In Against Purity, Alexis Shotwell proposes a powerful new conception of social movements as custodians for the past and incubators for liberated futures. Against Purity undertakes an analysis that draws on theories of race, disability, gender, and animal ethics as a foundation for an innovative approach to the politics and ethics of responding to systemic problems.

A fundamental fact is “pure” just in case it has no grounded entities—ex. Tokyo, President Biden, the River Nile, {Socrates}, etc.—among its constituents. Purity is the thesis that every fundamental fact is pure. I argue that Purity is false. My argument begins with a familiar conditional: if Purity is true, then there are no fundamental “grounding facts” or facts about what grounds what. This conditional is accepted by virtually all of Purity’s defenders. However, I argue that (...) it is also the first step toward Purity’s undoing. For, if every grounding fact has a ground, then some grounded entities have “groundmates” or distinct grounded entities that share their full grounds. But, if there are groundmates, then Purity is false. So Purity leads to a contradiction. Therefore, it is false. I close by noting that my argument against Purity also gives us a powerful reason to think that some grounding facts are fundamental. (shrink)

In his 1978 paper “Mathematical Explanation”, Mark Steiner attempts to modernize the Aristotelian idea that to explain a mathematical statement is to deduce it from the essence of entities figuring in the statement, by replacing talk of essences with talk of “characterizing properties”. The language Steiner uses is reminiscent of language used for proofs deemed “pure”, such as Selberg and Erdős’ elementary proofs of the prime number theorem avoiding the complex analysis of earlier proofs. Hilbert characterized pure proofs as those (...) that use only “means that are suggested by the content of the theorem”, a characterization we have elsewhere called “topical purity”. In this paper we will examine the connection between Steiner’s account of mathematical explanation and topical purity. Are Steiner-explanatory proofs necessarily topically pure? Are topically pure proofs necessarily Steiner-explanatory? Answers to these questions will shed light on the general question of the relation between purity and explanatory power. (shrink)

Throughout history, mathematicians have expressed preference for solutions to problems that avoid introducing concepts that are in one sense or another “foreign” or “alien” to the problem under investigation. This preference for “purity” (which German writers commonly referred to as “methoden Reinheit”) has taken various forms. It has also been persistent. This notwithstanding, it has not been analyzed at even a basic philosophical level. In this paper we give a basic analysis of one conception of purity—what we call (...) topical purity—and discuss its epistemological significance. (shrink)

Over the years many mathematicians have voiced a preference for proofs that stay “close” to the statements being proved, avoiding “foreign”, “extraneous”, or “remote” considerations. Such proofs have come to be known as “pure”. Purity issues have arisen repeatedly in the practice of arithmetic; a famous instance is the question of complex-analytic considerations in the proof of the prime number theorem. This article surveys several such issues, and discusses ways in which logical considerations shed light on these issues.

Various ideals of purity are surveyed and discussed. These include the classical Aristotelian ideal, as well as certain neo-classical and contemporary ideals. The focus is on a type of purity ideal I call topical purity. This is purity which emphasizes a certain symmetry between the conceptual resources used to prove a theorem and those needed for the clarification of its content. The basic idea is that the resources of proof ought ideally to be restricted to those (...) which determine its content. (shrink)

The central aim of this book is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories.

Purity is known as an ideal of proof that restricts a proof to notions belonging to the ‘content’ of the theorem. In this paper, our main interest is to develop a conception of purity for formal (natural deduction) proofs. We develop two new notions of purity: one based on an ontological notion of the content of a theorem, and one based on the notions of surrogate ontological content and structural content. From there, we characterize which (classical) first-order (...) natural deduction proofs of a mathematical theorem are pure. Formal proofs that refer to the ontological content of a theorem will be called ‘fully ontologically pure’. Formal proofs that refer to a surrogate ontological content of a theorem will be called ‘secondarily ontologically pure’, because they preserve the structural content of a theorem. We will use interpretations between theories to develop a proof-theoretic criterion that guarantees secondary ontological purity for formal proofs. (shrink)

Standard defences of preservationism, and of the intrinsic value of nature more generally, are vulnerable to at least three objections. The first of these comes from social constructivism, the second from the claim that it is incoherent to argue that nature is both 'other' and something with which we can feel unity, whilst the third links defences of nature to authoritarian objectivism and dangerously misanthropic normative dichotomies which set pure nature against impure humanity. I argue that all these objections may (...) be answered by recasting the relationship between man and nature into a tripartite spectrum of ontological form between nature and artifact, with the key question being the extent to which nature has been humanised in accordance with certain modes of strongly instrumental rationality, these in turn being defined by reference to the split between abstract reason and natural feeling which was exacerbated by specific elements in the Enlightenment period. This new model may grant normative force by linking external nature to a broader conception of human psychological wellbeing than that offered by the quantitatively orientated models of human rationality and agency. (shrink)

In her account of a debate held at Princeton University between herself and Peter Singer, the lawyer and disability rights activist Harriet McBryde Johnson criticizes the ‘terrible purity of Singer's vision’. Although she certainly disagrees with the substance of Singer's arguments concerning disability and infanticide, this remark is best understood as a critique of their form. In this paper, I attempt to make sense of this critique. I argue that Singer's characteristic mode of argument, with its appeal to a (...) universal, neutral point of view, makes it impossible for McBryde Johnson to give voice to her particular experience and thus obscures her humanity. In order to clarify the positive contribution that an appeal to particular experience may make to moral reasoning, I draw a parallel with the transformative effects of the experience of beauty, arguing that McBryde Johnson's writing ought to be regarded as both morally and philosophically instructive. (shrink)

By the early 80s, kids were already trawling the message boards of the Internet for perverse kicks. Well before Star Ways Kid or "flash mobs," one of the first online fads was the "Purity Test," a series of questions to rate your moral purity, from the raunchy to the absurd.The tests would be printed out, brought to school, and pored over with friends in the back of the gym during recess. Then kids would modify the original with their (...) own prurient additions before sending it along. Eventually, the tests became bloated thousand-question Franken-tests that took hours to complete.Doing the test with friends was like playing an endless, filthy, wildly enlightening game of "Did You Ever?"--and because it was a standardized test, you could compare your scores. Assuming everyone was being honest--which they weren't. The Purity Test will offer both a humorous history and analysis of the Purity Test as well as several versions of the test to take at home. (shrink)

Fitouchi et al. claim that seemingly victimless pleasures and nonproductive activities are moralized because they alter self-control. Their account predicts that: (1) victimless excesses are negatively moralized because they diminish self-control, and (2) restrained behaviors are positively moralized because they enhance self-control. Several examples run contrary to these predictions and call into question the general relationship between self-control and cooperation.

Pragmatic Genealogy involves constructing fictional, quasi-historical models in order to discover what might explain and justify our concepts, ideas or practices. It arguably originated with Hume, but its most prominent practitioners are Edward Craig, Bernard Williams and Mathieu Queloz. Its defenders allege that the method allows us to understand “what the concept does for us, what its role in our life might be” (Craig, 1990), and that this in turn can ground practical reasons to preserve or further a conceptual practice. (...) In this paper, I argue that none of this is true, and that only a turn to the actual recent history of such practices can reveal those sorts of practical reasons. (shrink)

Purity violations overlap with other moral domains. They are not uniquely characterized by hypothesized markers of purity – the witness's emotion of disgust, taint to perpetrator's soul, or the diminished role of intention in moral judgment. Thus, Fitouchi et al.'s proposition that puritanical morality (a subset of violations in the purity domain) is part of cooperation-based morality is an important advance.

In lieu of an abstract, here is a brief excerpt of the content:Purity and Pollution: Resisting the Rehabilitation of a VirtueAmy Mullin“Purity” is a term used infrequently in contemporary academic literature. A survey of periodical indexes for the past ten years shows that references to purity occur predominantly in metallurgy. Purity is an increasingly important topic in anthropology, religious studies, and history, but it is a decidedly rare concern in philosophy. In my most recent search I (...) found three references.Yet “purity” was once a recurrent term in the philosophical tradition ranging from Plato through Augustine and Kant to Kierkegaard. Today when we encounter the many references to purity in the history of philosophy we too often filter them out. We assume either that “pure” is a generic term for good, or, in what seems a more knowing and sophisticated response, we read “pure” as a code term for chastity or sexual morality, the elimination, suppression or control of sexual desire. In both cases purity is written off either as a generic or as an old fashioned and rather embarrassing virtue. Hence it seems there is little reason for contemporary philosophical investigation into the rhetorical use of the language of purity and pollution.Three assumptions account for the lack of contemporary philosophical interest in the topic. First, it is assumed that purity is no longer a concern in twentieth-century philosophy. Second, purity in historical discourse is considered to be limited to a prudish or downright misogynist hostility to sex. Third and finally, it is assumed that the work historians and anthropologists have done recently into connections between purity beliefs and practices and social cohesion is irrelevant for philosophy. This is because purity in philosophy is supposed to be a resolutely individualist virtue, having little or nothing to do with unified and coherent communities.There are elements of truth to all three beliefs, but they also contain important distortions of the truth. As regards the first assumption, purity remains a concern in contemporary aesthetics, where it often means roughly something like a priori and apolitical; but I am interested in whether the concern with purity has survived in philosophies with ethical implications. [End Page 509] Here it is my contention that authenticity is the twentieth-century descendant of the virtue of purity.Second, there is much more to the rhetoric and practices of purity than concern with the sexual dimension of life, though this is a key aspect of most, and the beliefs and practices are often misogynist. There have been numerous anthropological documentations of ways in which purity beliefs, particularly an emphasis on sexual purity, are used to control women. Santi Rozario’s work, for instance, makes this point in her analysis of contemporary Bengali village life. 1 The connection between the language of purity and the practice of female circumcision, which I will not discuss in this paper, is in itself evidence enough of connections between purity beliefs and practices harmful to women. 2 However, I hope to show that there is more to purity than misogyny. Purity most basically is about order, both social and personal. 3My response to the second assumption, that purity masks an obsession with sexual control, indicates the source of my disagreement with the third, the contention that purity in philosophy is exclusively an individual virtue. Communal beliefs and practices associated with the language of purity and pollution are relevant to the philosophical treatment of purity because of the presence in both the practices and the philosophies of an interplay between social and personal order. As a result I believe an understanding of the dynamics of beliefs about purity in social practice can inform a philosophical concern with purity.First I investigate shifts in beliefs and practices concerning purity and pollution. I will concentrate on three models: ancient Greek (from the eighth to the third century BC), biblical to Talmudic Judaism (from the third century BC to the third century AD), and early Christian (from the first to the fifth century AD). These represent three traditions which have played a very significant role in shaping western civilization, theology, and philosophy. 4 They were also frequently interrelated in this period, as Christian and Jewish Platonists writing in Greek attest and of course as... (shrink)

A critical discussion of Kelsen's philosophy of law.

ArgumentAfter World War II, blood groups became a symbol of anti-racial science. This paper aims to shed new light on the post-WWII history of blood groups and race, illuminating the postcolonial revitalization of racial serology in South Korea. In the prewar period, Japanese serologists developed a serological anthropology of Koreans in tandem with Japanese colonialism. The pioneering Korean hematologist Yi Samyŏl (1926–2015), inspired by decolonization movements during the 1960s, excavated and appropriated colonial serological anthropology to prove Koreans as biologically independent (...) from the Japanese. However, his racial serology of Koreans shared colonial racism with Japanese anthropology, despite his anti-colonial nationalism. (shrink)

Through a reinterpretation of publications, interviews with long-term activists, and an analysis of change in the social environment, this article explains why feminist ideology failed to create unity among feminist women in the United States during the period 1966-1975, the years when contemporary feminism emerged. In spite of the desire to create a community of women to challenge the existing sociocultural structure, schisms within the movement often created divisive and antagonistic feminist group relations. In contrast to earlier research that attributed (...) this lack of unity to competing ideologies, this article argues that, in many cases, feminist leaders used ideology and theory to promote radical self-identities that maintained existing social structural divisions. Thus, while feminism established a principle of unity for women as a group, disputes over ideological purity created divisions within the movement based on differences among women. (shrink)

Nietzsche’s relationship to his contemporaries, as expressed in his writings, was often figured by corporeal imagery evocative of disgust. For instance, in On the Genealogy of Morality Nietzsche declared himself to suffer from mankind—which he then proceeds to describe as “maggot”—or worm-like. Nietzsche’s philosophical project can be interpreted as a visceral protest against, and attempt to overcome, humanity. This paper argues that Nietzsche attempted through his writings to create a future community of like-constituted companions in his readers through a transmission (...) of affect and education in taste. This would-be "community" is premised on a curious affective dialectic that seeks to transform disgust for humanity into a pure movement of self-creation. The socio-political effects of this dialectic of disgust will be examined alongside Nietzsche's co-option of images of purity, in order to evaluate his response to modern nihilism. (shrink)

In his penetrating and thought-provoking article “What Is Logic?” Ian Hacking flags an issue that he leaves undiscussed.

David Lewis has argued against the thesis he calls "Desire as Belief", claiming it is incompatible with the fundamentals of evidential decision theory. I show that the argument is unsound, and demonstrate that a version of desire as belief is compatible with a version of causal decision theory.

Hans Kelsen’s purity thesis is the basic methodological principle of the Pure Theory of Law. Indeed, it is no exaggeration to say that virtually everything that is peculiar to Kelsen’s legal theory stems from the purity thesis. This includes Kelsen’s normativism or non‐naturalism and his polemic against various dualisms in legal science. I set out Kelsen’s position on these issues after looking at the nomenclature of purity in his writings as well as the philosophical and contextual sources (...) of purity as he understands them. (shrink)

"Moore's provocative conclusion is that monotheism - with its monopoly on virtue and failure to provide supernatural scapegoats - is responsible for some of the most virulent forms of intolerance and is a major cause of human nastiness and suffering.

Turning to the question of morality's content, Scheffler undertakes a defense of the view that morality is moderate – that it makes demands and imposes constraints but still allows people, under favorable circumstances, to do as they please within broad limits. Those who oppose this view and see morality as stringent are, according to Scheffler, attributing a kind of purity to the moral point of view, and so he presents the contrast between the stringent and moderate views as a (...) contrast between an Ideal of Purity and an Ideal of Humanity. Scheffler considers and rejects two argumentative strategies that are frequently used in defense of the Ideal of Purity, one that derives stringency from an allegedly uncontroversial property of morality, such as universality or impartiality and another that derives it from ordinary moral language and ordinary moral concepts. Scheffler suggests that, because the claims of stringency and moderation each have a place in our moral consciousness, neither claim can be adequately defended by appealing either to formal properties of morality or to facts about ordinary usage. (shrink)

Our recent review demonstrates that “purity” is a messy construct with at least nine popular scientific understandings. Cultural beliefs about self-control help unify some of these understandings, but much messiness remains. The harm-centric theory of dyadic morality suggests that purity violations can be comprehensively understood as abstract harms, acts perceived by some people (and not others) to indirectly cause suffering.

The essay analyses the notion of ‘purity’ in the early writings of Walter Benjamin, focusing more specifically on three essays written around the crucial year 1921: ‘Critique of Violence’, ‘The Task of the Translator’, and ‘Goethe's Elective Affinities’. In these essays, ‘purity’ appears in the notions of ‘pure means’, ‘pure violence’, ‘pure language’, and, indirectly, the ‘expressionless’. The essay argues, on the one hand, that the ‘purity’ of these concepts is one and the same notion, and, on (...) the other, that it is strongly indebted to, if not a by-product of, Kant's theorisation of the moral act. In order to make this claim, the essay analyses Benjamin's intense engagement with Kant's writings in the 1910s and early 1920s: ‘purity’ is a category strongly connoted within the philosophical tradition in which the young Benjamin moved his first steps, namely Kantian transcendental criticism. The essay argues that the notion of ‘purity’ in Benjamin, though deployed outside and often against Kant's theorisation and that of his followers, and moreover influenced by different and diverse philosophical suggestions, retains a strong Kantian tone, especially in reference to its moral and ethical aspects. Whereas Benjamin rejects Kant's model of cognition based on the ‘purity’ of the universal laws of reason, and thus also Kant's theorisation of purity as simply non empirical and a priori, he models nonetheless his politics and aesthetics around suggestions that arise directly from Kant's theorisation of the moral act and of the sublime, and uses a very Kantian vocabulary of negative determinations construed with the privatives-los and -frei (motiv-frei, zweck-los, gewalt-los, ausdrucks-los, intention-frei, etc). The essay explores thus the connections that link ‘pure means’, ‘pure language’ and ‘pure violence’ to one another and to the Kantian tradition. (shrink)

In this paper, I draw on the principles of Aristotelian ethics, the work of modern virtue ethicists, and previous feminist critiques of purity balls to interrogate the effects of this practice on moral development. I argue that purity balls discourage young women from making autonomous, informed, and virtuously motivated decisions regarding their sexuality. While most critiques of purity balls are rooted in the explicitly patriarchal structure of these events, my analysis emphasizes the negative impact they have on (...) moral agency. I conclude that purity balls are unethical because of the detrimental effects they have on the becoming of virtuous agents. (shrink)

Once an artist imagined how he would look if he plucked out an offending eye. He painted a self-portrait in which the orbit on the right side of his face was gaping, dolorous. Seven years passed, and then there came a day when the artist tried to break up a fight among his friends. In the ensuing melee he lost his left eye—the one he must have painted out all those years before, when working on the self-portrait, if he based (...) his image on the sight of himself in a mirror. Mirrors, of course, reverse the images before them.If we could forget niggling qualifications, epistemological hedges, all the huffing and puffing of the sense of responsibility that distinguishes intellectuals from assassins, then this story might be frightening, uncanny. As it is, I suspect most of my readers would find it terrible only in the derogatory sense. Although it has a certain primitive simplicity, it seems facile, as if it might have served for one of the weaker episodes in Walter Scott’s Waverley novels or Rod Serling’s “Twilight Zone.” Even if it were presented by a master of simple plots, I can imagine it succeeding only as an occasion for metaphysical conjectures, glistening thorns and blossoms of irony, and the like. And even if I were to say that this is a true story, that Victor Brauner painted this Autoportrait in 1931 and suffered this injury in 1938, it seems unlikely that it would be more affecting. How could such a corny plot raise a shiver from anyone past the age of reason? If this story is true, so much the worse for truth. It ought to know better than to seek us out with such shopworn devices. Daniel Cottom is a professor in the English department at the University of Florida. His most recent book is Text and Culture: The Politics of Interpretation . He is currently completing a book on spiritualism and surrealism. (shrink)

In this paper I will be concerned primarily with purity in morals. I will begin by considering an analysis of the pure person offered by Nicolai Hartmann. While I think there is much that is correct in his discussion, I will criticize it for focusing on naive innocence. I will then suggest some components of what I refer to as “mature purity,” and contrast it with Hartmann’s conception. I will also consider whether mature purity involves certain sorts (...) of attitudes and feelings, or merely conscientious action. I go on to discuss forms of impurity, and finally to discuss the relation of purity to other virtues. (shrink)

I argue for a novel understanding of the nature of agent-regret. On the standard picture, agent-regret involves regretting the result of one’s action and thus regretting one’s action. I argue that the standard picture is a flawed analysis of agent-regret. I offer several cases of agent-regret where the agent feels agent-regret but does not regret the result itself. I appeal to other cases where an agent’s attitude towards something depends upon whether or not they are involved in that thing. I (...) argue that the same applies to actions: sometimes an agent’s attitude towards a result differs from their attitude to their involvement in bringing about that result. Agent-regret is regret about my own action, but it need not involve regret about something in the world. I end by considering how this picture of agent-regret allows us to respond to a particular criticism of agent-regret. (shrink)

This is the first complete English translation of _On the Purity of the Art of Logic, _a handbook of logic written in Latin by English philosopher Walter Burley. The work circulated in the Middle Ages in two versions, a shorter and a longer one, both translated here by Paul Vincent Spade. The translations are based on the only complete edition of Burley’s treatises, corrected by Spade on the basis of one of the surviving manuscripts. The book also includes an (...) extensive introduction, explanatory notes, a table of corresponding passages between the two versions, a select annotated bibliography, and three indexes. A contemporary of John Duns Scotus and William of Ockham, Burley was active at the universities of both Paris and Oxford. He became one of the most important figures in the transformation of medieval logic and semantics that took place in the early fourteenth century. Burley used new tools and techniques of logical and semantical analysis, yet in many cases he used them in defense of traditional views, such as a realist metaphysical theory of “universals_._”_ On the Purity of the Art of Logic_ shows_ _both these sides of Burley—the innovator and the conservative—as well as some of the ways in which his views corresponded or clashed with those of William of Ockham. (shrink)

In Glas Derrida asserts that Hegel’s Phenomenology of Spirit, in its reading of Antigone, favors consciousness (over the unconscious) by first acknowledging the achievement of ethical plenitude by Antigone, as she comes to full recognition of two contradictory laws, that of the divine and that of the communal spheres, and consequently repressing this speculative accomplishment by her fateful disappearance from both texts. This article complicates the argument by looking at the role that literature takes not only in philosophy, but in (...) the expression of speculative dialectics as such. What for Hegel can be included in a system? How does the impossible figure (Antigone), its expression and then exclusion enter and abandon the system? This text looks at war, burial and incest expressed by the role of Antigone in the Phenomenology of Spirit. (HC) © 2011 by The Board of Regents of the University of Wisconsin System . (shrink)

We emphasize the role of the choice of vocabulary in formalization of a mathematical area and remark that this is a particular preoccupation of logicians. We use this framework to discuss Kennedy’s notion of ‘formalism freeness’ in the context of various schools in model theory. Then we clarify some of the mathematical issues in recent discussions of purity in the proof of the Desargues proposition. We note that the conclusion of ‘spatial content’ from the Desargues proposition involves arguments which (...) are algebraic and even metamathematical. Hilbert showed that the Desargues proposition implies the coordinatizing ring is associative, which in turn implies the existence of a three-dimensional geometry in which the given plane can be embedded. With W. Howard we give a new proof, removing Hilbert’s ‘detour’ through algebra, of the ‘geometric’ embedding theorem. Finally, our investigation of purity leads to the conclusion that even the introduction of explicit definitions in a proof can violate purity. We argue that although both involve explicit definition, our proof of the embedding theorem is pure while Hilbert’s is not. Thus the determination of whether an argument is pure turns on the content of the particular proof. Moreover, formalizing the situation does not provide a tool for characterizing purity. (shrink)

These are some of the central questions that Robert Proctor addresses in his study of the politics of modern science.

There are some people whose actions are much more often good than evil. If their infrequent immorality does not cause much harm, it is reasonable to regard such people as morally good. Nevertheless, moral goodness remains an elusive quality, because it is difficult to identify good actions. Motives, consequences, knowledge of alternatives and of the conventions prevailing in the context, the agent's history, character, and information all have a bearing on whether particular actions are good. These facts are not easy (...) to ascertain in any case, but when we are looking for a pattern formed of countless good actions over a lifetime, the difficulties are compounded. (shrink)

In a morally perfect world we would not face many of the hard choices which confront us in the real world. If everyone were fully conscientious, moral dilemmas might still be posed by natural circumstances; but many of our most difficult and tragic choices would not arise. In particular, we would never need to decide whether we should ourselves do a lesser evil in order to prevent someone else from doing a greater one. Unfortunately we do not live in such (...) a perfect world. Through greed, malice, jealousy, false pride, or whatever, people are prepared to commit the most heinous crimes against innocent victims; and sometimes, it seems, they can be prevented only by means which no one would consider in the morally perfect world. One must choose among evils; doing a lesser evil oneself or allowing others to do an even greater evil. (shrink)

Aristotle analyses a large range of objects as composites of matter and form. But how exactly should we understand the relation between the matter and form of a composite? Some commentators have argued that forms themselves are somehow material, that is, forms are impure. Others have denied that claim and argued for the purity of forms. In this paper, I develop a new purist interpretation of Metaphysics Z.10-11, a text central to the debate, which I call 'hierarchical purism'. I (...) argue that hierarchical purism can overcome the difficulties faced by previous versions of purism as well as by impurism. Roughly, on hierarchical purism, each composite can be considered and defined in two different ways: From the perspective of metaphysics, composites are considered only insofar as they have forms and defined purely formally. From the perspective of physics, composites are considered insofar as they have forms and matter and defined with reference to both. Moreover, while the metaphysical definition is a definition in the strict sense of 'definition', the physical definition is a definition in a loose sense. Analogous points hold for intelligible composites and geometry. Finally, neither sort of definitional practice implies that, for Aristotle, forms are impure. (shrink)

Critical discussion of Quine's concepts of purely referential occurrence/position. It is argued from the perspective of a Russellian view of truth that existential generalization and substitutivity of identity are non-equivalent tests for referential occurrence/position, and that the former rather than the latter is the appropriate test.