Cet article analyse un bref texte arabe qui propose une division des catégories d’Aristote, en catégories simples et catégories composées ; ce fragment est attribué à Aḥmad Ibn al-Ṭayyib al-Saraḫsī, philosophe du neuvième siècle et disciple majeur d’al-Kindī, le « premier philosophe des Arabes ». L’article montre que la division d’al-Saraḫsī trouve son origine dans la tradition alexandrine des commentateurs aristotéliciens. Le fragment est replacé dans le contexte de la philosophie arabe en analysant différentes divisions des catégories avancées, respectivement, par (...) Ibn al-Muqaffaʿ, al-Kindī, les Frères de la Pureté et Abū l-Faraǧ ibn al-Ṭayyib. Des collections de définitions et de divisions philosophiques en grec et en syriaque constituent très probablement le mode de transmission de la division au monde de l’islam. Le fragment illustre également que, pour ce qui concerne la philosophie aristotélicienne, al-Saraḫsī ne suit pas toujours l’exemple de son maître al-Kindī. (shrink)

Milner and Goodale's influential account of the primate cortical visual streams involves a division of consciousness between them, for it is the ventral stream that has the responsibility for visual consciousness. Hence, the dorsal visual stream is a ‘zombie’ stream. In this article, I argue that certain information carried by the dorsal stream likely plays a central role in the egocentric spatial content of experience, especially the experience of visual spatial constancy. Thus, the dorsal stream contributes to a pervasive feature (...) of consciousness. (shrink)

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an (...) interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship be- tween division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science. (shrink)

For Marx, capitalism’s division of labour between mental and mate-rial labour is the condition of possibility for the creation of its alien, out of control, and contradictory effects. This paper will analyze the proletarian class, the capitalist class, and the world market qua ef-fects of the division of labour. The division of labour conceptualized fundamentally as a dynamic division between activity and passivity informs the analysis of these contradictory effects. This conceptual-ization of the division of labour provides the framework for (...) under-standing the striving toward activity and self-determination, de-scribed by Marx, of that which falls on the side of material labour. (shrink)

According to a standard interpretation of Hume’s argument against infinite divisibility, Hume is raising a purely formal problem for mathematical constructions of infinite divisibility, divorced from all thought of the stuffing or filling of actual physical continua. I resist this. Hume’s argument must be understood in the context of a popular early modern account of the metaphysical status of the parts of physical quantities. This interpretation disarms the standard mathematical objections to Hume’s reasoning; I also defend it on (...) textual and contextual grounds. (shrink)

Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods, or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, 'I cut, you choose', the authors show how it has been adapted in a number (...) of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular they focus on procedures which provide 'envy-free' allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures. (shrink)

We further investigate a divisibility relation on the set of BN ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.

The new mythology for which the German Romantic period called was not envisioned as antithetical to empiricism or experiential/experimental knowledge, but rather as emerging in dialogue with it to form a cultural foundation for such inquiry. Central to the mytho-scientific project were problematic theories of sexual division and generativity that established cultural baselines. This article examines the mythological investments of two influential thinkers of the period—Goethe and Schelling. It then analyzes Goethe’s unique merger of mythological approaches to sex and generation (...) with empirical observation in The Metamorphosis of Plants. It next traces Schelling’s expansion of Goethe’s theories of nature beyond their empirical justifications to develop a metaphysics of sexual differentiation. Finally, the article illuminates Goethe’s final reply to the sexual dynamics of Naturphilosophie at the end of his life, through the analysis of a single poem, “Finding Again,” in the collection God and World. Ultimately and in spite of its empirical commitments, Goethe’s more flexible view of sexual correlations would lose ground to the powerful metaphysical mythology of sexual opposition as both scientific and cultural bedrock. (shrink)

This paper presents a simple mathematical model that shows how economic inequality between social groups can arise and be maintained even when the only adaptive learning process driving cultural evolution increases individuals’ economic gains. The key assumptions are that human populations are structured into groups and that cultural learning is more likely to occur within than between groups. Then, if groups are sufficiently isolated and there are potential gains from specialization and exchange, stable stratification can sometimes result. This model predicts (...) that stratification is favored, ceteris paribus, by (1) greater surplus production, (2) more equitable divisions of the surplus among specialists, (3) greater cultural isolation among subpopulations within a society, and (4) more weight given to economic success by cultural learners. (shrink)

The phenomenon of twinning in early fetal development has become a popular source for doubt regarding the ascription of moral status to early embryos. In this paper, the possible moral basis for such a line of reasoning is critically analysed with sceptical results. Three different versions of the argument from twinning are considered, all of which are found to rest on confusions between the actual division of embryos involed in twinning and the property of early embryos to be divisible, be (...) based on highly questionable ethical assumptions, or to imply inconsistent claims regarding the moral importance of potentiality and/or the moral status of embryos. This is taken to expose a number of related inconsistencies in the moral basis of pro-life positions. In particular, ascribing moral significance to the property of being (in)divisible is found to be incompatible with the claim that human individuals possess unique values which could underpin an absolute moral ban on murder. (shrink)

In this article we revisit a number of disputes regarding significance logics---i.e., inferential frameworks capable of handling meaningless, although grammatical, sentences---that took place in a series of articles most of which appeared in the Australasian Journal of Philosophy between 1966 and 1978. These debates concern (i) the way in which logical consequence ought to be approached in the context of a significance logic, and (ii) the way in which the logical vocabulary has to be modified (either by restricting some notions, (...) or by adding some vocabulary) to keep as much of Classical Logic as possible. Our aim is to show that the divisions arising from these disputes can be dissolved in the context of a novel and intuitive proposal that we put forward. (shrink)

Aristotle's syllogistic theory, as developed in his Prior Analytics, is often regarded as the birth of logic in Western philosophy. Over the past century, scholars have tried to identify important precursors to this theory. I argue that Platonic division, a method which aims to give accounts of essences of natural kinds by progressively narrowing down from a genus, influenced Aristotle's logical theory in a number of crucial respects. To see exactly how, I analyze the method of division as it was (...) originally conceived by Plato and received by Aristotle. I argue that, while Plato allowed that some divisions fail to rigorously investigate the essence, he began a program continued by Aristotle (and others in antiquity and the middle ages) of seeking norms for division that would apply in any domain whatsoever. This idea of a rigorous, general method was taken up and developed by Aristotle in his syllogistic. Aristotle also used Plato's conception of predication as parthood in his semantics for syllogistic propositions. As part of my argument, I prove that a semantics based on Platonic divisional structures is sound and complete for the deduction system used in the literature to model Aristotle's syllogistic. (shrink)

How do scientists generate knowledge in groups, and how have they done so in the past? How do epistemically motivated social interactions influence or even drive this process? These questions speak to core interests of both history and philosophy of science. Idealised models and formal arguments have been suggested to illuminate the social epistemology of science, but their conclusions are not directly applicable to scientific practice. This paper uses one of these models as a lens and historiographical tool in the (...) examination of actual scientific collectives. It centres on the analysis of two episodes from the history of photosynthesis research of the late nineteenth- to mid-twentieth centuries, which display a wide and coordinated intellectual diversity similar to Kitcher’s “division of cognitive labour”. The concept, I argue, captures important aspects of the photosynthesis research communities, but the underlying process unfolded in ways that differ from the model’s assumption in interesting ways. The paper unravels how the self-organised interplay of cooperation and competition, and the dynamics of individual and collective goals within scientific communities were influential factors in the generation of knowledge. From there, some thoughts are developed on how historical and philosophical approaches in the analysis of science can productively interact. (shrink)

In this paper I formulate the thesis of the Division of Epistemic Labor as a thesis of epistemic dependence, illustrate several ways in which individual subjects are epistemically dependent on one or more of the members of their community in the process of knowledge acquisition, and draw conclusions about the cognitively distributed nature of some knowledge acquisition.

In Plato’s Statesman, the Eleatic Stranger applies a specialized method of inquiry—the “method of collection and division”, or “method of division”—in order to discover the nature of statecraft. This paper articulates some consequences of the fact that the method is both a tool for identifying natural kinds—that is, a tool for carving the world by its joints (Phaedrus 265b-d)—and social kinds—that is, the kinds depending on human beings for their existence and explanation. A central goal of the paper is to (...) illuminate the extent to which this use of the method of division allows us to identify Plato as an early historical forerunner of racialism, which is an ideology according to which humanity divides into races differentiated by heritable physiological, cultural, and intellectual traits, as a way of vindicating oppressive and exploitative social, political, and economic systems. -/- I defend an interpretation of the Stranger’s claim, much discussed in the literature, that the division of humankind into Greek and barbarian is unnatural (Politicus 262c-263a). I argue that, in the Stranger’s view, this division reflects subjective illusion and prejudice, rather than the fundamental, and teleological, structure of human social organization, which concerns how human beings rationally cooperate to self-produce as a species. Nonetheless, the Stranger’s alternative theory of the natural structure of human society, I suggest, is proto-racial in another way. Through a brief consideration of the Stranger’s affirmative and complex division of kinds in the city, I argue that he re-introduces naturalistic foundations for unjust human hierarchies through his alternative theory of natural kinds and human social teleology. (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)

Left distributive algebras arise in the study of classical structures such as groups, knots, and braids, as well as more exotic objects like large cardinals. A long-standing open question is whether the set of left divisors of every term in the free left distributive algebra on any number of generators is well-ordered. A conjecture of J. Moody describes a halting condition for descending sequences of left divisors in the free left distributive algebra on an arbitrary number of generators. In this (...) paper we present progress toward an affirmative answer to the open question mentioned above, namely we prove that the many generator form of Moody’s conjecture holds if each member of the free left distributive algebra has a “division form” representation in an expanded algebra. (shrink)

The UK-based deliberations that led up to the legalisation of two new ‘mitochondrial donation’ techniques in 2015, and which continued after that time as regulatory details were determined, featured a division of advisory labour that is common when decisions are made about new technologies. An expert panel was convened by the Human Fertilisation and Embryology Authority, charged with assessing the scientific and technical aspects of these techniques. Meanwhile, the Nuffield Council on Bioethics addressed the ethical issues. While this division of (...) labour was undertaken in the name of thoroughness, I argue here that it can have the unintended consequence that hybrid questions that simultaneously involve ethical and technical aspects—especially questions about where to set evidential thresholds for the acceptance of new technology—do not receive enough attention. (shrink)

The UK-based deliberations that led up to the legalisation of two new ‘mitochondrial donation’ techniques in 2015, and which continued after that time as regulatory details were determined, featured a division of advisory labour that is common when decisions are made about new technologies. An expert panel was convened by the Human Fertilisation and Embryology Authority (HFEA), charged with assessing the scientific and technical aspects of these techniques. Meanwhile, the Nuffield Council on Bioethics addressed the ethical issues. While this division (...) of labour was undertaken in the name of thoroughness, I argue here that it can have the unintended consequence that hybrid questions that simultaneously involve ethical and technical aspects—especially questions about where to set evidential thresholds for the acceptance of new technology—do not receive enough attention. (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)

The question of the division of cognitive labor has given rise to various models characterizing the way scientists should distribute their efforts. These models often consider the scientific community as a self-governed sphere constituted by rational agents making choices on the basis of fixed rules. Such models have recently been criticized for not taking into account the real mechanisms of science funding. Hence, the question of the utility of the DCL models in guiding science policy remains an open one. In (...) this paper, we show that two unconsidered dimensions would have to be taken into account. First, DCL studies miss the existence of distinct levels of epistemic objectives organizing the research process. Indeed, the scientific field is structured as a system of hierarchical, interconnected practices which are defined both by their inherent purposes and by various superposed external functions. Second, I criticize the absence of ontological considerations, since the epistemological significance of pluralism is highly dependent on the nature of the object under study. Because of these missing dimensions, current DCL models might have a limited usefulness to identify good practices of research governance. (shrink)

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of (...) this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch. (shrink)

A number of philosophers maintain that the destruction of an embryo in the first 2 weeks after fertilization is not morally problematic as it is metaphysically impossible for any human organism to then have existed. We contend that the typical adult human organism was once a zygote so there is no metaphysical shortcut to justify early abortion. We show that five arguments against human organisms ever having been zygotes fail. All of the arguments have to do with one variant or (...) another of the zygote or early embryo dividing. They do not provide any reason to believe that since some adult organisms are not identical to zygotes due to earlier divisions, none could have been. (shrink)

In this article, I will begin by describing recent divisive concepts legislation, which bans teaching about aspects of racism, sexism, and equity, speculating briefly on the motivations behind it and the implications resulting from it. I will then describe how discussing divisive concepts in classrooms may be a helpful way for students to better understand the particular concepts and for students to take a stand on them. While I will briefly argue for the importance of classroom discussion of divisive concepts, (...) my central claim will be that we must do more than merely discuss these concepts. Instead, we should engage in classroom inquiry about them. Inquiry positions students to not be silent regarding divisive concepts, as some legislation may cause, and inquiry positions students to not just talk about divisive concepts, but to solve social problems related to them in our world today. In other words, inquiry enables us to do something about divisive concepts, rather than just learning about them, as some educators currently advocate in calls for discussion. And inquiry is certainly more effective than banning divisive concepts or pushing them to the background, as recent legislation attempts to do. I argue that rather than excluding divisive concepts or the divisions they may provoke from our classrooms, we need educative spaces where we inquire into what divides us, why we are divided, and how we might respond to such division. Within that inquiry, we can better attend to our divisions while also taking up the specific concepts prohibited in recent legislation. (shrink)

In Republic II Glaucon assigns to Socrates the task of praising justice for itself. What it means to praise justice for itself is unclear. A new interpretation is offered on the basis of an analysis of Glaucon's division of goods. A distinction is developed between criterial benefits, those valuable consequences of a thing which provide a standard for evaluating a thing as a good instance of its type, and fringe benefits, valuable consequences which do not provide such a standard. Socrates (...) is expected to praise justice by describing the benefits it constitutes as a valuable activity of soul. He may also use the criterial benefits of justice but not its fringe benefits. This account of Socrates' task is superior to those interpretations which rule out all use of valuable consequences in praising justice and to those interpretations which fail to preserve the distinction between the second and third classes of goods. (shrink)

Durante los últimos decenios del siglo XX la filosofía de Francisco Suárez fue considerada parte integrante de un movimiento escolástico comúnmente mencionado como escuela tomista. La perspectiva de abordaje, según el mote impuesto, colocaba la posición especulativa del Dr. Eximio más próxima al dominico Tomás de Aquino de acuerdo con los siguientes matices: a. en el ámbito epistémico la figura del Aquinate eclipsaba ampliamente aquella de Suárez, promoviendo una auténtica desconsideración de sus tesis originales; b. el jesuita español fundaba, igual (...) que Tomás de Aquino, la división de las ciencias especulativas en el acto intelectual de abstracción; c. la diferencia entre ambas concepciones metafísicas no implicaba necesariamente una comprensión epistémica distinta. Ahora bien, contra estas interpretaciones aparece en el siglo XXI otra lectura, donde se acentúa la diferencia decisiva de la filosofía del jesuita del siglo XVI, quien, en letras medievales, escribe y piensa en permanente tensión entre la herencia de la filosofía antigua y medieval por una parte, y una neo-escolástica de aires renacentistas por la otra. De acuerdo con ello, si bien su pensamiento discurre por una tradición aristotelizante del saber, la comprensión de las ciencias se asienta, a diferencia de Tomás de Aquino, en clave objetiva. Sobre esta premisa, el siguiente estudio abordará con exclusividad la originalidad epistémica de Suárez según la división de las ciencias especulativas y reales, mostrando el orden, el principio y las relaciones entre las ciencias física, matemática y metafísica. (shrink)

Recent debates over adults' theory of mind use have been fueled by surprising failures of perspective-taking in communication, suggesting that perspective-taking may be relatively effortful. Yet adults routinely engage in effortful processes when needed. How, then, should speakers and listeners allocate their resources to achieve successful communication? We begin with the observation that the shared goal of communication induces a natural division of labor: The resources one agent chooses to allocate toward perspective-taking should depend on their expectations about the other's (...) allocation. We formalize this idea in a resource-rational model augmenting recent probabilistic weighting accounts with a mechanism for (costly) control over the degree of perspective-taking. In a series of simulations, we first derive an intermediate degree of perspective weighting as an optimal trade-off between expected costs and benefits of perspective-taking. We then present two behavioral experiments testing novel predictions of our model. In Experiment 1, we manipulated the presence or absence of occlusions in a director–matcher task. We found that speakers spontaneously modulated the informativeness of their descriptions to account for “known unknowns” in their partner's private view, reflecting a higher degree of speaker perspective-taking than previously acknowledged. In Experiment 2, we then compared the scripted utterances used by confederates in prior work with those produced in interactions with unscripted directors. We found that confederates were systematically less informative than listeners would initially expect given the presence of occlusions, but listeners used violations to adaptively make fewer errors over time. Taken together, our work suggests that people are not simply “mindblind”; they use contextually appropriate expectations to navigate the division of labor with their partner. We discuss how a resource-rational framework may provide a more deeply explanatory foundation for understanding flexible perspective-taking under processing constraints. (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)

The aim of this article is twofold: first, to identify and address three central divisions in the field of authentic education that introduce ambiguity and at times inconsistencies within the field of authentic education. These divisions concern a) the relationship between autonomy and authenticity; b) the division between the two basic attitudes towards ‘care’ in the authenticity literature, and; c) the well-worn division between objective and subjective realms of knowledge and identity construction. Addressing these divisions through Charles Taylor's distinction between (...) active and passive aspects of authenticity, I believe, will lead to a better understanding of the main issues involved in conceptualising and applying authenticity-based education. Second, to present what I call The Postconventional Authentic Relation-to-Self as a basis for overcoming and reconciling the above divisions. I shall conclude by providing some examples of the way the perspective envisioned by PARTS can be applied to educational practices. (shrink)

The question of the division of cognitive labor has given rise to various models characterizing the way scientists should distribute their efforts. These models often consider the scientific community as a self-governed sphere constituted by rational agents making choices on the basis of fixed rules. Such models have recently been criticized for not taking into account the real mechanisms of science funding. Hence, the question of the utility of the DCL models in guiding science policy remains an open one. In (...) this paper, we show that two unconsidered dimensions would have to be taken into account. First, DCL studies miss the existence of distinct levels of epistemic objectives organizing the research process. Indeed, the scientific field is structured as a system of hierarchical, interconnected practices which are defined both by their inherent purposes and by various superposed external functions. Second, I criticize the absence of ontological considerations, since the epistemological significance of pluralism is highly dependent on the nature of the object under study. Because of these missing dimensions, current DCL models might have a limited usefulness to identify good practices of research governance. (shrink)

La division du travail physiologique est un concept tombé en désuétude en biologie. Quand l’expression est employée, c’est sans égard pour sa fonction nomologique importante dans la biologie du second xixe. Nous analyserons l’importation de la division du travail de l’économie à la biologie, malgré les difficultés de validation que posait son transfert d’une science à l’autre. La notion a ainsi continué sa carrière dans une biologie gagnée à la théorie cellulaire, cependant que ses déterminations économiques perdaient leur pertinence. Nous (...) terminerons en interrogeant sa disparition au début du xxe. La division du travail physiologique, une fois purifiée de son économicité primitive, ne pouvait sans doute que retourner à un stade métaphorique. (shrink)

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)

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)

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)

Morality, according to some theories, demands a lot of us. One way to defend such demanding moral theories is through an appeal to the division of normativity; on this picture, morality is only one of the normative domains that guides us, so it should be expected that we often fail to follow that guidance. This paper defends the division of normativity as a response to demandingness objections against an alternative: moral rationalism. It does this by addressing and refuting three arguments: (...) the argument from blameworthiness, the argument from agency, and the argument from authority. In turn, I show that none of these arguments work as responses to the division of normativity – if normativity generally is divided, so too must be blameworthiness, agency, and authority. (shrink)

Aristotle proposed in the famous part of his 6th Book of Metaphysics a triple categorization of speculative sciences (physics, mathematics, first philosophy). Some scholars have considered this classical division as an unlawful and inconsistent Platonic residue of the parallelism between knowledge and reality. Others have numbered Aristotle among the upholders of the scholastic doctrine of the so-called degrees of abstraction. After having profoundly examined texts of the Corpus Aristotelicum (Metaphysics E 1, 1025b 1 - 1026a 32; On the soul A (...) 1, 403a 27 - 403b 19) not only we can refute the accusation of Platonism and the unlawful and anachronistic attribution of degrees of abstraction doctrine to the Stagirite, but principally understand the real importance of Aristotle's proposition. That is to say: its role in determining the epistemic character of the science on which all this deep inquiry takes place: the "filosofia prima". (shrink)

The paper mobilizes Adam Smith’s treatment of the division of labour in relation to the production, consumption and exchange of knowledge. One aspect of this mobilization deals with the epistemic demands that exchange makes on its participants. The other deals with increasing returns in the provision of knowledge itself, treating knowledge creation as just another example of specialization and exchange. These two aspects come together in relation to the epistemic demands associated with assessing knowledge quality. These demands differ according to (...) whether the knowledge is embodied in products or whether the knowledge is an object for its own sake. It is argued that disciplines play a critical role as institutions for meeting the epistemic demands that the division of labour creates in the ‘knowledge’ case. (shrink)

It is well known that in the Republic, Socrates presents a view of the soul or the psyche according to which it has three distinct parts or aspects, which he calls the reasoning, spirited, and appetitive parts. Socrates’ clearest characterization of these parts of the soul occurs in Republic IX, where he suggests that they should be understood in terms of the various goals or ends that give rise to the particular desires that motivate our actions. In Republic X, however, (...) Socrates uses the phenomenon of cognitive conflict about matters of fact to show that the soul has only two parts, the rational and the irrational. Moreover, he characterizes these parts in terms of cognitive tendencies, such as forming beliefs on the basis of reason versus forming beliefs on the basis of perceptual appearances. In this chapter, I explain how these divergent accounts of the soul and its parts are legitimate alternative characterizations. A consequence of my argument is that we should not think of the divided soul as primarily a division of desires, but rather as a division of cognitive attitudes towards the world, each of which yields different sorts of desires. (shrink)

Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.

It is shown that a stable division ring with positive characteristic has finite dimension over its centre. This is then extended to simple division rings.