Preface: The dog's bollocks-- at the media dinner party -- Introduction: "The Marx brothers", "The Elvis of cultural theory", and other media clichés -- The mediated imp of the perverse -- Žižek's tickling shtick -- Big (Br)other : psychoanalysing the media -- Understanding the media : the sublime objectification of ideology -- The media's violence -- The joker's little shop of ideological horrors -- Conclusion: Don't just do it : negative dialectics in the age of Nike.

I argue that when we interpret a literary work, we engage with at least two different kinds of meaning, each requiring a distinct mode of interpretation. These kinds of meaning are literary varieties of what Paul Grice called nonnatural and natural meaning. The long-standing debate that began with Beardsley and Wimsatt's attack on the intentional fallacy is, I argue, really a debate about nonnatural meaning in literature. I contend that natural meaning has been largely neglected in our theorizing about (...) literary interpretation and that this comes at a serious cost, resulting in an inadequate account of what interpretation involves. I argue, first, that by recognizing that literary meaning includes both nonnatural and natural meaning, we are better placed to understand the interpreter's relationship with the author, and, second, that recognition of the distinction between nonnatural and natural meaning advances the established debate about literary meaning, offering support for actual intentionalism. The more inclusive view of literary meaning helps resolve an apparent difficulty raised by Noël Carroll. (shrink)

Zizek Studies: The Greatest Hits (So Far) assembles and presents the best work published in the field of Zizek Studies over the last ten years, providing teachers, students, and researchers with a carefully curated volume of leading-edge scholarship addressing the unique and sometimes eclectic work of Slovenian philosopher and cultural critic Slavoj Zizek. The chapters included in this collection have been rigorously tested in and culled from the (virtual) pages of the International Journal of Zizek Studies, a leading open access (...) journal that began publication in 2007. The book is organized into three sections or subject areas where Zizek and his seemingly indefatigable efforts have had significant impact: philosophy, politics, and popular culture. As a "greatest hits," the book offers the long-time fan and uninitiated newcomer alike a comprehensive overview of the wide range of opportunity in the field of Zizek studies and a remarkable collection of truly interdisciplinary "hits" from a diverse set of innovative and accomplished writers. (shrink)

David Lowenthal offers a serious treatment of the idea that Shakespeare was a serious thinker, indeed a philosopher who chose to develop his ideas in dramatic form. Readers accustomed to contemporary Shakespeare criticism may be puzzled by Lowenthal’s book. He makes no effort to historicize his discussion of Shakespeare and never invokes the unholy trinity of race, class, and gender in analyzing the plays. Compared to new historicist, feminist, Marxist, and deconstructionist critics of Shakespeare, Lowenthal may seem to be a (...) naive reader; he is looking for what he can read out of the plays, not what he can read into them. Grounding himself in the older tradition of Shakespeare criticism, from Ben Jonson to Samuel Johnson, from Samuel Taylor Coleridge to A. C. Bradley, Lowenthal views the playwright as a source of genuine wisdom. He assumes that Shakespeare knew what he was doing and was fully in control of his dramatic material, shaping his plays into artistic wholes that allow him to raise fundamental questions about the human condition. (shrink)

Proponents of public reason views hold that the exercise of political power ought to be acceptable to all reasonable citizens. This article elucidates the common structure shared by all public reason views, first by identifying a set of questions that all such views must answer and, second, by showing that the answers to these questions stand in a particular relationship to each other. In particular, we show that what we call the ‘rationale question’ is fundamental. This fact, and the common (...) structure more generally, are often overlooked or distorted within the literature. As a result, we argue, several prominent argumentative moves made by both critics and defenders of public reason are unsuccessful. Our overall conclusion is that discussions of public reason views would be more fruitful if they made consistent use of the common structure we identify. (shrink)

Recovering Reason: Essays in Honor of Thomas L. Pangle is a collection of essays composed by students and friends of Thomas L. Pangle to honor his seminal work and outstanding guidance in the study of political philosophy. These essays examine both Socrates' and modern political philosophers' attempts to answer the question of the right life for human beings, as those attempts are introduced and elaborated in the work of thinkers from Homer and Thucydides to Nietzsche and Charles Taylor.

I present the foundational structure for a life-centered theory of environmental ethics. The structure consists of three interrelated components. First is the adopting of a certain ultimate moral attitude toward nature, which I call “respect for nature.” Second is a belief system that constitutes a way of conceiving of the natural world and of our place in it. This belief system underlies and supports the attitude in a way that makes it an appropriate attitude to take toward the Earth’s natural (...) ecosystems and their life communities. Third is a system of moral rules and standards for guiding our treatment of those ecosystems and life communities, a set of normative principles which give concrete embodiment or expression to the attitude of respect for nature. The theory set forth and defended here is, I hold, structurally symmetrical with a theory of human ethics based on the principle of respect for persons. (shrink)

Public reason views hold that the exercise of political power must be acceptable to all reasonable citizens. A growing number of philosophers argue that this reasonable acceptability principle (RAP) can be justified by appealing to the value of civic friendship. They claim that a valuable form of political community can only be achieved among the citizens of pluralistic societies if they refrain from appealing to controversial ideals and values when justifying the exercise of political power to one another. This paper (...) argues against such accounts. In order to justify RAP, one must explain and defend a conception of reasonableness. Civic friendship is unfit to perform this task, rendering it unable to ground public reason alone. Meanwhile, pluralist views that combine civic friendship with other considerations in order to specify RAP either fail or make civic friendship a spare wheel in the argument for public reason. (shrink)

What rational justification is there for conceiving of all living things as possessing inherent worth? In _Respect for Nature_, Paul Taylor draws on biology, moral philosophy, and environmental science to defend a biocentric environmental ethic in which all life has value. Without making claims for the moral rights of plants and animals, he offers a reasoned alternative to the prevailing anthropocentric view--that the natural environment and its wildlife are valued only as objects for human use or enjoyment. _Respect (...) for Nature_ provides both a full account of the biological conditions for life--human or otherwise--and a comprehensive view of the complex relationship between human beings and the whole of nature. This classic book remains a valuable resource for philosophers, biologists, and environmentalists alike--along with all those who care about the future of life on Earth. A new foreword by Dale Jamieson looks at how the original 1986 edition of _Respect for Nature_ has shaped the study of environmental ethics, and shows why the work remains relevant to debates today. (shrink)

Paul C. Taylor provides an accessible guide to a well-travelled but still-mysterious area of the contemporary social landscape. The result is the first philosophical introduction to the field of race theory and to a non-biological and situational notion of race. Provides the first philosophical introduction to the field of race theory. Outlines the main features and implications of race-thinking; asks questions such as: What is race-thinking? Don’t we know better than to talk about race now? Are there any (...) races? What is it like to have a racial identity? Engages with the ideas of such important figures as Linda Alcoff, K. Anthony Appiah, W.E.B. Du Bois, Howard Winant, and Naomi Zack. Explores the enduring significance of race in relation to culture, personal relationships and social justice. (shrink)

The aim of this review is to show the fruitfulness of using images of facial expressions as experimental stimuli in order to study how neural systems support biologically relevant learning as it relates to social interactions. Here we consider facial expressions as naturally conditioned stimuli which, when presented in experimental paradigms, evoke activation in amygdala–prefrontal neural circuits that serve to decipher the predictive meaning of the expressions. Facial expressions offer a relatively innocuous strategy with which to investigate these normal variations (...) in affective information processing, as well as the promise of elucidating what role the aberrance of such processing might play in emotional disorders. (shrink)

Those who know anything about black history and culture probably know that aesthetics has long been a central concern for black thinkers and activists. The Harlem Renaissance, the Negritude movement, the Black Arts Movement, and the discipline of Black British cultural studies all attest to the intimate connection between black politics and questions of style, beauty, expression, and art. And the participants in these and other movements have made art and offered analyses that wrestle with clearly philosophical issues. In _A (...) Philosophy of Black Aesthetics_, I propose to identify and explore the most significant philosophical issues that emerge from the aesthetic dimensions of black life. The book will consist of eight short chapters, each of which will discuss a complex of related themes and phenomena. Every chapter will begin with one or two illustrative real-world examples, and then use the complexities of these opening cases to introduce the relevant issues. Many people in several fields have explored various bits of the terrain that I’ll cover. But none has surveyed the entire terrain in the name of aesthetics, and none has conducted this survey from an explicitly philosophical perspective. Setting up the project in this way means that its main conclusions will come in two forms. One kind of conclusion will emerge from the way I frame the issues. The two most important points here are that the field of aesthetics ought to cover more than the study of western fine art, and that the field of black aesthetics allows and requires the sort of comprehensive and philosophical analysis that I’ll offer. Another set of conclusions will emerge from my treatment of the specific issues in each chapter. In each case the aim will be to defend, albeit briefly, some position on the major issues raised in each chapter. (shrink)

Louis G. Lombardi’s arguments in support of the claim that humans have greater inherent worth than other living things provide a clear account of how it is possible to conceive of the relation between humans and nonhumans in this way. Upon examining his arguments, however, it seems that he does not succeed in establishing any reason to believe that humans actually do have greater inherent worth than animals and plants.

That Ernst Gombrich was one of the most important art historians of the 20th century would seem to go without saying. And so one might expect him to feature prominently in the numerous surveys, guides and introductions to the history and methods of art history produced during the past two decades. Precisely the opposite, however, is the case. One reason for this certainly was that Gombrich was an avowed enemy of 'big ideas', interested not in generalizations but in the specifics (...) of individual cases. Avoiding jargon or rhetoric, standing for 'common sense', he always argued from clear premises, and his thought was also very wide-ranging. He never 'owned' a subject, remarking It cannot be too often repeated that the best tribute one can pay a scholar is to take him seriously and constantly to reappraise his lines of argument.The importance of Gombrich's work on the history of taste has yet to be fully recognized, and when it comes to the application of developments in psychology to the visual arts he has remained largely, among art historians, on his own. These essays assess the nature of his empiricism, the degree to which his ideas have been adopted, overturned or developed, and his contribution to the dialogue of art and perception. (shrink)

Was W. E. B. Du Bois a pragmatist? Does it matter? This essay argues that reading Du Bois as a pragmatist highlights aspects of his work and life that might otherwise go unnoticed, while also highlighting aspects of pragmatism that often go unappreciated. In addition, this double revelation may help restore to us some important resources for dealing with current social problems.

Gene Spitler has raised certain objections to my views on the biocentric outlook: that a factual error is involved in the assertion that organisms pursue their own good, that there is an inconsistency in the biocentric outlook, that it is impossible for anyone to adopt that outlook, and that the outlook entails unacceptable moral judgments, for example, that killing insects and wildfiowers is as morally reprehensible as killing humans. I reply to each of these points, showing that the biocentric outlook (...) on nature is not only a possible, but also a reasonable world view. (shrink)

I present the foundational structure for a life-centered theory of environmental ethics. The structure consists of three interrelated components. First is the adopting of a certain ultimate moral attitude toward nature, which I call “respect for nature.” Second is a belief system that constitutes a way of conceiving of the natural world and of our place in it. This belief system underlies and supports the attitude in a way that makes it an appropriate attitude to take toward the Earth’s natural (...) ecosystems and their life communities. Third is a system of moral rules and standards for guiding our treatment of those ecosystems and life communities, a set of normative principles which give concrete embodiment or expression to the attitude of respect for nature. The theory set forth and defended here is, I hold, structurally symmetrical with a theory of human ethics based on the principle of respect for persons. (shrink)

This book is a collection of secondary essays on America's most important philosophic thinkers—statesmen, judges, writers, educators, and activists—from the colonial period to the present. Each essay is a comprehensive introduction to the thought of a noted American on the fundamental meaning of the American regime.

Intellectual humility, which entails openness to other views and a willingness to listen and engage with them, is crucial for facilitating civil dialogue and progress in debate between opposing sides. In the present research, we tested whether intellectual humility can be reliably detected in discourse and experimentally increased by a prior self-affirmation task. Three-hundred and three participants took part in 116 audio and video-recorded group discussions. Blind to condition, linguists coded participants’ discourse to create an intellectual humility score. As expected, (...) the self-affirmation task increased the coded intellectual humility, as well as participants’ self-rated prosocial affect (e.g., empathy). Unexpectedly, the effect on prosocial affect did not mediate the link between experimental condition and intellectual humility in debate. Self-reported intellectual humility and other personality variables were uncorrelated with expert-coded intellectual humility. Implications of these findings for understanding the social psychological mechanisms underpinning intellectual humility are considered. (shrink)

For many decades, race and racism have been common areas of study in departments of sociology, history, political science, English, and anthropology. Much more recently, as the historical concept of race and racial categories have faced significant scientific and political challenges, philosophers have become more interested in these areas. This changing understanding of the ontology of race has invited inquiry from researchers in moral philosophy, metaphysics, epistemology, philosophy of science, philosophy of language, and aesthetics. The Routledge Companion to Philosophy of (...) Race offers in one comprehensive volume newly written articles on race from the world's leading analytic and continental philosophers. It is, however, accessible to a readership beyond philosophy as well, providing a cohesive reference for a wide student and academic readership. The Companion synthesizes current philosophical understandings of race, providing 37 chapters on the history of philosophy and race as well as how race might be investigated in the usual frameworks of contemporary philosophy. The volume concludes with a section on philosophical approaches to some topics with broad interest outside of philosophy, like colonialism, affirmative action, eugenics, immigration, race and disability, and post-racialism. By clearly explaining and carefully organizing the leading current philosophical thinking on race, this timely collection will help define the subject and bring renewed understanding of race to students and researchers in the humanities, social science, and sciences. (shrink)

This essay uses the concept of reconstruction to make an argument and an intervention in relation to the practice and study of black aesthetics. The argument will have to do with the parochialism of John Dewey, the institutional inertia of professional philosophy, the aesthetic dimensions of the US politics of reconstruction, the centrality of reconstructionist politics to the black aesthetic tradition, and the staging of a reconstructionist argument in the film, Black Panther (Coogler 2018). The intervention aims to address the (...) fact that arguments like these tend not to register properly because of certain reflexive and customary limits on some common forms of philosophical inquiry. The sort of professional philosophy I was raised to practise and value tends not to be particularly inclusive and open-minded, especially when it comes to subjects that bear directly on the thoughts, lives, and practices of people racialized as black. black aesthetics, by contrast, is an inherently ecumenical enterprise, reaching across disciplinary and demographic boundaries to build communities of practice and exchange. Hence the need for an intervention: to create the space for arguments and the people who work with them to function across disciplinary and demographic contexts. (shrink)

This book compares two major leisure activities – watching sport and engaging with art. It explores a range of philosophical questions that arise when sport and art are placed side by side: The works of Shakespeare, Rembrandt and Mozart have continued to fill playhouses, galleries and concert halls for centuries since they were created, while our interest in even the most epic sporting contests fades after just a few years, or even a single season. What explains this difference? Sporting contests (...) are merely games. So why do sports fans attach such great importance to whether their team wins or loses? Do sporting contests have meaning in the way works of art do? Beauty is a central value in art. Is it important in sport? What role does morality play in sport and art? What value do sport and art contribute to the world and to the meaning of people’s lives? (shrink)

BackgroundInaccurate, false or incomplete research publications may mislead readers including researchers and decision-makers. It is therefore important that such problems are identified and rectified promptly. This usually involves collaboration between the research institutions and academic journals involved, but these interactions can be problematic.MethodsThese recommendations were developed following discussions at World Conferences on Research Integrity in 2013 and 2017, and at a specially convened 3-day workshop in 2016 involving participants from 7 countries with expertise in publication ethics and research integrity. The (...) recommendations aim to address issues surrounding cooperation and liaison between institutions and journals about possible and actual problems with the integrity of reported research arising before and after publication.ResultsThe main recommendations are that research institutions should: develop mechanisms for assessing the integrity of reported research that are distinct from processes to determine whether individual researchers have committed misconduct;release relevant sections of reports of research integrity or misconduct investigations to all journals that have published research that was investigated;take responsibility for research performed under their auspices regardless of whether the researcher still works at that institution or how long ago the work was done;work with funders to ensure essential research data is retained for at least 10 years.Journals should: respond to institutions about research integrity cases in a timely manner;have criteria for determining whether, and what type of, information and evidence relating to the integrity of research reports should be passed on to institutions;pass on research integrity concerns to institutions, regardless of whether they intend to accept the work for publication;retain peer review records for at least 10 years to enable the investigation of peer review manipulation or other inappropriate behaviour by authors or reviewers.ConclusionsVarious difficulties can prevent effective cooperation between academic journals and research institutions about research integrity concerns and hinder the correction of the research record if problems are discovered. While the issues and their solutions may vary across different settings, we encourage research institutions, journals and funders to consider how they might improve future collaboration and cooperation on research integrity cases. (shrink)

The scale and variety of acts of religious intolerance evident in so many countries today are of enormous contemporary concern. This 2005 study attempts a thorough and systematic treatment of both Universal and European practice. The standards applicable to freedom of religion are subjected to a detailed critique, and their development and implementation within the UN is distinguished from that within Strasbourg, in order to discern trends and obstacles to their advancement and to highlight the rationale for any apparent departures (...) between the two systems. This dual focus also demonstrates the acute need for the European Court to heed the warnings from various patterns of violation throughout the world illustrated by the Human Rights Committee and the Special Rapporteur on freedom of religion or belief. (shrink)

Gene Spitler has raised certain objections to my views on the biocentric outlook: (1) that a factual error is involved in the assertion that organisms pursue their own good, (2) that there is an inconsistency in the biocentric outlook, (3) that it is impossible for anyone to adopt that outlook, and (4) that the outlook entails unacceptable moral judgments, for example, that killing insects and wildfiowers is as morally reprehensible as killing humans. I reply to each of these points, showing (...) that the biocentric outlook on nature is not only a possible, but also a reasonable world view. (shrink)

Louis G. Lombardi’s arguments in support of the claim that humans have greater inherent worth than other living things provide a clear account of how it is possible to conceive of the relation between humans and nonhumans in this way. Upon examining his arguments, however, it seems that he does not succeed in establishing any reason to believe that humans actually do have greater inherent worth than animals and plants.

Early in World War I, Virginia Woolf wrote these words: ‘The future is dark, which is on the whole, the best thing the future can be […]’. It is tempting to assume that darkness simply hides the unknown and the threatening. It is more challenging to think of it as Woolf did: rich with possibility in even the most desperate times.We live in what many would readily describe as dark times. These times have brought (among much else) a once-in-a-century public (...) health crisis, the continued redemption of toxic white supremacy, declining trust in and support for public institutions, and growing evidence of impending climate devastation. ‘Dark Futures’ will consider some of the scenes of this devastation and mine them for insights into our predicaments and our prospects. (shrink)

This article introduces the preoccupations and themes that define the study and practice of black aesthetics. It presents a provisional sketch of a field that has long been recognized in other humanities disciplines, but that is only now gaining wide notice in academic philosophy. This sketch emphasizes the aspects of the field that invite specifically philosophic scrutiny, while touching lightly on specific artworks, critical literatures and historical developments. Among the topics that receive attention are the following: race, aesthetic politics, creolization, (...) nationalism, modernity, white supremacy and the blues. (shrink)

Views of the self may be plotted on a set of coordinates. On the axis that runs from fragmentation to unity, Rorty and Rorty's Freud champion the decentered self while Wallwork, Taylor, and Ricoeur argue for a sovereign, unified self. On the other axis, which runs from the disengaged, inward-turning self to the engaged and "sedimented" self, Wallwork, would be positioned near Rorty, defending self-creation against the narrative identity affirmed by Taylor and Ricoeur. Despite his skepticism concerning the (...) communitarian agenda of the narrativists, Flanagan grants that the self is social and relational--a position further explored by Oliver, Stendahl, Deutsch, and Mack in "Selves, People, and Persons". (shrink)

Working in the fragment of Martin-Löfs extensional type theory [12] which has products (but not sums) of dependent types, we consider two additional assumptions: firstly, that there are (strong) equality types; and secondly, that there is a type which is universal in the sense that terms of that type name all types, up to isomorphism. For such a type theory, we give a version of Russell's paradox showing that each type possesses a closed term and (hence) that all terms of (...) each type are provably equal. We consider the kind of category theoretic structure which corresponds to this kind of type theory and obtain a categorical version of the paradox. A special case of this result is the degeneracy of a locally cartesian closed category with a morphism which is generic in the sense that every other morphism in the category can be obtained from it via pullback. (shrink)

Although rationality is a central topic in contemporary analytic philosophy and in the social sciences, literary scholars generally assume that the notion has little or no relevance to literature. In this interdisciplinary study, Paisley Livingston promotes a dialogue between these different fields, arguing that recent theories of rationality can contribute directly to literary enquiry and that literary analysis can in turn enhance our understanding of human agency. The result is a work that helps bring literary studies into a more productive (...) relationship to the human sciences. Livingston provides a broad survey of the basic assumptions and questions associated with concepts of rationality in philosophical accounts of action, in decision theory, and in the theory of rational choice. He challenges prevalent irrationalist and mechanistic conceptions of human motivation and gives examples of the ways in which rationality is involved in the writing and reading of literary works, ranging from Icelandic sagas to Beckett, Dreiser, Kafka, Lem, Poe, and Zola. Livingston’s critical analyses show how theoretically oriented readings of literature can contribute to the formation of hypotheses about the dynamics of human action and interaction. (shrink)

In his article “Ethics and the Environment” William K. Frankena distinguishes eight types of ethical theories which could generate moral rules and/or judgments concerning how rational agents should act with regard to the natural environment. The eight types are differentiated by their conceptions of moral subjects or patients. Each has its own view of the class of entities with respect to which moral agents can have duties and responsibilities. The eight types may be briefly delineated as follows: 1. Only what (...) benefits or harms the agent himself is morally relevant to how anything else in existence should be treated. 2. Only humans are proper moral patients. How we ought to act with respect to the environment is determined ultimately by the effects of our actions on humans or on persons. 3. All conscious beings are proper moral patients. Conduct with regard to the environment is right if it alleviates the suffering or increases the pleasure of beings that can suffer or experience pleasure. 4. All living beings, conscious or not, are proper moral patients. Our moral concern should extend beyond humans to all animals and plants. 5. Everything in existence, whether taken distributively or collectively, is to be considered as that toward which we may have duties and responsibilities. 6. God is the only ultimate moral subject as far as human action is concerned. We owe duties only to God, and we should treat the natural world in such a way as to fulfill our duties to God. 7. Combinations of any two or more of the above. 8. Nature itself is a moral patient. We should either follow the ways of nature or let the ways of nature take their course without our intervention. (shrink)

This paper presents a dilemma for Matthew Kramer’s view, as defended in his _Liberalism with Excellence_. A central aim of that book is to critique existing liberal perfectionist theories, which he labels “edificatory,” and to defend a different such theory, which he calls “aspirational.” Edificatory perfectionism holds that governments ought to promote citizens’ well-being directly by inducing them to live lives that are more wholesome, cultivated, or autonomous. Aspirational perfectionism, meanwhile, holds that governments ought to promote the conditions under which (...) every citizen can be warranted in harboring a strong sense of self-respect, by promoting the occurrence of outstanding achievements within society. We first argue that Kramer’s two central arguments against edificatory perfectionism, which appeal to the value of freedom and to moral integrity, fail to establish the impermissibility of edificatory policies. His critique could be salvaged by holding that the ambit of legitimate government activity is limited to the provision and distribution of primary goods. However, we argue, second, that Kramer’s own aspirational perfectionism also runs afoul of this restriction, because his conception of warranted self-respect is not a primary good. Kramer is thus faced with a choice between upholding his objections to edificatory perfectionism and maintaining the coherence of his aspirational perfectionism. -/- . (shrink)

There is an odd duality in Cornel West's work. He is a generous thinker and voracious interlocutor, willing to learn from anyone on a sincere quest for insight. But he is also he is an unapologetic admirer of greatness, as stingy with ascriptions of genius as he is lavish with praise for the select few who qualify. "Making Niagara a Cataract" reflects on this duality. I try to explain what motivates West's commitment to the importance of greatness, and how these (...) motivations emerge from and shape his intellectual project. (shrink)

Transitive extensional well founded relations provide an intuitionistic notion of ordinals which admits transfinite induction. However these ordinals are not directed and their successor operation is poorly behaved, leading to problems of functoriality. We show how to make the successor monotone by introducing plumpness, which strengthens transitivity. This clarifies the traditional development of successors and unions, making it intuitionistic; even the (classical) proof of trichotomy is made simpler. The definition is, however, recursive, and, as their name suggests, the plump ordinals (...) grow very rapidly. Directedness must be defined hereditarily. It is orthogonal to the other four conditions, and the lower powerdomain construction is shown to be the universal way of imposing it. We treat ordinals as order-types, and develop a corresponding set theory similar to Osius' transitive set objects. This presents Mostowski's theorem as a reflection of categories, and set-theoretic union is a corollary of the adjoint functor theorem. Mostowski's theorem and the rank for some of the notions of ordinal are formulated and proved without the axiom of replacement, but this seems to be unavoidable for the plump rank. The comparison between sets and toposes is developed as far as the identification of replacement with completeness, and there are some suggestions for further work in this area. Each notion of set or ordinal defines a free algebra for one of the theories discussed by Joyal and Moerdijk, namely joins of a family of arities together with an operation s satisfying conditions such as x ≤ sx, monotonicity or s(x ∨ y) ≤ sx ∨ sy. Finally we discuss the fixed point theorem for a monotone endofunction s of a poset with least element and directed joins. This may be proved under each of a variety of additional hypotheses. We explain why it is unlikely that any notion of ordinal obeying the induction scheme for arbitrary predicates will prove the pure result. (shrink)