While Bernard Suits's understanding of games has significantly influenced the philosophy of sport, the longest sustained investigation in The Grasshopper is of make-believe and roleplaying games. Suits’s discussion of make-believe and roleplaying is found in chapters 9 through 12, but what he says there is uncharacteristically unclear. To clarify Suits’s account, the present paper distinguishes between two arguments that Suits interweaves. In the first, Suits argues that game playing is not a species of play. In the second, Suits argues that (...) playing a make-believe or role-playing game is the same — at heart — as playing a game of any type. While the paper takes no position on the former, it defends the latter argument against several important objections by Thomas Hurka and C. Thi Nguyen. It contends, furthermore, that Suits is not simply trying to show that his theory of game playing can account for make-believe and roleplaying games. Rather, Suits is also using make-believe and roleplaying games to clarify exactly how his theory of game playing should be understood. (shrink)

Drawing on recently published correspondence as well as on a survey of Polish and international philosophical activity published in 1937 and details concerning the publisher and bookseller Aleksander Mazzucato, I provide evidence that, contrary to some recent assertions (but in line with older bibliographical entries), Tarski's ‘Der Wahrheitsbegriff in den formalisierten Sprachen’ was not published in journal form until 1936, although preprints, lacking two corrections and a small addendum, were likely available in the late months of 1935.

Using data on submitted and published manuscripts in Feminist Economics from 1995 to 2019, we examine differences in method and scope used by authors residing in the Global North and Global South. We specifically focus on research methods, intersectional analyses, region of analysis, and co-authorship status. Further, using logistic regression models, we examine the relationship between authors’ location and use of research methods. We find authors in the Global South are more likely to engage in empirical and mixed-methods papers compared (...) to Global North authors in our sample. Moreover, a greater share of Global South authors engage in intersectional analysis and exhibit geographical focus on developing countries. Drawing insights from the Feminist Economics manuscripts data, we argue that encouraging Global South research can contribute to the goals of the field of feminist economics – aimed at inclusivity, diversity of standpoints, and plurality in research methods, thereby improving overall economic research. (shrink)

The notion of the ‘division of physiological labour’ is today an outdated relic in the history of science. This contrasts with the fate of another notion, which was so frequently paired with the division of physiological labour, which is the concept of ‘morphological differentiation.’ This is one of the elementary modal concepts of ontogenesis. In this paper, we intend to target the problems and causes that gradually led biologists to combine these two notions during the 19th century, and (...) to progressively dissociate them, retaining only the concept of differentiation by the early 20th century. We shall adhere to the following: 1. The primitive economic concept of the division of labour is not a descriptive notion denoting a type of organisation of labour, but an etiological one: the idea of a causal relationship between this type of organization and the improvement of the whole. 2. This concept rapidly interested naturalists such as Henri Milne-Edwards, who were keen to find a rational ground for hierarchizing living forms based on anatomical complexity. 3. The validation of this notion in the realms of biology was subject to at least two conditions which were far from being fully satisfied. This did not prevent, however, the initial success of the concept of the division of physiological labour during the second half of the 19th century. 4. Finally, the gradual disqualification, within the Darwinian theoretical context, of the conception of an intrinsic hierarchical rank of organisms, led to a lack of interest in the concept of the physiological division of labour, at least in its non-Darwinian and non-ecological variant. (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)

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 introduceself-divisibleultrafilters, which we prove to be precisely those$w$such that the weak congruence relation$\equiv _w$introduced by Šobot is an equivalence relation on$\beta {\mathbb Z}$. We provide several examples and additional characterisations; notably we show that$w$is self-divisible if and only if$\equiv _w$coincides with the strong congruence relation$\mathrel {\equiv ^{\mathrm {s}}_{w}}$, if and only if the quotient$(\beta {\mathbb Z},\oplus )/\mathord {\mathrel {\equiv ^{\mathrm {s}}_{w}}}$is a profinite group. We also construct an ultrafilter$w$such that$\equiv _w$fails to be symmetric, and describe the interaction between the (...) aforementioned quotient and the profinite completion$\hat {{\mathbb Z}}$of the integers. (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)

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)

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)

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.

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)

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 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)

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)

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 (...) class='Hi'>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)

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.

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)

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)

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 division of cognitive labor is fundamental to all cultures. Adults have a strong sense of how knowledge is clustered in the world around them and use that sense to access additional information, defer to relevant experts, and ground their own incomplete understandings. One prominent way of clustering knowledge is by disciplines similar to those that comprise the natural and social sciences. Seven studies explored an emerging sense of these discipline‐based ways of clustering of knowledge. Even 5‐year‐olds could cluster (...) knowledge in a manner roughly corresponding to the departments of natural and social sciences in a university, doing so without any explicit awareness of those academic disciplines. But this awareness is fragile early on and competes with other ways of clustering knowledge. Over the next few years, children come to see discipline‐based clusters as having a privileged status, one that may be linked to increasingly sophisticated assumptions about essences for natural kinds. Possible mechanisms for this developmental shift are examined. (shrink)

“In modern political economy the division of labor is a main aspect.”.

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)

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)

The Renaissance perspective represents the three-dimensional space onto a bi-dimensional one. This cultural construction, which unifies real and virtual, like all simulations, has some limitations – the main one is that it only works from a precise viewpoint that rules the illusion. When moving away from this position the illusion becomes imperfect. Similar to physics, where reality depends on the observer’s position, perspective depends on the viewer’s position. Since perspective has been inherited by photography, cinema, video, computer images, virtual reality, (...) 3D videogames, we live in a perspective-based culture. In perception the boundaries between opposite qualities are often blurred and even indistinguishable. A screen is generally considered as rectangular, but it can be viewed as really rectangular only from its central perpendicular axis, at the crossing of the diagonals. When moving from this position it should appear as trapezoidal, but people still say it is rectangular: because they see it as rectangular or because they know it is rectangular? This threshold between vision and knowledge is imperceptible and obscure. Something similar happens with the senses. They are considered as separate entities: touch, hear, sight, smell and taste are described as distinct ways to detect the phenomenal world. But they are intermingled; the boundaries that are supposed to separate them are apparent: they are logically separable but not separate. The sensorial system is a cohesive and interrelated continuum where the senses act in synergy with each other. Continuity and discreteness, indistinguishability and distinction, inseparability and division are qualities to individuate, describe, classify and/or communicate the phenomena. These qualities are both theoretical and technical, since they depend on the general perspective of the analysis, on the goals to pursue, on the scale at which the phenomena are observed and on the accuracy of the instruments that are used. (shrink)

As is true for most small divisions, membership in PIRI overlaps with membership in all other APA divisions. Thus, our members include hardcore experimentalists teaching in Christian colleges, social psychologists focusing on research in the psychology of religion, pastoral counselors, transpersonal psychologists, religiously-committed psychologists attempting to integrate psychology and theology, and numerous others. Our roots lie in the American Catholic Psychological Association; our branches point to religion in all its forms. Our common commitment is to the assertion that religion is (...) a critical psychological variable. Examples are given of our theoretical and philosophical interests, including Philosophy of Science; Anthropologies/Theories of Human Nature; Spiritual or Religious Development; Psychology, Politics, and Ethics; Religion as a Significant Psychological Variable; and Critique of Psychological Theories. 2012 APA, all rights reserved). (shrink)

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)

Aristotle refers to some animal kinds as μέγιστα γένη, or greatest kinds. The goal of this paper is to make clear the nature and significance of these kinds. I argue that Aristotle thinks of greatest kinds as the most general kinds within a specified domain. I then consider the fact that Aristotle’s discussion of animals’ reproductive parts and modes of reproduction in Generation of Animals is organized around divisions related to the cause of each of the features being explained. I (...) conclude that, while classification is an important goal in Aristotle’s biological treatises, it is of little significance that some of the kinds he identifies are referred to as greatest kinds. The important divisions are, for Aristotle, the divisions that best serve his goal of explaining the various features of animals and these divisions sometimes group together and sometimes cut across the commonly recognized, including the greatest, animal kinds. (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)

Some scholars claim that Critical Realism promises well for the unification of the social sciences, e.g., "Unifying social science: A critical realist approach" in this volume. I will first show briefly how Critical Realism might unify social science. Secondly, I focus on the relation between the ontology and methodology of Critical Realism, and unveil the politics of metaphysics. Subsequently, it is argued that the division of labour between social scientific disciplines should not be metaphysics-driven, but rather question-driven. In conclusion, (...) I will therefore defend a question-driven pluralism as a guide for interdisciplinarity. (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)

The Augustine’s doctrine on human will is proposed as an original contribution. His conception of will as act and power of the soul is explained. The main question is the inner division or breaking of the will, and the conflict between the two wills. Finally and shortly, we examine love as the Augustine’s «solution» to this problem: the resolution of the inner conflict of the will through his transformation in love.

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)

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)

In this article I deal with a problem concerning the ‘divisions of nature’ in Maximus the Confessor’s Ambiguum 41. These ‘divisions’ are five categories that describe how creatures differ from one another and God in natural, physical ways. Later, Maximus discusses the way that the human person may follow Christ to mediate between these divisions. This becomes problematic however as the ascetic practice associated with this mediating power occurs within a sphere we usually define as ‘ethical’. In conflating these physical (...) and ethical dimensions it becomes unclear how our actions can overcome and unite the physical differences described in Maximus’ divisions of nature’. In this article I demonstrate how this problem may be overcome by using Maximus’ own logic of division and unity within this very Ambiguum. It is shown that Maximus does not see these two spheres of ‘physical’ and ‘ethical’ as separate. The ethical is part of the natural trajectory of the physical. Maximus is simply talking about the natural world and the way in which it moves towards its Creator. I build upon Tollefsen’s work on universals and Cvetković’s on circle and radii analogy in order to support this position. Finally, I suggest that we ought to think of Maximus’ ‘divisions of nature’ in this Ambiguum rather as ‘divisions and unity of nature’, since physical differences also promise the possibility of movement of all creation toward unity with God. (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)

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)

This paper analyzes classical concepts of division of labour and offers some contemporary theoretical model which includes causes and effects of it. For Smith, the main cause is a tendency of human nature to exchange and the main effect is a progress of the country. For Marx, the fundamental cause is historical development of productive forces and effects are accumulation of capital on the one side but also an alienation of working class on the other. Spencer considers as the (...) main cause specialization of functions in generally, which consequence is integration of society. For Durkheim, causes are social density and volume, and its effect or function is new interconnection in society known as term organic solidarity. Weber derives division of labour from his theory of rational economic actions, and its most important effect is development of occupational structure. (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 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)

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)

Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the ‘three-fold way’. (...) It is perhaps easiest to see it in the study of irreducible unitary representations of groups on complex Hilbert spaces. These representations come in three kinds: those that are not isomorphic to their own dual (the truly ‘complex’ representations), those that are self-dual thanks to a symmetric bilinear pairing (which are ‘real’, in that they are the complexifications of representations on real Hilbert spaces), and those that are self-dual thanks to an antisymmetric bilinear pairing (which are ‘quaternionic’, in that they are the underlying complex representations of representations on quaternionic Hilbert spaces). This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics. More generally, Hilbert spaces of any one of the three kinds—real, complex and quaternionic—can be seen as Hilbert spaces of the other kinds, equipped with extra structure. (shrink)

Conditioning can make imprecise probabilities uniformly more imprecise. We call this effect "dilation". In a previous paper (1993), Seidenfeld and Wasserman established some basic results about dilation. In this paper we further investigate dilation on several models. In particular, we consider conditions under which dilation persists under marginalization and we quantify the degree of dilation. We also show that dilation manifests itself asymptotically in certain robust Bayesian models and we characterize the rate at which dilation occurs.

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)

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.

Aquinas accepts that (i) some kinds of voluntary action are (qua voluntary) “basic,” not divisible into (non-fictional) further kinds; (ii) a concrete individual action may belong to more than one basic kind; (iii) the basic kinds to which it belongs are determined by the agent’s intentions qua performing the action; (iv) some intentions may stand to others as means to ends; (v) there can be concrete individual actions in which the agent’s intended means are disordered with respect to the ends; (...) (vi) such actions are morally wrong; (vii) whether a given intention is disordered as means to a given end is determined solely by the natures of the agent and of the intended means or ends. Together, these propositions entail that, pace many analytic philosophers, concrete individual actions can have a moral wrongness that consists neither in expectation of disutility nor in violation of the pure logic of practical reason. (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)