The omen of the door and the eagle at Iliad 24.314–21 appears to have sparked scant scholarly interest, but deserves careful attention. The omen itself forms part of an analogy, for the eagle is likened in the size of its wingspan to a large, barred door. This simile might seem unremarkable, merely a convenient means of depicting great size, a casual juxtaposition of two ordinary nouns. The omen, on the whole, might be dismissed as nothing more than a conventional expression (...) of divine favor. But closer scrutiny will reveal that there is, in fact, nothing arbitrary or haphazard in the selection of the terms of the analogy. Appreciation of the elegance and subtlety of the simile in turn reveals the full import of the omen. (shrink)

An incisive exploration of the way Greek myths empower us to defeat tyranny. As tyrannical passions increasingly plague twenty-first-century politics, tales told in ancient Greek epics and tragedies provide a vital antidote. Democracy as a concept did not exist until the Greeks coined the term and tried the experiment, but the idea can be traced to stories that the ancient Greeks told and retold. From the eighth through the fifth centuries BCE, Homeric epics and Athenian tragedies exposed the tyrannical potential (...) of individuals and groups large and small. These stories identified abuses of power as self-defeating. They initiated and fostered a movement away from despotism and toward broader forms of political participation. Following her highly praised book Enraged: Why Violent Times Need Ancient Greek Myths, the classicist Emily Katz Anhalt retells tales from key ancient Greek texts and proceeds to interpret the important message they hold for us today. As she reveals, Homer's Iliad and Odyssey, Aeschylus's Oresteia, and Sophocles's Antigone encourage us—as they encouraged the ancient Greeks—to take responsibility for our own choices and their consequences. These stories emphasize the responsibilities that come with power (any power, whether derived from birth, wealth, personal talents, or numerical advantage), reminding us that the powerful and the powerless alike have obligations to each other. They assist us in restraining destructive passions and balancing tribal allegiances with civic responsibilities. They empower us to resist the tyrannical impulses not only of others but also in ourselves. In an era of political polarization, Embattled demonstrates that if we seek to eradicate tyranny in all its toxic forms, ancient Greek epics and tragedies can point the way. (shrink)

: Metaphysics B considers two sets of views that hypostatize mathematicals. Aristotle discusses the first in his B.2 treatment of aporia 5, and the second in his B.5 treatment of aporia 12. The former has attracted considerable attention; the latter has not. I show that aporia 12 is more significant than the literature suggests, and specifically that it is directly addressed in M.2 – an indication of its importance. There is an immediate problem: Aristotle spends most of M.2 refuting the (...) view that mathematicals are separate; but the B.5 mathematicals are inherent. I argue that the B.5 inherence is compatible with the M.2 separateness, and further, that aporia 12 is more than just a puzzle about the hypostatization of mathematicals. It is also a puzzle about the ontological status of mathematicals relative to sensibles. (shrink)

Frege argues that number is so unlike the things we accept as properties of external objects that it cannot be such a property. In particular, (1) number is arbitrary in a way that qualities are not, and (2) number is not predicated of its subjects in the way that qualities are. Most Aristotle scholars suppose either that Frege has refuted Aristotle's number theory or that Aristotle avoids Frege's objections by not making numbers properties of external objects. This has led some (...) to conclude that Aristotle's accounts of arithmetical and geometrical objects differ substantially. I close this supposed gap by showing that Aristotle's arithmetical objects, like geometrical objects, are just certain sensible things qua certain properties they in fact possess. Specifically, numbers are pluralities qua quantitative or relational properties like ten units or ten. I show that this view is resistant to the Fregean concerns about arbitrariness and numerical predication. (shrink)

Ontological separation plays a key role in Aristotle’s metaphysical project: substances alone are ontologically χωριστόν. The standard view identifies Aristotelian ontological separation with ontological independence, so that ontological separation is a non-symmetric relation. I argue that there is strong textual evidence that Aristotle employs an asymmetric notion of separation in the Metaphysics—one that involves the dependence of other entities on the independent entity. I argue that this notion allows Aristotle to prevent the proliferation of substance-kinds and thus to secure the (...) unity of his metaphysical system. (shrink)

There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...) continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous. (shrink)

The opening argument in the Metaphysics M.2 series targeting separate mathematical objects has been dismissed as flawed and half-hearted. Yet it makes a strong case for a point that is central to Aristotle’s broader critique of Platonist views: if we posit distinct substances to explain the properties of sensible objects, we become committed to an embarrassingly prodigious ontology. There is also something to be learned from the argument about Aristotle’s own criteria for a theory of mathematical objects. I hope to (...) persuade readers of Metaphysics M.2 that Aristotle is a more thoughtful critic than he is often taken to be. (shrink)

I argue that intelligible matter, for Aristotle, is what makes mathematical objects quantities and divisible in their characteristic way. On this view, the intelligible matter of a magnitude is a sensible object just insofar as it has dimensional continuity, while that of a number is a plurality just insofar as it consists of indivisibles that measure it. This interpretation takes seriously Aristotle's claim that intelligible matter is the matter of mathematicals generally – not just of geometricals. I also show that (...) intelligible matter has the same meaning in all three places where it is explicitly invoked: Z.10, Z.11, and H.6. Since the H.6 passage involves a mathematical definition, this requires determining what the mathematician defines and how she defines it. I show that, as with natural scientific definitions, there must be a matterlike element in mathematical definitions. This element is not identical with, but rather refers to, intelligible matter. (shrink)

According to Aristotle, those who seek mathematical principles of sensible things are looking in entirely the wrong place. But despite his strong opposition to mathematized metaphysics, Aristotle does not outright reject mathematical explanation of the natural world. In fact, he argues that mathematics does explain certain sensible phenomena, that the natural world has many mathematical patterns and features, and that this is often not mere coincidence. That he devotes two books of his Metaphysics to shoring up the boundary between mathematics (...) and metaphysics indicates that this issue is crucially important to him. Yet it receives little systematic scholarly discussion. I take up the issue by examining Aristotle’s treatment of the sensible phenomena that have mathematical explanations. This examination shows that—and why—on his view, mathematics explains many things about the natural world, but not the most fundamental things. (shrink)

Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even scholars who give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors (and of the Platonists in particular), is widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical objects is the subject of particularly strong (...) criticism by Annas and Ross. Two related arguments in this series (1077a14-20 and 1077a24-31) will serve as cases in point. The principal charges made against these arguments (that Aristotle misunderstands or misrepresents his opponents' views, and that he engages in question-begging because he presupposes his own metaphysical views) are frequently made against Aristotle's critique of Platonist positions more generally. If, as I argue, these charges are false for our two test case arguments, then there is good reason to think that they might also be false when they are leveled against the other arguments in this M 2 series. And, although presenting an argument for this is beyond the scope of this paper, this suggests that these two charges are more often than not false when applied to Aristotle's critique of Platonist mathematical views in M-N and beyond. (shrink)

In Metaphysics B.2 and M.2, Aristotle gives a series of arguments against Platonic mathematical objects. On the view he targets, mathematicals are substances somehow intermediate between Platonic forms and sensible substances. I consider two closely related passages in B2 and M.2 in which he argues that Platonists will need intermediates not only for geometry and arithmetic, but also for the so-called mixed mathematical sciences, and ultimately for all sciences of sensibles. While this has been dismissed as mere polemics, I show (...) that the argument is given in earnest, as Aristotle is committed to its key premises. Further, the argument reveals that Annas’ uniqueness problem is not the only reason a Platonic ontology needs intermediates. Finally, since Aristotle’s objection to intermediates for the mixed mathematical sciences is one he takes seriously, so that it is unlikely that his own account of mathematical objects would fall prey to it, the argument casts doubt on a common interpretation of his philosophy of mathematics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Suñña at the Bone:Emily Dickinson’s Theravadin RomanticismAdam KatzA narrow Fellow in the GrassOccasionally rides—You may have met him? Did you notHis notice instant is—The Grass divides as with a Comb—A spotted Shaft is seen,And then it closes at your FeetAnd opens further on—He likes a Boggy Acre—A Floor too cool for Corn—But when a Boy and BarefootI more than once at NoonHave passed I thought a Whip LashUnbraiding (...) in the SunWhen stooping to secure itIt wrinkled And was gone—Several of Nature’s PeopleI know and they know meI feel for them a transportOf CordialityBut never met this FellowAttended or aloneWithout a tighter BreathingAnd Zero at the Bone.1Via the Arabic word cipher, the English word “zero” comes straight from the Sanskrit word shunya (empty). In Pali, the early Buddhist liturgical language, it is suñña. This poem’s story recalls the common Buddhist simile where a rope is mistaken for a snake in the dim light. There is nothing in the rope that should be feared as a snake, and likewise there is ultimately nothing in the five aggregates—basically, everything—that [End Page 111] can be regarded as atman (soul, self). So the aggregates are empty of self: anatta, in Pali. This is the doctrine of emptiness. Fallaciously imputing selfhood to the inherently selfless flux of the aggregates is a major source of suffering, so realizing emptiness brings liberation, just as investigating the rope and finding it empty of snakehood liberates one from fright.Recognizing that the rope is a rope and not a snake is a simile for realizing emptiness. Likewise, in the poem, recognizing that the snake is a snake and not a “Whip Lash / Unbraiding in the Sun” catapults the speaker into a sublime experience of “Zero at the Bone.” This last line may be a metaphor for being chilled to the bone, but the absence of a subject for zero to modify and the sonic and aesthetic overload in an otherwise mostly matter-of-fact nature poem suggest that the sudden recognition of the snake scares us out of ourselves, empties us out, providing a Romantic corollary for Buddhist emptiness.In the Buddhist simile and in the poem, the correction of faulty recognition precipitates the realization of emptiness. But in the simile, what is primarily important is that the rope is recognized as not a snake. One Tibetan text says that substantial progress can be made by, as it were, mistaking the rope for a vine, just so the scary snake perception is cleared away.2 A slightly later Tibetan text says that, simile aside, recognizing that the rope is not a snake and not even a vine but precisely a rope is merely a matter of “conventional valid cognition,” which stops far short of liberating insight into the selflessness of phenomena as such.3 Believing the rope really is a rope is the same as, in the simile, mistaking the rope for a snake, because in both cases it is a matter of perceiving substantiality where there is impermanence. By contrast, Dickinson’s poem emphasizes neither clearing up a particularly pernicious and persistent misconception about existence nor replacing this misconception with complete insight; rather, the poem emphasizes “conventional valid cognition” itself as a vehicle for sublime transcendence. The ecstatic experience of “Zero at the Bone” requires that the snake be accurately recognized as a snake.This “conventional valid cognition” is technically compatible with complete insight into the selflessness of phenomena as such, and it is certainly possible that the speaker experiences zeroness due to an optical illusion or hallucination or dream rather than recognizing a real snake, but the poem does not highlight either of these possibilities. It emphasizes recognitional accuracy, and being thrown from the quotidian as a result. This is quite different from the lesson of the Buddhist simile, where, again, the emphasis is on what is not there, specifically selfhood, rather than on what is there in its precise distinctness from other things. In this regard the poem is, however, eminently compatible... (shrink)

In this response to Emily Katz’s “Aristotle’s Rejection of Mathematized Metaphysics,” I raise questions about her central interpretive claim that mathematical forms cannot, for Aristotle, appear among first principles of nature. Topics addressed include the notion of priority, especially in the sciences; the relationship between natural change and material realization; and the general nature and scope of mathematical explanations for physical phenomena.

Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is (...) supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem. (shrink)

I argue that the Oxford school Everett interpretation is internally incoherent, because we cannot claim that in an Everettian universe the kinds of reasoning we have used to arrive at our beliefs about quantum mechanics would lead us to form true beliefs. I show that in an Everettian context, the experimental evidence that we have available could not provide empirical confirmation for quantum mechanics, and moreover that we would not even be able to establish reference to the theoretical entities of (...) quantum mechanics. I then consider a range of existing Everettian approaches to the probability problem and show that they do not succeed in overcoming this incoherence. (shrink)

We describe how the set of tools, practices, and social relations known as “precision agriculture” is defined, promoted, and debated. To do so, we perform a critical discourse analysis of popular and trade press websites. Promoters of precision agriculture champion how big data analytics, automated equipment, and decision-support software will optimize yields in the face of narrow margins and public concern about farming’s environmental impacts. At its core, however, the idea of farmers leveraging digital infrastructure in their operations is not (...) new, as agronomic research in this vein has existed for over 30 years. Contemporary discourse in precision ag tends to favour emerging digital technologies themselves over their embeddedness in longstanding precision management approaches. Following several strands of science and technology studies research, we explore what rhetorical emphasis on technical innovation achieves, and argue that this discourse of novelty is a reinvention of precision agriculture in the context of the growing “smart” agricultural economy. We overview six tensions that remain unresolved in this promotional rhetoric, concerning the definitions, history, goals, adoption, uses, and impacts of precision agriculture. We then synthesize these in a discussion of the extent to which digital tools are believed to displace farmer decision-making and whether digital agriculture addresses the biophysical heterogeneity of farm landscapes or land itself has become an “experimental technology”—a way to advance the general development of artificial intelligence. This discussion ultimately helps us name a larger dilemma: that the smart agricultural economy is perhaps less about supporting land and its stewards than promising future tech and profits. (shrink)

This article examines the regulation of Latina youth sexualities in the context of sexual and reproductive health care provision. In-depth interviews with health care providers working in two Latino-serving community health centers are analyzed for how they interpret and respond to the sexual and reproductive practices of their low-income Latina teen patients. The author finds that providers emphasize teenage pregnancy as a social problem among this population to the exclusion of other dimensions of youth sexualities and encourage Latina girls’ adherence (...) to a life course trajectory that conforms to middle-class, heteronormative ideals as a solution to this problem. By relying on such understandings, providers construct meanings of sexual citizenship that require participation in bourgeois heteronormativity. These findings suggest that Latino-serving community health centers, their providers, and their teen patients could benefit from questioning the assumptions that inform providers’ appraisals of Latina youth and developing a more inclusive approach to Latina youth sexualities beyond a discourse of pregnancy prevention. Such efforts could allow community health centers to actively participate in disrupting the structural inequalities that shape their young patients’ lives. (shrink)

Play is a vital component of the social life and well-being of both children and adults. This book examines the concept of play and considers a variety of the related philosophical issues. It also includes meta-analyses from a range of philosophers and theorists, as well as an exploration of some key applied ethical considerations. The main objective of The Philosophy of Play is to provide a richer understanding of the concept and nature of play and its relation to human life (...) and values, and to build disciplinary and paradigmatic bridges between scholars of philosophy and scholars of play. Including specific chapters dedicated to children and play, and exploring the work of key thinkers such as Plato, Sartre, Wittgenstein, Gadamer, Deleuze and Nietzsche, this book is invaluable reading for any advanced student, researcher or practitioner with an interest in education, playwork, leisure studies, applied ethics or the philosophy of sport. (shrink)

Everything is constantly changing. Our emotions are one of the primary ways we track, evaluate, organize, and motivate responsive action to those changes. Furthermore, emotions are inherently interpersonal. We learn what to feel from others, especially when we are children. We “catch” other people’s emotions just by being around them. We get caught in escalating response–counterresponse emotional sequences. This all takes place in time, generating complex patterns of interpersonal emotional dynamics. This review summarizes theory, empirical findings, and key challenges for (...) future research regarding three processes that contribute to interpersonal affective dynamics: (a) Convergence of social partners’ emotional responses to the external world, (b) emotional reactivity of social partners to each other, and (c) interpersonal emotion regulation. (shrink)

Most research on the corporate philanthropy of organizations has focused on the external benefits of such initiatives for firms, such as benefits for firm reputation and opportunities. However, many firms justify their giving, in part, due to the positive impact it has on their employees. Little is known about the effectiveness of such efforts, or how they can be managed strategically to maximize impact. We hypothesize a main effect of office-level corporate philanthropy on average employee attitudes in that office, but (...) also investigate three strategies that offices may use to enhance this impact. Testing our hypotheses with 3 years of data on attitudes of an average of 14,577 employees in 53 offices we find support for the main effect, but mixed support for the specific strategies used to enhance impact. (shrink)

In Physics 2.4–6, Aristotle offers an account of things that happen “by luck” and “spontaneously”. Many of these things are what we might think of as “lucky breaks”: cases where things go well for us, even though we don’t expect them to. In Physics 2.5, Aristotle illustrates this idea with the case of a man who goes to the market for some reason unrelated to collecting a debt he is owed. While he is there, this man just so happens to (...) run into his debtor and get his money back—which is what he “wanted” all along. This case has a number of features that have proved puzzling. Most notably, Aristotle seems to think that while “it happened accidentally to him to come and to do this for the sake of getting the money”, nevertheless the man “did not come for the sake of this”—though he “would have”. What must such a proceeding be like to be described in these ways? Physics 2.4–6 makes several important moves towards answering this question. One of them—among the earliest and seemingly a foundational one—is the claim that “for the sake of something are as many things as could be done by thought and by nature”. The aim of this paper is to identify the role that this claim plays in Aristotle’s account of spontaneous proceedings. It defends two main claims. First, Aristotle’s suggestion that spontaneous proceedings could be done by nature and by thought is the product of a more general strategy. His approach is to sketch an intuitive pattern of explanation for proceedings that happen for the sake of something in the ordinary—non-spontaneous—way, and then to try to extend that model to the case of things that do so spontaneously, preserving as much of it as possible. Applying this strategy reveals that whereas nature and thought in fact function as efficient causes of ordinary proceedings that are for the sake of something, this cannot be the case in spontaneous ones. Instead, nature and thought could function as their causes. Second, I argue that Aristotle’s implementation of this strategy is rooted in his account of causation and especially Physics 2.3’s list of “modes” of causes. When he claims that spontaneous proceedings “could” be done by nature and by thought, he is saying that nature and thought are their efficient causes in capacity. In the practical case, spontaneous proceedings are caused by agents who have certain capacities, connected with their desires and abilities. In the right circumstances, these agents would actively exercise those capacities in acting for the sake of a given end. (shrink)

Der Aufsatz bietet einen Einblick in die Möglichkeiten, Normen zu umgehen - einer Praxis mit, wie gezeigt wird, langer Tradition. Die dargestellten Methoden reichen von einer Beeinflussung des Wissens des Täters, über das Heranziehen "anderer", seien es Menschen oder Maschinen, um die gewünschte aber verbotene Handlung vorzunehmen, bis hin zu Änderungen in den Kausalverläufen. Der Grund für diese Umgehungsmöglichkeiten liegt im Formalismus deontologischer Systeme, die im Gegensatz zu utilitaristischen Positionen gerade nicht auf die Folgen einer Handlung abstellen.

Children bring intuitive arithmetic knowledge to the classroom before formal instruction in mathematics begins. For example, children can use their number sense to add, subtract, compare ratios, and even perform scaling operations that increase or decrease a set of dots by a factor of 2 or 4. However, it is currently unknown whether children can engage in a true division operation before formal mathematical instruction. Here we examined the ability of 6- to 9-year-old children and college students to perform symbolic (...) and non-symbolic approximate division. Subjects were presented with non-symbolic or symbolic dividends ranging from 32 to 185, and non-symbolic divisors ranging from 2 to 8. Subjects compared their imagined quotient to a visible target quantity. Both children and adults were successful at the approximate division tasks in both dots and numeral formats. This was true even among the subset of children that could not recognize the division symbol or solve simple division equations, suggesting intuitive division ability precedes formal division instruction. For both children and adults, the ability to divide non-symbolically mediated the relation between Approximate Number System acuity and symbolic math performance, suggesting that the ability to calculate non-symbolically may be a mechanism of the relation between ANS acuity and symbolic math. Our findings highlight the intuitive arithmetic abilities children possess before formal math instruction. (shrink)

This article contributes to a growing conversation about the role of numbers in promoting gendered agendas in potentially contradictory ways. Drawing from interviews with gender advisors—the professionals tasked with mainstreaming gender in development projects—in an East African country, I begin from the paradox that gender advisors articulate a strong preference for qualitative data to best capture the lives of the women they aim to assist while voicing a need for quantitative metrics. I demonstrate that gender advisors come to imagine metrics (...) as expeditious bureaucratic tools able to inspire cooperation from otherwise reluctant coworkers. I argue that development organizations are gendered in ways—acutely seen in how advisors struggle, are sidelined, and attempt to advance their goals with numbers—that lead to the utility of valuing quantitative metrics over qualitative ones. I establish two theoretical contributions: Gendered organizations theory is essential to understanding the adoption and globalization of performance metrics, and in an age of evidence-based decision making, the utility of quantified data to garner resources is heightened, rewarding those who adopt quantified knowledge production. I coin the term “the paradox of quantified utility” to describe how these material advantages encourage even skeptics to value quantitative metrics. (shrink)

In the Buddhist ethical traditions, equanimity along with love, compassion, and sympathetic joy form what are called the four boundless qualities, which are affective states one cultivates for moral and spiritual development. But there is a sense in which equanimity seems very unlike the three others: love, compassion, and sympathetic joy all imply an emotional investment in others, whereas equanimity seems to imply an absence of such investment. This observation has provoked debate as to how to properly understand the relationship (...) between equanimity and the other three qualities. In this paper, I propose that equanimity - like love, compassion, and sympathetic joy - is itself a virtue of good intimate relationships and not in conflict with such virtues. (shrink)

This article briefly considers current positions about whether the inclusion of the perspectives and interests of marginalised groups in the construction of knowledge is of epistemic value. It is then argued that applied social epistemology is the proper epistemic stance to take in evaluating this question. Theorists who have held that diversity makes an epistemic contribution are interpreted as attempting to reform social pathways to knowledge in ways that make true belief more likely. Thus, the demand for diversity challenges the (...) individualistic and a priori nature of traditional epistemology. This stance has consequences for education. It supports greater attention to helping students examine the testimonial bases for their beliefs. And it prepares students for their role as citizens in supporting policies that maintain credible inclusive institutions of public knowledge. (shrink)

Music exists not to be parsed, categorized, or otherwise processed, but because it provides enjoyment. Thus methodologies that concentrate on the cognitive aspects of music alone omit what is essential about this aesthetic form. This paper provides an alternative approach by proposing a measure of musical preference. Specifically, it is argued that a musical passage will be preferred to the extent that it induces synchrony in those brain structures that are responsible for processing the passage. It is first shown that (...) this conception is consistent with time-honored principle of unity in diversity. It is then argued that the synchrony measure follows from more recent results regarding a possible solution to the binding problem. The bulk of the paper, however, is concerned with verifying the measure via simulation. It is shown, in particular, that the measure applied to a network of interacting integrate and fire neurons responsible for the processing of musical stimuli produces results consistent with human musical preference. This was carried out in three areas in the context of Western classical and popular musical forms. First, the model was applied to the laws of voice leading and other principles developed in the period of common harmonic practice. Next, it was shown that the three most salient aspects of melody, the preponderance of stepwise transitions, the theme and variation nature of phrase development, and increased positive affect with exposure all follow directly from the model. Finally, it was demonstrated how a steady rhythm can increase neural synchrony and presumably positive affect. Additional simulations run on Turkish art songs show that the synchrony measure may have some applicability to non-Western musical forms. The paper concludes by arguing that the synchrony measure may, in certain cases, apply to non-musical aesthetic stimuli. (shrink)