The purpose of this paper is to apply Crispin Wright’s criteria and various axes of objectivity to mathematics. I test the criteria and the objectivity of mathematics against each other. Along the way, various issues concerning general logic and epistemology are encountered.

The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...) established by the neo-logicist. (shrink)

Graham Priest's In Contradiction (Dordrecht: Martinus Nijhoff Publishers, 1987, chapter 3) contains an argument concerning the intuitive, or ‘naïve’ notion of (arithmetic) proof, or provability. He argues that the intuitively provable arithmetic sentences constitute a recursively enumerable set, which has a Gödel sentence which is itself intuitively provable. The incompleteness theorem does not apply, since the set of provable arithmetic sentences is not consistent. The purpose of this article is to sharpen Priest's argument, avoiding reference to informal notions, consensus, or (...) Church's thesis. We add Priest's dialetheic semantics to ordinary Peano arithmetic PA, to produce a recursively axiomatized formal system PA★ that contains its own truth predicate. Whether one is a dialetheist or not, PA★ is a legitimate, rigorously defined formal system, and one can explore its proof‐theoretic properties. The system is inconsistent (but presumably non‐trivial), and it proves its own Gödel sentence as well as its own soundness. Although this much is perhaps welcome to the dialetheist, it has some untoward consequences. There are purely arithmetic (indeed, Π0) sentences that are both provable and refutable in PA★. So if the dialetheist maintains that PA★ is sound, then he must hold that there are true contradictions in the most elementary language of arithmetic. Moreover, the thorough dialetheist must hold that there is a number g which both is and is not the code of a derivation of the indicated Gödel sentence of PA★. For the thorough dialetheist, it follows ordinary PA and even Robinson arithmetic are themselves inconsistent theories. I argue that this is a bitter pill for the dialetheist to swallow. (shrink)

I argue that Hobbes isn't really a materialist in the early 1640s (in, e.g., the Third Objections to Descartes's Meditations). That is, he doesn't assert that bodies are the only substances. However, he does think that bodies are the only substances we can think about using imagistic ideas.

The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.

In recent years, there has been a rapid growth in the use of autologous stem cell-based interventions to treat a wide range of medical conditions, including those for which there is limited evidence of safety and efficacy. One justification for this growth in the use of unproven interventions is that clinicians should be free to innovate, as long as consumers are adequately informed about risks and benefits. In this essay, we systematically refute the strong claim that consumer and clinician autonomy (...) provide sufficient justification for clinical innovation with autologous stem cells. While we do not deny the importance of consumer and clinician autonomy, we argue that equal consideration needs to be given... (shrink)

"The picture of Hume clinging timidly to a raft of custom and artifice, because, poor skeptic, he has no alternative, is wrong," writes John Stewart. "Hume was confident that by experience and reflection philosophers can achieve true principles." In this revisionary work Stewart surveys all of David Hume's major writings to reveal him as a liberal moral and political philosopher. Against the background of seventeenth-and eighteenth-century history and thought, Hume emerges as a proponent not of conservatism but of (...) reform. Stewart first presents the dilemma over morals in the modern natural-law school, then examines the new approach to moral and political philosophy adopted by Hume's precursors Shaftesbury, Mandeville, Hutcheson, and Butler. Illuminating Hume's explanation of the standards and rules that should govern private and public life, the author challenges interpretations of Hume's philosophy as conservative by demonstrating that he did not dismiss reason as a key factor determining right and wrong in moral and political contexts. Stewart goes on to show that Hume viewed private property, the market, contracts, and the rule of law as essential to genuine civilized society, and explores Hume's criticism of contemporary British beliefs concerning government, religion, commerce, international relations, and social structure. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Classically, the question of recognizing another subject is posed unilaterally, in terms of the observed behaviour of the other entity. Here, we propose an alternative, based on the emergent patterns of activity resulting from the interaction of both partners. We employ a minimalist device which forces the subjects to externalize their perceptual activity as trajectories which can be observed and recorded; the results show that subjects do identify the situation of perceptual crossing with their partner. The interpretation of the results (...) is guided by comparable evolutionary robotics simulations. There are two components to subjects’ recognition capacities: distinguishing mobile and fixed entities; and behaving so as to interact with their partner rather than with a mobile lure. The “Other” is characterized by the feature that there is sufficient regularity in the interactions to encourage the formation of anticipations; but sufficient indetermination that the actual behaviour is consistently surprising. Keywords: Recognition of other; perceptual crossing; evolutionary robotics. (shrink)

‘The Gift’ is the English title of a small book first published in French in 1925 by sociologist Marcel Mauss, which catalyzed an ongoing debate linked to a wide range of scholarship. Mauss’s gift theory included the Māori example of the ‘hau of the gift’ which Mauss explained as a spiritual force, seeking to return to its original owner or place of origin. This article brings a critical Māori perspective to Mauss’ notion of the hau of the gift, in an (...) indigenous philosophical response to Eurocentric social science that combines critical discourse analysis with Kaupapa Māori theory and principles of research. The paper introduces Mauss’ arguments about gifting, and the role of hau in those arguments, before turning to a close examination of the concept of ‘hau’ as presented in the original Māori letters, the primary data used by Elsdon Best to write his anthropological articles, from which Mauss developed his ideas about hau. These letters, which sparked the whole debate, are material artefacts of the cross-cultural educational relationship between Tamati Ranapiri as teacher, and Elsdon Best as student. Common-sense Māori readings of Ranapiri find no mystery in what he wrote about hau, but reinforce the significance of his correspondence, from the perspective of Kaupapa Māori versions of the history of Māori education. (shrink)

The presumption of innocence has often been understood as a doctrine that can be explained primarily by instrumental concerns relating to accurate fact-finding in the criminal trial and that has few if any implications outside the trial itself. In this paper, I argue, in contrast, that in a liberal legal order everyone has a right to be presumed innocent simply in virtue of being a person. Every person has a right not to be subjected to criminal punishment unless and until (...) he or she has done something that is criminally wrong. Since disagreements about allegations of criminal wrongdoing are inevitable, the liberal legal order requires a process for determining whether wrongdoing has occurred. In order to preserve the right not to be punished without wrongdoing, the accused person must be presumed innocent throughout this process. The presumption of innocence is therefore as much a basic human right as, for example, the right to bodily integrity or the right to freedom of expression. Specifications of and limitations on the right should therefore be justified not primarily in terms of their instrumental effectiveness in fact-finding or crime control but in terms of the role of the criminal process in a liberal legal order. I consider some implications of this view of the presumption of innocence for the pre-trial process and for substantive criminal law. I argue that the presumption of innocence, understood as a basic human right, should condition the entire pre-trial process; it has, however, minimal implications for the definition of offences. (shrink)

What is the point of developing an epistemology for a topic—for example, morality? When is it appropriate to develop the epistemology of a topic? For many topics—for example, the topic of socks—we see no need to develop a special epistemology. Under what conditions, then, does a topic deserve its own epistemology? I seek to answer these questions in this article. I provide a criterion for deciding when we are warranted in developing an epistemological theory for a topic. I briefly apply (...) this criterion to moral epistemology and argue that some approaches to moral epistemology should be abandoned. I also argue that we can develop an epistemology for a topic without committing ourselves to a specific substantive theory of justification, such as reliabilism or coherentism, if we work within a suitably neutral framework. (shrink)

Augustine’s homiletical exhortations display a strong eschatological emphasis in his approach to cultivating rightly ordered emotions. According to critics such as Hannah Arendt, Martha Nussbaum, and Thomas Dixon, this orientation risks denigrating the earthly life and its attendant emotions, while also promoting a crippling resignation to suffering. This article discusses Augustine’s eschatological frame for ordering the emotions through a focused treatment of en. Ps. 36 in conversation with Nussbaum’s critique in particular. In en. Ps. 36.1, Augustine deploys eschatological rhetoric to (...) discourage the believer’s envious response to a prosperous, profligate neighbor. This entails disposing the believer in weariness toward life’s temporal disparities and exhorting the believer to work in love to alleviate suffering with a view to heavenly flourishing. In this sense, a disposition of “world-weariness” works in concert with eschatological hope to rightly order both emotion and action in this present world. (shrink)

The most complete collection of essays on Hegel's Phenomenology of Spirit available in any language, with essays by distinguished international Hegel scholars.

The aim of this paper is to examine the current state of development of Mäori science curriculum policy, and the roles that various discourses have played in shaping these developments. These discussions provide a background for suggestions about a possible future direction, and the presentation of a new concept for Mäori science education.

Open peer commentary on the target article “How and Why the Brain Lays the Foundations for a Conscious Self” by Martin V. Butz. Excerpt: The article opens with the statement “perceived reality is a complex construct”; clearly, no constructivist could disagree with that! However, in the very next sentence Butz simply assumes, without argument, that we are dealing with an “inner” construct; he goes on, throughout the article, to speak of “inner realities.” I would like to explain (a) why I (...) think this is a mistake; and (b) why it is a serious mistake ... especially for constructivists. (shrink)

Consumer psychologists now have a wide array of tools for studying the behavior of individuals in the marketplace. Attitudes, opinions, and activities are monitored on a regular basis by a large number of research organizations. Within the past half dozen years it has even become possible to merge all of those data at the level of the individual household. The result is a powerful tool for the analysis of consumer behavior. Such powerful tools for observation and analysis are the dream (...) of many social scientists and they certainly provide important and useful information for scholars, commercial organizations, and government regulators. Yet, for all the power offered by these research tools and data sources consumer psychologists still find the answer to the "why" question elusive. 2012 APA, all rights reserved). (shrink)

In recent years interest in the thought of Kierkegaard has grown dramatically, and with it the body of secondary literature has expanded so quickly that it has become impossible for even the most conscientious scholar to keep pace. The problem of the explosion of secondary literature is made more acute by the fact that much of what is written about Kierkegaard appears in languages that most Kierkegaard scholars do not know. Kierkegaard has become a global phenomenon, and new research traditions (...) have emerged in different languages, countries, and regions. The present volume is dedicated to trying to help to resolve these two problems in Kierkegaard studies. Its purpose is, first, to provide book reviews of some of the leading monographic studies in the Kierkegaard secondary literature so as to assist the community of scholars to become familiar with the works that they have not read for themselves. The aim is thus to offer students and scholars of Kierkegaard a comprehensive survey of works that have played a more or less significant role in the research. Second, the present volume also tries to make accessible many works in the Kierkegaard secondary literature that are written in different languages and thus to give a glimpse into various and lesser-known research traditions. The six tomes of the present volume present reviews of works written in Catalan, Chinese, Czech, Danish, Dutch, English, Finnish, French, Galician, German, Greek, Hebrew, Hungarian, Italian, Japanese, Norwegian, Polish, Portuguese, Romanian, Russian, Slovak, Spanish, and Swedish. (shrink)