We describe an infinitary logic for metric structures which is analogous to Lω1,ω. We show that this logic is capable of expressing several concepts from analysis that cannot be expressed in finitary continuous logic. Using topological methods, we prove an omitting types theorem for countable fragments of our infinitary logic. We use omitting types to prove a two-cardinal theorem, which yields a strengthening of a result of Ben Yaacov and Iovino concerning separable quotients of Banach spaces.

We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal. Utilizing the failure of a weak version of a square, we show that the best currently known lower bounds for the consistency strength of these principles can be applied.

The classical doctrine that the moral virtues are unified is widely rejected. Some argue that the virtues are disunified, or even mutually incompatible. And though others have argued that the virtues form some sort of unity, these recent defenses of unity are always qualified, advocating only a partial unity: the unity of the virtues is limited to certain practical domains, or weak in that one virtue implies only moral decency in the fields of other virtues. I argue that something like (...) the classical doctrine—a full unity of the virtues thesis—remains defensible. After reviewing the arguments of partial unity theorists for the claim that the virtues form at least some sort of unity, I examine their main arguments for thinking that this unity is only partial (limited or weak). I then show that these arguments fail, and address some further criticisms (such as the argument that full unity implausibly requires that a person must attain the virtues “all at once”). I do not seek here to prove the truth of the full unity thesis (in fact I suggest a modification of it), but only to refute important extant criticisms of it, and thus to show that it remains a plausible view. (shrink)

The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as to allow for (...) the existence of wide sets. Drawing upon Cantor’s notion of the absolute infinite, the paper argues that the modifications are warranted and preserve a robust iterative conception of set. The resulting theory is proved consistent relative to ZFC + “there exists an inaccessible cardinal number.”. (shrink)

This essay addresses the first century of English colonization of the North American mainland. Rather than narrate a familiar story of events--migration, settlement, the creation of viable Anglophone cultures amid hardship and danger--it pursues a less familiar track by examining the terms upon which English adventurers and their contemporaries understood the world they inhabited, the process of transatlantic expansion upon which they were engaged, and, in particular, the justifications they espoused for their appropriations of space from its existing inhabitants. My (...) examination concentrates in particular on the conjoined discourses, literary and legal, in which the meanings of those terms are most clearly displayed. Through analysis of Shakespeare's early play Titus Andronicus, I demonstrate the salience of Tudor political economy--principally of sovereign power and invasion, of land and inhabitation, and of the city and barbarism--to the discourse of early-modern English colonizing. I show how the same complex of ideas animated the founding legal texts of English "settlement," revealed in the jurisdictional structures created and spaces occupied by the projectors of colonies. Finally, through reference to another foundational text, not of colonizing but of modern American legal history, I show the cardinal importance to contemporary America's historical self-construction of a refusal to acknowledge America's historical origins in a political economy of "colonization" and its violence, and its preference for a narrative of "energy" and "freedom" and their occlusion of violence. (shrink)

Daniel Russell's Practical Intelligence and the Virtues is principally a defense of the Aristotelian claim that phronesis is part of every unqualified virtue—a defense of what Russell calls "hard virtue theory" and "hard virtue ethics." The main support for this is the further claim that we would be unable to act well reliably, or form our character reliably, without phronesis performing its "twin roles": correctly identifying the mean of each virtue, and integrating the mean of each virtue with those of (...) others so as to enable us to act in an overall virtuous manner. In following Russell's argument for these claims, we find much else of interest, including a persuasive account of right action and a resurrection of the old doctrine of cardinal virtues. Here I seek first to give readers a sense of the range and depth of this important book by summarizing the main lines of its argument. But I also raise some critical points, the most substantive of which concern his treatments of the unity of the virtues and of responsibility for character. (shrink)

We study the problem of existence and generic existence of ultrafilters on ω. We prove a conjecture of $J\ddot{o}rg$ Brendle's showing that there is an ultrafilter that is countably closed but is not an ordinal ultrafilter under CH. We also show that Canjar's previous partial characterization of the generic existence of Q-points is the best that can be done. More simply put, there is no normal cardinal invariant equality that fully characterizes the generic existence of Q-points. We then sharpen (...) results on generic existence with the introduction of $\sigma-compact$ ultrafilters. We show that the generic existence of said ultrafilters is equivalent to $\delta = c$ . This result taken along with our result that there exists a $K_{\sigma}$ non-countably closed ultrafilter under CH, expands the size of the class of ultrafilters that were known to fit this description before. From the core of the proof, we get a new result on the cardinal invariants of the continuum, i.e., the cofinality of the sets with $\sigma-compact$ closure is δ. (shrink)

The response mode bias, in which subjects exhibit different risk attitudes when assessing certainty equivalents versus indifference probabilities, is a well-known phenomenon in the assessment of utility functions. In this empirical study, we develop and apply a cardinal measure of risk attitudes to analyze not only the existence, but also the strength of this phenomenon. Since probability levels involved in decision problems are already known to have a strong impact on behavior, we use this approach to study the impact (...) of probabilities on the extent of the response mode bias. We find that the direction in which probabilities influence measured risk aversion is the opposite in the certainty equivalence (CE) method versus in the probability equivalence (PE) method. Utilizing the CE elicitation approach leads to an increase of risk seeking for gambles involving high probabilities. For the PE method, subjects tend to behave risk averse with gambles of high probabilities. This behavior is reversed in the gain domain. This “tailwhip” effect is consistently replicated in several experiments, involving both loss and gain domains of lotteries. (shrink)

Alisdair Macintyre's defense of the tradition of Aristotle and St. Thomas Aquinas offers a way to answer the question "What is the good of history?" By his use of dialectical reasoning in defense of the Thomist tradition, Macintyre helps Catholic historians to see that the good of history comes from its being a handmaiden to tradition. The writings of St. Bede the Venerable and John Henry Cardinal Newman are used as examples of how Catholic historians can know and draw (...) upon their own tradition. (shrink)

Scientific models are often said to be more or less general depending on how many cases they cover. In this paper we argue that the cardinality of cases is insufficient as a metric of generality, and we present a novel account based on measure theory. This account overcomes several problems with the cardinality approach, and additionally provides some insight into the nature of assessments of generality. Specifically, measure theory affords a natural and quantitative way of describing local spaces of possibility. (...) The generality of models can be understood as the measure of possibilities to which the models apply. In order to illustrate our view, we consider the example of structural genomics, the ongoing project of building three-dimensional models of biological macromolecules like proteins. Using measure theory, we interpret the practice of homology modeling, where such models are understood to apply widely but imperfectly to the space of possible proteins. (shrink)

We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals and of partial orders: certain notions of distributivity, strategic closure, and precipitousness.

Memory for numbers improves with age. One source of this improvement may be learning linear spatial-numeric associations, but previous evidence for this hypothesis likely confounded memory span with quality of numerical magnitude representations and failed to distinguish spatial-numeric mappings from other numeric abilities, such as counting or number word-cardinality mapping. To obviate the influence of memory span on numerical memory, we examined 39 3- to 5-year-olds’ ability to recall one spontaneously produced number (1-20) after a delay, and the relation between (...) numeric recall (controlling for non-numeric recall) and quality of mapping between symbolic and non-symbolic quantities using number-line estimation, give-a-number estimation, and counting tasks. Consistent with previous reports, mapping of numerals to space, to discrete quantities, and to numbers in memory displayed a logarithmic-to-linear shift. Also, linearity of spatial-numeric mapping correlated strongly with multiple measures of numeric recall (percent correct and percent absolute error), even when controlling for age and non-numeric memory. Results suggest that linear spatial-numeric mappings may aid memory for number over and above children’s other numeric skills. (shrink)

This paper argues that we should replace the common classification of theories of welfare into the categories of hedonism, desire theories, and objective list theories. The tripartite classification is objectionable because it is unduly narrow and it is confusing: it excludes theories of welfare that are worthy of discussion, and it obscures important distinctions. In its place, the paper proposes two independent classifications corresponding to a distinction emphasised by Roger Crisp: a four-category classification of enumerative theories (about which items constitute (...) welfare), and a four-category classification of explanatory theories (about why these items constitute welfare). (shrink)

Group-based reasons are reasons to play one’s part in some pattern of action that the members of some group could perform, because of the good features of the pattern. This paper discusses three broad conceptions of such reasons. According to the agency-first conception, there are no group-based reasons in cases where the relevant group is not or would not be itself an agent. According to the behaviour-first conception, what matters is that the other members of the group would play their (...) parts in the relevant pattern, not whether they would have the cooperative intentional states constitutive of group agency in doing so. This paper argues against these conceptions and in favour of the powers-first conception, according to which what matters is that the members of the group have practically relevant powers. (shrink)

Are we witnessing progress or regress in the recent increasing popularity and electoral success of populist politicians and parties in consolidated democratic nations? ... Is the innovative use of popular referendum in Great Britain to settle fundamental constitutional questions a progressive or regressive innovation? ... Similarly, is the increasing use of constituent assemblies to change constitutions across the world evidence of progress in democratic constitutionalism, or, a worryingly regressive change back toward unmediated popular majoritarianism? ... This paper reflects on some (...) of the perils and promise of framing such questions with the conceptual couplet of progress and regress. It considers four compelling critiques of the use of ‘progress’ and its cognates in sociopolitical theory, as well as arguing that such concepts are nevertheless ineliminable for our normative theories. The paper concludes by suggesting that we can avoid the most serious problems by employing only conceptions of political progress and regress that are piecemeal, pragmatic, and processual. (shrink)

This article proposes a way of understanding Kantianism, act-utilitarianism and some other important ethical theories according to which they are all versions of the same kind of theory, sharing a common structure. I argue that this is a profitable way to understand the theories discussed. It is charitable to the theories concerned; it emphasizes the common ground between them; it gives us insights into the differences between them; and it provides a method for generating new ethical theories worth studying. The (...) article briefly discusses the relationship between these ideas and some other recent proposals that emphasize the common ground between Kantianism and versions of consequentialism. (shrink)

This chapter surveys hybrid theories of well-being. It also discusses some criticisms, and suggests some new directions that philosophical discussion of hybrid theories might take.

In the last homily he gave before becoming Pope Benedict XVI, Cardinal Joseph Ratzinger described modern life as ruled by a “dictatorship of relativism which does not recognize anything as definitive and whose ultimate goal consists solely” of satisfying “the desires of one’s own ego.” An eminent scholar familiar with the centuries-old debates over relativism, Ratzinger chose to oversimplify or even caricature a philosophical approach of great sophistication and antiquity. His homily depicts the relativist as someone blown about “by (...) every wind of doctrine,” whereas the relativist sticks firmly to one argument—that human knowledge is not absolute. Gathering prominent intellectuals from disciplines most relevant to the controversy—ethics, theology, political theory, anthropology, psychology, cultural studies, epistemology, philosophy of science, and classics—this special double issue of _Common Knowledge_ contests Ratzinger’s denunciation of relativism. One essay relates the arguments of Ratzinger to those of two other German scholars—the conservative political theorist Ernst Wolfgang Böckenförde and the liberal philosopher and sociologist Jürgen Habermas—since all three men assume that social order depends on the existence of doctrinal authority. The contributors here argue for an intellectual and social life free of the desire for an “infantilizing” authority. One proposes that the Christian god is a relativist who prefers limitation and ambiguity; another, initially in agreement with Ratzinger about the danger relativism poses to faith and morals, then argues that this danger is what makes relativism valuable. The issue closes with the first English translation of an extract from a book on Catholic-Jewish relations by Cardinal Carlo Maria Martini, one of the Catholic Church’s most progressive figures. _Contributors_. David Bloor, Daniel Boyarin, Mary Baine Campbell, Lorraine Daston, Arnold I. Davidson, John Forrester, Kenneth J. Gergen, Simon Goldhill, Jeffrey F. Hamburger, Julia Kristeva, Carlo Maria Cardinal Martini, Christopher Norris, Joseph Cardinal Ratzinger, Richard Shusterman, Barbara Herrnstein Smith, Jeffrey Stout, Gianni Vattimo. (shrink)

Difficult Atheism shows how contemporary French philosophy is rethinking the legacy of the death of God in ways that take the debate beyond the narrow confines of atheism into the much broader domain of post-theological thinking. Christopher Watkin argues that Alain Badiou, Jean-Luc Nancy and Quentin Meillassoux each elaborate a distinctive approach to the post-theological, but that each approach still struggles to do justice to the death of God.

Theorists of public reason such as John Rawls often idealize constitutional courts as exemplars of public reason. This paper raises questions about the seduction and limits of analogies between theorists’ account of public reason and actual constitutional jurisprudence. Examining the work product of the United States Supreme Court, the paper argues that while it does engage in reason-giving to support its decisions—as the public reason strategy suggests— those reasons are (largely) legalistic and specifically juristic reasons—not the theorists’ idealized moral-political reasons (...) on matters of fundamental principle. But if constitutional courts do not engage on matters of fundamental principle, then a public reason strategy for assuaging democratic worries about judicial review would no longer be open: prominent liberal and deliberative democratic theorists could no longer point to the alleged superiority of constitutional courts to speak in the name of, and for, the people’s shared political principles. The paper extends beyond the U.S. case study by pointing to three institutional factors explaining the disanalogy between what some constitutional courts do and what public reason theories require them to do. It concludes with considerations about whether the public reason strategy might be more successfully applied to international courts. (shrink)

Authentizitat ist ein in unserem kulturellen Raum allgegenwartiges Phanomen. Doch wem oder was begegnen wir, wenn wir meinen, uns selbst verwirklichen oder alternativ einfach uns selbst treu sein zu mussen? Christoph Wiesinger zeigt, dass wir auf ein Selbst geworfen werden, das zwar als homogener Nukleus der Person projiziert werden kann, sich aber bei genauerem Hinsehen als komplexe sozial verinnerlichte Struktur entpuppt. Das Selbst ist keineswegs objektiv zu fassen, sondern unterliegt sozialen Genesen und wird durch soziale Adressierung unterschiedlich formiert. Das (...) Ereignis von Authentizitat gibt somit Anlass zur Reflexion der Differenz zwischen Erwartung und Erfahrung. Christoph Wiesinger legt die Strukturen des Phanomens der Authentizitat frei, zeigt die theologischen Implikationen auf und diskutiert die praktisch-theologischen Konsequenzen. (shrink)

One recently popular strategy for avoiding the moral error theory is via a ‘companions in guilt’ argument. I focus on those recently popular arguments that take epistemic facts as a companion in guilt for moral facts. I claim that there is an internal tension between the two main premises of these arguments. It is a consequence of this that either the soundness or the dialectical force of the companions in guilt argument is undermined. I defend this claim via (i) analogy (...) with philosophical debates concerning the indispensability of mathematical objects to natural science, and (ii) discussion of the ‘entanglement’ of epistemic concepts and moral concepts in deliberation. I conclude by proposing a positive view of what kind of argument must be used if moral error theories are to be successfully undermined. (shrink)

Die Kernthese der Paracelsischen Naturphilosophie, die Ahnlichkeit von Mensch und Welt, festgelegt in der Analogie von Mikro- und Makrokosmos, enthullt einen -Code-, der als konstitutives Moment samtliche Aussagen auf einer prakonzeptionellen Ebene organisiert, samtliche Teilbereiche in ihrer funktionalen Bedeutung fur das -Ganze- markiert und schliesslich im Sinne Foucaults zu einer -diskursiven Formation- werden lasst. Die auf diese Weise vorgefuhrte Erfahrungsform von Welt und Natur steht zu dem neuzeitlich-technischen Verfugungswissen in einer historischen Diskontinuitat.".

This paper connects two ideas. The first is that some common responses to ethical views are responses to their degrees of pragmatism, where a view’s degree of pragmatism is its sensitivity to ethically relevant changes in the actor’s circumstances. I claim that we feel the pull of opposing pro-pragmatic and antipragmatic intuitions in certain cases. This suggests a project, of searching for an ethical view capable of doing justice to these opposing intuitions in some way. The second central idea is (...) that a theory of pattern-based reasons looks more promising than the obvious alternatives to fulfil this role, amongst Teleological theories at least. Pattern-based reasons are reasons to perform some action because of the goodness or rightness of a larger pattern of action—such as a pattern that a group could perform or that the actor could perform over an extended period—of which the immediate action is a mere part. Existing theories of such reasons share two features that prevent them explaining the intuitions we wish to explain: they consider only one pattern at a time (they are monist), and they treat patterns as eligible only if the agents concerned are willing to realise them (they accept the Willingness Requirement). But we need not accept these doctrines. Moreover, a theory of patternbased reasons without them is able to explain the pro- and anti-pragmatic intuitions in an elegant way, and has other attractive features. (shrink)

Basing his view on the object relations theories of the "British School" of psychoanalysis, Christopher Bollas examines the human subject's memories of its earliest experiences (during infancy and childhood) of the object, whether it be mother, father, or self. He explains in well-written and non-technical language how the object can affect the child, or "cast in shadow," without the child being able to process this relation through mental representations of language.

In the Gorgias, Plato explores the relationship between statesmanship and rhetoric. Socrates argues that the true statesman uses the true rhetoric in the attempt to make others better through speeches. In the conversation with Gorgias, Socrates forces him to see the potentially disastrous consequences of teaching a kind of rhetoric that is morally neutral, which suggests the need for an uncompromisingly true or just rhetoric. In the exchange with Polus, Socrates attempts the just reformation of rhetoric into true rhetoric to (...) counter the unjust rhetoric of Polus. In his discussion with Callicles, Socrates uses the true rhetoric to try to moderate him, but his failure reveals the limits of true statesmanship. By examining these three exchanges, I shed light on a unique and neglected paradox of the Gorgias. As clearly as the dialogue articulates what constitutes a true statesman, it challenges his own practice. Socrates, as the true statesman possessing the true rhetoric, is powerless to achieve his goals. However, a potential way to expand the success of the true statesman can be seen by going back to the discourse between Socrates and Gorgias and forging an alliance between them. (shrink)

Here, for the first time, Christopher Kul-Want brings together twenty-five texts on art written by twenty philosophers. Covering the Enlightenment to postmodernism, these essays draw on Continental philosophy and aesthetics, the Marxist intellectual tradition, and psychoanalytic theory, and each is accompanied by an overview and interpretation. The volume features Martin Heidegger on Van Gogh's shoes and the meaning of the Greek temple; Georges Bataille on Salvador Dal’'s The Lugubrious Game; Theodor W. Adorno on capitalism and collage; Walter Benjamin and Roland (...) Barthes on the uncanny nature of photography; Sigmund Freud on Leonardo Da Vinci and his interpreters; Jacques Lacan and Julia Kristeva on the paintings of Holbein; Freud's postmodern critic, Gilles Deleuze on the visceral paintings of Francis Bacon; and Giorgio Agamben on the twin traditions of the Duchampian ready-made and Pop Art. Kul-Want elucidates these texts with essays on aesthetics, from Hegel and Nietzsche to Badiou and Rancire, demonstrating how philosophy adopted a new orientation toward aesthetic experience and subjectivity in the wake of Kant's powerful legacy. (shrink)

In this article Cristoph Wulf examines the basic concepts of pedagogy and educational science in the German-speaking world, looking at education and socialization from the perspective of educational anthropology. He makes evident that the complex German concept of Bildung, in particular, can only be fully understood by means of a historical and philosophical analysis.

The idea of the ‘executive technician’ or the teacher who follows theoretically prescribed rules is outlined. Through a discussion of the ideas of Oakeshott the idea of a rule‐following rigid practitioner of prescribed protocols is developed. The advantages of this conception of teaching as well as its disadvantages are outlined. Some practical applications of the executive technician conception of the teacher in both developed and developing countries are presented.

This chapter will outline a third conception of the role of the teacher, the professional technician or professional for short. The professional teacher is one who most corresponds to the description of professional occupations described in the literature already discussed. The professional described in this chapter will be an ideal type, whose attributes will be found to a greater or lesser degree in actual teachers around the world. Should this be a preferred model of what a teacher should be? The (...) answer depends on what kind of education system a society wants and the degree to which it is prepared to invest in such a kind of education system. (shrink)

It was not so long ago that the dominant picture of Kant’s practical philosophy was formalistic, focusing almost exclusively on his Groundwork of the Metaphysics of Morals and Critique of Practical Reason. However, the overall picture of Kant’s wide-ranging philosophy has since been broadened and deepened. We now have a much more complete understanding of the range of Kant’s practical interests and of his contributions to areas as diverse as anthropology, pedagogy, and legal theory. What remains somewhat obscure, however, is (...) how these different contributions hang together in the way that Kant suggests that they must. This book explores these different conceptions of humanity, morality, and legality in Kant as main ‘manifestations’ or ‘dimensions’ of practical normativity. These interrelated terms play a crucial role in highlighting different rational obligations, their source, and their applicability in the face of changing circumstances. (shrink)

In its own contemporary context, Kant’s views on the relationship between reason and religion played a crucial role in debates about the nature of the Enlightenment. The terms of that debate, as they were most sharply formulated by F. H. Jacobi, posed an either/or choice of reason or faith, between which Kant offered a third option that would synthesize reason and faith. A newly published collection of essays, Kant’s Philosophy of Religion Reconsidered, not only echoes this debate in current terms (...) but also suggests that the unfinished business of the Enlightenment in regard to morality, religion, and the historicity of reason is still with us. (shrink)

In its own contemporary context, Kant’s views on the relationship between reason and religion played a crucial role in debates about the nature of the Enlightenment. The terms of that debate, as they were most sharply formulated by F. H. Jacobi, posed an either/or choice of reason or faith, between which Kant offered a third option that would synthesize reason and faith. A newly published collection of essays, Kant’s Philosophy of Religion Reconsidered, not only echoes this debate in current terms (...) but also suggests that the unfinished business of the Enlightenment in regard to morality, religion, and the historicity of reason is still with us. (shrink)

Scheler's philosophic reflections on religious experience and on the connections between this experience and those reflections seek to found a phenomenological personalism. Hence I first delineate his conception of person via his view of phenomenology as resulting from a critique of husserl. I then elaborate scheler's conception of philosophy in terms of the intentional acts involved. After a similar elaboration of scheler's view of religion, I present his 'system of conformity' of the proper interplay of philosophy and religion. I conclude (...) by indicating why his phenomenological anthropology is not only inadequate to the foundational task assigned to it but methodologically incoherent. (shrink)

One of the most important elements of Hegel’s philosophical anthropology is his moral psychology. In particular, his understanding of the relation between motivations and reason plays a crucial intermediate role in connecting his anthropological meditations on the complete nature of the human being with his political theory of actualized freedom. Whereas recent important work on Hegel’s moral psychology has detected a Kantian distinction between natural desires and the rational perspective, the activity of practical reason actually takes place within motivations themselves (...) on Hegel’s view. The exercise of the free, rational will is best understood in terms of its role in shaping the experience of malleable, indeterminate motivations. Rather than stepping back, the free agent on Hegel’s account delves further into the motivation, acting on it in the dual sense of being guided by and transforming it. This is what it means for Hegel to conceive of agency as self-expression while maintaining the centrality of reason for Free Will. Hegel says that when we go further into the motivations in this way, we should stop speaking of motivation in terms of drives and instead begin speaking of character. (shrink)