ability level appear inclined to use mental strategies that lead to lower performance. The current study uses a pretest-training-posttest design to investigate the extent to which these students’ choices for written strategies and performance may be increased. Sixth graders (...) of below-average mathematics level (N = 147) participated in one of two training conditions: an explicit-scaffolding training designed to promote writing down calculations or a practice-only training where strategy use was not explicitly targeted. Written strategy choices and performance increased considerably from pretest to posttest for students in both training conditions, but not in different amounts. Exploratory results suggest that students’ strategy choices may also be affected by their attitudes and beliefs and the sociocultural context regarding strategy use. (shrink)

In the Statesman (287c3-5), Plato proposes that the philosophical divider should divide analogously to how the butcher divides a sacrificial animal. According to the common interpretation, the example of animal sacrifice illustrates that we should “cut off limbs” (kata mele), that is, divide non-dichotomously into functional parts of a living whole. We argue that this interpretation is historically inaccurate and philosophically problematic: it relies on an inaccurate understanding of sacrificial butchery and leads to textual puzzles. Against the common interpretation, we (...) argue that the example of animal sacrifice illustrates that correct division minimizes (it cuts into the smallest number possible) by first dividing dichotomously and then dividing non-dichotomously into “parts,” not “limbs.” We will show that both the philosophical divider and sacrificial butcher proceed exactly in this way. By taking Plato’s comparison to the historical practice of animal sacrifice seriously, our interpretation provides better solutions to the textual puzzles than the common interpretation. (shrink)

The core of this book is a novel theory of distributive justice premised on the fundamental moral equality of persons. In the light of this theory, Rakowski considers three types of problems which urgently require solutions-- the distribution of resources, property rights, and the saving of life--and provides challenging and unconventional answers. Further, he criticizes the economic analysis of law as a normative theory, and develops an alternative account of tort and property law.

We consider countable so‐called rich subsemigroups of ; each such semigroup T gives a variety CPEAT that is axiomatizable by a finite schema of equations taken in a countable subsignature of that of ω‐dimensional cylindric‐polyadic algebras with equality where substitutions are restricted to maps in T. It is shown that for any such T, if and only if is representable as a concrete set algebra of ω‐ary relations. The operations in the signature are set‐theoretically interpreted like in polyadic equality set (...) algebras, but such operations are relativized to a union of cartesian spaces that are not necessarily disjoint. This is a form of guarding semantics. We show that CPEAT is canonical and atom‐canonical. Imposing an extra condition on T, we prove that atomic algebras in CPEAT are completely representable and that CPEAT has the super amalgamation property. If T is rich and finitely represented, it is shown that CPEAT is term definitionally equivalent to a finitely axiomatizable Sahlqvist variety. Such semigroups exist. This can be regarded as a solution to the central finitizability problem in algebraic logic for first order logic with equality if we do not insist on full fledged commutativity of quantifiers. The finite dimensional case is approached from the view point of guarded and clique guarded (relativized) semantics of fragments of first order logic using finitely many variables. Both positive and negative results are presented. (shrink)

The main aim of this study is to analyse how time use, individual resources, distributive justice and gender ideology influence perceptions of fairness concerning housework and gender equality. The analyses are based on survey data as well as on an interview study, both including Swedish couples. The quantitative results show that it is only factors connected to time use that are significantly correlated to both perceptions of fairness concerning division of household labour and gender equality. Although the qualitative results (...) in part confirm this picture, they also illustrate the complexity of concepts like fairness and equality. The interviews show that there are several factors and mechanisms at work in influencing perceptions of fairness and equality that were not possible to see from the quantitative analysis alone. (shrink)

Justice makes demands upon us. But these demands, important though they may be, are not the only moral demands that we face. Our lives ought to be responsive to other values too. However, some philosophers have identified an apparent tension between those values and norms, such as justice, that seem to transcend the arena of small-scale interpersonal relations and those that are most at home in precisely that arena. How, then, are we to engage with all of the values and (...) norms that we take to apply to us? In this article, I discuss one way that we might hope to resolve the tension and its relation to John Rawls's `basic structure restriction'. The prospect of resolution is offered by the idea of a `division of moral labour', according to which the pursuit of certain values is assigned to institutions and not to individuals. According to Rawls's basic structure restriction, principles of justice are applicable only to the institutions of the basic structure of society. The possibility of a connection between the division of moral labour and the basic structure restriction readily suggests itself. Taking G.A. Cohen's well-known `incentives' critique of the basic structure restriction as a starting point, I consider five ways in which that restriction might be defended by appeal to the division of moral labour. I conclude that none of these defences succeeds, for none convinces that the conditions in which it makes sense to apply the division of moral labour idea obtain for Rawls's conception of distributive justice. Although the division of moral labour is an attractive proposal, it can do no work in a Rawlsian context. Key Words: Cohen • distributive justice • egalitarian ethos • equality • Rawls. (shrink)

Research on gender and antimicrobial resistance (AMR) beyond women’s biological susceptibility is limited. A gender and equity lens in AMR research is necessary to promote gender equality and support the effectiveness, uptake, and sustainability of real-world AMR solutions. We argue that it is an ethical and social justice imperative to include gender and related intersectional issues in AMR research and implementation. An intersectional exploration of the interplay between people’s diverse identities and experiences, including their gender, socio-economic status, race, disability, age, (...) and sexuality, may help us understand how these factors reinforce AMR risk and vulnerability and ensure that interventions to reduce the risk of AMR do not impact unevenly. This paper reports on the findings of a systematic scoping review on the interlinkages between AMR, gender and other socio-behavioural characteristics to identify priority knowledge gaps in human and animal health in LMICs. The review focused on peer-reviewed and grey literature published between 2017 and 2022. Three overarching themes were gendered division of caregiving roles and responsibilities, gender power relations in decision-making, and interactions between gender norms and health-seeking behaviours. Research that fails to account for gender and its intersections with other lines of disadvantage, such as race, class and ability, risks being irrelevant and will have little impact on the continued and dangerous spread of AMR. We provide recommendations for integrating an intersectional gender lens in AMR research, policy and practice. (shrink)

It seems plausible that (i) how much punishment a person deserves cannot be affected by the mere existence or nonexistence of another person. We might have also thought that (ii) how much punishment is deserved cannot increase merely in virtue of personal division. I argue that (i) and (ii) are inconsistent with the popular belief that, other things being equal, when people culpably do very wrong or bad acts, they ought to be punished for this—even if they have (...) repented, are now virtuous, and punishing them would benefit no one. Insofar as we cannot deny (i), we are either forced to abandon the popular belief in desert, or else allow that personal division could, as I put it, “multiply desert.” Some may not find the latter, considered by itself, troubling. But I argue that the thesis that division multiplies desert faces a potentially serious problem, which arises in the context of personal fusion. It is difficult to see how to maintain a particular family of desert views in light of the cases here presented. (shrink)

Valuing -- Morality and reasonable partiality -- Doing and allowing -- The division of moral labour : egalitarian liberalism as moral pluralism -- Is the basic structure basic? -- Cosmopolitanism, justice, and institutions -- What is egalitarianism? -- Choice, circumstance, and the value of equality -- Is terrorism morally distinctive? -- Immigration and the significance of culture -- The normativity of tradition -- The good of toleration.

In this paper, we address an infamous argument against divisibility that dates back to Zeno. There has been an incredible amount of discussion on how to understand the critical notions of divisibility, extension, and infinite divisibility that are crucial for the very formulation of the argument. The paper provides new and rigorous definitions of those notions using the formal theories of parthood and location. Also, it provides a new solution to the paradox of divisibility which does not face some (...) threats that can possibly undermine the standard Lebesgue measure solution to such a paradox. (shrink)

[ Samuel Scheffler] Some egalitarian liberals have proposed a division of moral labour between social institutions and individual agents, but the division-of-labour metaphor has been understood in different ways. This paper aims to disentangle some of these different understandings, with an eye to clarifying the appeal of the egalitarian-liberal project and the challenges that it faces. The idea of a division of moral labour is best understood as the expression of a strategy for accommodating diverse values. It (...) is not an apology for economic self-interest or a device for justifying personal acquisitiveness. /// [Véronique Munoz-Dardé] Are there distinctively political values? Certain egalitarians seem to think that equality is one such value. Scheffler's contribution to the symposium seeks to articulate a division of moral labour between norms of personal morality and the principles of justice that regulate social institutions, and using this suggests that the egalitarian critique of Rawls can be deflected. In this paper, instead, I question the status of equality as an intrinsic value. I argue that an egalitarianism which focuses on the status of equality as valuable in itself embraces a theory of value with the worst elements of utilitarianism while leaving behind any of the intuitive appeal that utilitarianism has. In its place I press that we need a political conception of egalitarianism which stresses the role we engage beyond those found in the norms of personal morality. (shrink)

This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest (...) to largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances. (shrink)

Two problems about rights have received so far little attention. One is the problem of identifying a general value in the practice of rights. The second is to see when, if at all, rights violations wrong the right-holder, in a morally significant sense. In the present essay, I address the first question by investigating the second. I first show that if we commit to the two ideas, common in the contemporary philosophy of rights, that claim-rights always correlate with directed duties (...) and that rights aspire to protect interests of the right-holder, we make it hard to explain why rights violations, in general, wrong right-holders. In the final section, I present what I see as a promising solution to the puzzle. I describe a particular social environment (the society of equals) where interacting with others through rights is indeed valuable because respecting rights communicates that one takes seriously others’ equal moral status. In such a society and only in such a society, I conclude, moral agents are required to treat all rights violations as wrongs perpetrated against the right-holder. (shrink)

Interdisciplinarity is strongly promoted in science policy across the world. It is seen as a necessary condition for providing practical solutions to many pressing complex problems for which no single disciplinary approach is adequate alone. In this article we model multi- and interdisciplinary research as an instance of collective problem solving. Our goal is to provide a basic representation of this type of problem solving and chart the epistemic benefits and costs of researchers engaging in different forms of cognitive coordination. (...) Our findings suggest that typical forms of interdisciplinary collaboration are unlikely to find optimal solutions to complex problems within short time frames and can lead to methodological conservatism. This provides some grounds for both reflecting on current science policy and envisioning more effective scientific practices with respect to interdisciplinary problem solving. (shrink)

In their justification of individual entitlements, libertarians appeal to the concept of self-ownership. This paper argues that taking into account the division of labour in society calls for a fundamental reassessment of the normative implications of self-ownership. How should the benefits from division of labour—in other words, how should the co-operative surplus—be distributed? On the assumption that the parties to the division of labour are interdependent, and that this interdependence is mutual and of the same degree, I (...) argue for an equal distribution of the co-operative surplus. In form, my argument bears similarities to the left-libertarian position that calls for an equal distribution of natural resources. Despite its radically egalitarian implications, an equal distribution of the co-operative surplus remains a libertarian principle. (shrink)

Increasingly, both mothers and fathers are expected to play an equal role in child rearing. Nonetheless, we know little about how child care arrangements affect couples’ sexual intimacy and relationship quality. Research has focused on the effect of the division of paid labor and housework on couples’ relationships, finding that egalitarianism is problematic for sexual intimacy, relationship quality, and relationship stability. These findings, however, come almost universally from studies utilizing decades-old data that fail to examine the division (...) of child care. In this study, we update this work by utilizing data from the 2006 Marital and Relationship Study to examine how the division of child care affects the relationship quality and sexual intimacy of heterosexual couples in the United States. Results indicate that men’s performance of child care is generally associated with more satisfaction with the division of child care, more satisfying sexual relationships, and higher quality relationships. Importantly, we find that egalitarian child care arrangements have positive consequences for both men and women. These findings contribute to a growing body of research that challenges the costs of egalitarianism and indicates instead that egalitarianism is associated with higher quality, more intimate relationships than gender traditional arrangements. (shrink)

This chapter contains sections titled: Mill's Liberal Feminism Objection: Mill's Defense of Gendered Division of Labor Further Reading.

Efforts to promote gender equality often encourage changes to interpersonal interactions as a way of undermining gender hierarchy. Such programs are premised on the idea that the gender system can be “undone” when individuals behave in ways that challenge prevailing gender norms. However, scholars know little about whether and under what conditions real changes to the gender system can result from changed behaviors. We use the context of a gender sensitization program in the Democratic Republic of Congo to examine prospects (...) for transformative change at the interactional level of the gender system. Over nine months, we observed significant changes in men’s quotidian practices. Further, we identified a new commitment among many men to a more equal division of household labor. However, participants consistently undermined the transformative potential of these behavioral changes through their dedication to maintaining control over the objective, process, and meaning of change, resisting conceptions of equality that challenged the gender system. Because quotidian changes left gender hierarchy intact, they appear unlikely to destabilize the logics that legitimate women’s subordination. (shrink)

This book examines responsibility and luck as these issues arise in tort law, criminal law, and distributive justice. The central question is: whose bad luck is a particular piece of misfortune? Arthur Ripstein argues that there is a general set of principles to be found that clarifies responsibility in those cases where luck is most obviously an issue: accidents, mistakes, emergencies, and failed attempts at crime. In revealing how the problems that arise in tort and criminal law as well as (...) distributive justice invite structurally parallel solutions, the author also shows the deep connection between individual responsibility and social equality. This is a challenging and provocative book that will be of special interest to moral and political philosophers, legal theorists, and political scientists. (shrink)

The range of opportunities people enjoy in life largely depends on social, biological, and genetic factors for which individuals are not responsible. Philosophical debates about equality of opportunities have focussed mainly on addressing social determinants of inequalities. However, the introduction of human bioenhancement should make us reconsider what our commitment to equality entails. We propose a way of improving morally relevant equality that is centred on what we consider a fair distribution of bioenhancements. In the first part, we identify three (...) main positions in the debate on bioenhancement and equality, and we show how each of them fails to meet the demands of a serious commitment to equality. In the second part, we formulate a new proposal that we think better promotes equality of opportunities: people from disadvantaged socio-economic backgrounds should be given access to bioenhancements while people from privileged socio-economic background should be prohibited from using them. We argue that those who are concerned about the inequality implications of bioenhancement should embrace this solution, rather than reject bioenhancement. (shrink)

A Dedekind-finite set is said to be divisible by a natural number n if it can be partitioned into pieces of size n. We study several aspects of this notion, as well as the stronger notion of being partitionable into n pieces of equal size. Among our results are that the divisors of a Dedekind-finite set can consistently be any set of natural numbers, that a Dedekind-finite power of 2 cannot be divisible by 3, and that a Dedekind-finite set (...) can be congruent modulo 3, to all of 0, 1, and 2 simultaneously. (shrink)

Plato recognizes faction as a serious threat to any political community. The Republic’s proposed solution to faction relies on bringing citizens into a relation of ὁμόνοια. On the dominant line of interpretation, ὁμόνοια is understood along the lines of “explicit agreement” or “consensus.” Commentators have consequently thought that the καλλίπολις becomes resistant to faction when all or most of its members explicitly agree with one another about certain fundamentals of their political association—for example, they agree regarding who should govern (...) in the καλλίπολις.We argue that ὁμόνοια in Plato’s political philosophy has been under-analyzed and misunderstood. We show that, in Alcibiades I, rendering ὁμόνοια simply as agreement results in confusion about how expertise, political friendship, and civic unity are compossible in a well-ordered political community. In our view, Plato refines and adds philosophical depth to the concept of ὁμόνοια in the Republic. We claim that ὁμόνοια is a relation of psychological “like-mindedness” that obtains among members of different occupational classes in a political community. A community is rendered resistant to faction, then, when its members are, in some significant way, psychologically alike. Additionally, while Platonic ὁμόνοια can naturally be expected to result in substantive agreement among citizens, we argue that Platonic ὁμόνοια does not consist solely in agreement. (shrink)

This is a three-part study and defense of the idea of basic human equality. (This is the idea that humans are basically one another's equals, as opposed to more derivative theories of the dimensions in which we ought to be equal or the particular implications that equality might have for public policy.) Part (1) of the paper examines the very idea of basic equality and it tries to elucidate it by considering what an opponent of basic human equality (e.g. (...) a philosophical racist) might hold. It explores the idea of there being no morally significant fundamental divisions among humans (of the kind that some people insist on as between humans and others animals). Part (2) considers whether basic human equality must be based on some descriptive similarity among us (naturalistic or metaphysical); it considers the positions of a number of thinkers who have denied this. Part (3) considers John Rawls's conception of basic equality in terms of range properties. (Being in Ohio is a range property; Columbus and Cincinnati are both equally in Ohio even though even though Columbus is in the center of the state, while Cincinnati is just over the river from Kentucky.) It explores the application of this Rawlsian idea to the descriptive properties that might be thought relevant to human equality. This three part paper is a rather technical philosophical exploration. And it is just a beginning; we need much more work on the idea of basic equality. Some of the energy that has gone into discussions of equality as a policy aim (e.g. in the Dworkin/Sen literature or in the literature surrounding Rawls's Difference Principle) needs to be devoted to this more fundamental conception. (shrink)

Women continue to be in charge of most childrearing; men continue to be responsible for most breadwinning. There is no consensus on whether this state of affairs, and the informal norms that encourage it, are matters of justice to be tackled by state action. Feminists have criticized political liberalism for its alleged inability to embrace a full feminist agenda, inability explained by political liberals’ commitment to the ideal of state neutrality. The debate continues on whether neutral states can accommodate two (...) feminist demands: to enact policies aimed at dismantling the feminization of caregiving, especially childrearing, and to compensate women for some of the disadvantages they incur by being primary care-givers. I contribute to this debate with three arguments in support of policies meant to de-gender care-giving and compensate care-givers. The first appeals to equality of opportunity to positions of advantage and justifies policies that prevent or mitigate statistical discrimination and implicit biases. The second draws attention to a possible causal relationship between the specialization of women in early childcare and misogyny; since the latter is incompatible with political liberal justice, it yields the conclusion that political liberals ought to further investigate the causal hypothesis with the aim of establishing or refuting it. The third argument concludes that legitimate childrearing prohibits adults from socializing children or, at least girls, into gender norms; it justifies duties of justice on the side of parents, educators, and economic agents, and state policies meant to offset foreseeable breaches of some of these duties. (shrink)