We consider intuitionistic number theory with recursive infinitary rules . Any primitive recursive binary relation for which transfinite induction schema is provable is in fact well founded. Its ordinal is less than ε 0 if the transfinite induction schema is intuitionistically provable in elementary number theory. These results are provable intuitionistically. In fact, it suffices to consider transfinite induction with respect to one particular number-theoretic property.

We consider formal theories synonymous with various free categories . Their Lindenbaum algebras may be described as the lattices of subobjects of a terminator. These theories have intuitionistic logic. We show that the Lindenbaum algebras of second order and higher order arithmetic , and set theory are not isomorphic to the Lindenbaum algebras of first order theories such as arithmetic . We also show that there are only five kernels of representations of the free Heyting algebra on one generator in (...) these Lindenbaum algebras. (shrink)

: The Newman programs established at secular colleges and universities provided an opportunity for intellectual, spiritual, and social growth among the Catholic student population. As a young physician and junior medical faculty member, André Hellegers took part in the early organization and ongoing work of Carroll House, the Newman Center at the Johns Hopkins Medical Institutions. Hellegers's experience at Carroll House enabled him to develop a clear blueprint of an academic center of excellence for the scientific, theological, and philosophical (...) exploration of the many problems that he had seen and foresaw in medicine. That center would become Georgetown's Kennedy Institute of Ethics. (shrink)

European Journal of Philosophy, EarlyView.

In this new book, David Harvey seeks to determine what is meant by the term in its different contexts and to identify how accurate and useful it is as a description of contemporary experience.

Is 'education' a thick epistemic concept? The answer depends, of course, on the viability of the 'thick/thin' distinction, as well as the degree to which education is an epistemic concept at all. I will concentrate mainly on the latter, and will argue that epistemological matters are central to education and our philosophical thinking about it; and that, insofar, education is indeed rightly thought of as an epistemic concept. In laying out education's epistemological dimensions, I hope to clarify the degree to (...) which it makes sense to regard the concept as 'thick'. I also discuss the relationship between philosophy of education and virtue epistemology and the sense in which being educated might itself be thought to be an epistemic virtue. Finally, I urge virtue epistemologists in particular and epistemologists generally to turn their attention to questions of education, to further both the philosophy of education and epistemology itself. (shrink)

A fascinating account of exemplarity in the context of deconstruction.

Without trust there is no credible human health research (HHR). This article accepts this truism and addresses a crucial question that arises: how can trust continually be promoted in an ever-changing and uncertain HHR environment? The article analyses long-standing mechanisms that are designed to elicit trust—such as consent, anonymization, and transparency—and argues that these are best understood as trust represented by proxies of trustworthiness, i.e., regulatory attempts to convey the trustworthiness of the HHR system and/or its actors. Often, such proxies (...) are assumed to operate as markers that trust exists or, at least, has not been lost. But, since trust can neither be “built” nor “secured,” this is a precarious assumption. Worryingly, there is no existing theoretical account of how to understand and evaluate these proxies of trustworthiness as part of a trusted HHR ecosystem. To remedy this, the paper argues for a radical reimagining of trust and trustworthiness as performative acts that ought to be understood in relation to each other and by reference to the common values at stake. It is shown that proxies of trustworthiness are the operational tools used to perform trustworthiness. It advocates for a values-based approach to understanding the relationship between trust and trustworthiness. This establishes a strong basis for an evaluative framework for proxies of trustworthiness, i.e., to determine how to perform trustworthiness well. Five common proxies in HHR are scrutinized from a values perspective. The contribution is to provide a far-reaching normative and practical framework by which existing and future proxies of trustworthiness can be identified, assessed, maintained, or replaced in rapidly changing HHR regulatory ecosystems where trust itself is crucial to the success of the entire HHR enterprise. (shrink)

‘Argument’ has multiple meanings and referents in contemporary argumentation theory. Theorists are well aware of this but often fail to acknowledge it in their theories. In what follows, I distinguish several senses of ‘argument’ and argue that some highly visible theories are largely correct about some senses of the term but not others. In doing so, I hope to show that apparent theoretical rivals are better seen as collaborators or partners, rather than rivals, in the multi-disciplinary effort to understand ‘argument,’ (...) arguments, and argumentation in all their varieties. I argue as well for a pluralistic approach to argument evaluation and argumentative norms, since arguments and argumentation can be legitimately evaluated along several dimensions, but urge that epistemic norms enjoy conceptual priority. (shrink)

According to relationism, for Alice to believe that some rabbits can speak is for Alice to stand in a relation to a further entity, some rabbits can speak. But what could this further entity possibly be? Higher-order metaphysics seems to offer a simple, natural answer. On this view (roughly put), expressions in different syntactic categories (for instance: names, predicates, sentences) in general denote entities in correspondingly different ontological categories. Alice's belief can thus be understood to relate her to a sui (...) generis entity denoted by "some rabbits can speak", belonging to a different ontological category than Alice herself. This straightforward account of the attitudes has historically been deemed so attractive that it was seen as providing an important motivation for higher-order metaphysics itself (Prior [1971]). But I argue that it is not as straightforward as it might seem, and in fact that propositional attitudes present a foundational challenge for higher-order metaphysics. (shrink)

Philosophy in the Seraglio -- The wisdom of the East -- The New World and the noble savage -- The last frontiers -- The varieties of man -- An indelible stain -- The apotheosis of Europe.

Maimonides requires the multitude to observe many ceremonial commandments, while Spinoza makes no such demand. This chapter focuses on some of the main points of agreement between Maimonides and Spinoza on true religion, the religion of reason, or philosophic religion. True religion includes also piety, that is, moral conduct, which follows from the rational life. The piety of the philosopher and the non‐philosopher both consist in doing good to others. Maimonides’ approach to true religion adumbrates Spinoza's. Spinoza's concept of amor (...) Dei intellectualis echoes Maimonides’ concept of the passionate intellectual love of God. Spinoza's concept of piety is adumbrated in Maimonides. The Maimonidean thrust of Spinoza's concept of true religion is evident in his discussion of “the divine Law” or, more precisely, “the natural divine Law” and the summum bonum in TTP4. In Maimonides’ language, true religion is based on the intelligibilia and popular religion on generally accepted opinions. (shrink)

The works of the early Greek philosophers are not only a fundamental source for understanding archaic Greek culture and the whole of ancient philosophy, but also a perennially fresh resource that has stimulated Western thought until the present day. This nine-volume edition presents all the major fragments from the sixth to the fourth centuries BC.

This is a book that opens up an area of contemporary experience that rarely sees the light of day. I believe readers from all walks of life and different educational backgrounds will be as excited to read about these experiences as my subjects were delighted to talk about them. One measure of the public's interest in relevant oral history is the current popularity of Brandon Stanton's Humans of New York, Stories, found in museums and bookstores throughout the city. And the (...) fact that the recent Nobel went to Svetlana Alexievich, a writer whose work is grounded in oral history, will expand the market for such books, and is a sign that more and more readers are interested in what ordinary people, whose voices are usually muted, have to say about crucial aspects of modern life. The book's interdisciplinary appeal will attract faculty and students in cultural studies, English, sociology, and other departments and programs interested in aesthetics. The book will have considerable crossover appeal to a wide general audience that especially includes women (most of my subjects are women) and women of color (a third of my subjects are members of a minority). The book is, in fact, eminently "Oprah-ble" because of its undoubted appeal to her vast audience. The challenge for an academic press, of course, will be to gain this audience's attention, a task to which I will be more than happy to devote substantial time and effort. (shrink)

This volume is a tribute by his peers, and by younger scholars of the next generation, to Harvey M. Friedman, perhaps the most profound foundationalist since Kurt Godel. Friedman's researches, beginning precociously in his mid-teens, have fundamentally shaped our contemporary understanding of set theory, recursion theory, model theory, proof theory and metamathematics. His achievements in concept formation and theory formulation have also renewed the standard set by Godel and Alfred Tarski for the general intellectual interest and importance of technical (...) work in foundations. Friedman pioneered the now well-established and flourishing field of Reverse Mathematics, whose aim is to calibrate the intrinsic logico-mathematical consistency-strength of all the important theorems of mathematics. He has relentlessly pursued the full extent of the incompleteness phenomena into which Godel provided the first revealing glimpse. The Godel--Friedman program, as it is now deservingly called, seeks to find simple, natural and elegant mathematical statements of a combinatorial nature, that can be proved to be independent of set theory even when extended by powerful large-cardinal existence axioms. (shrink)

'..... And then there were none', is a collaborative book by four New Zealand photographers and a writer. Developed over the last two years with regular meetings indulgent in wine and homemade cheese as excuses for friendship and banter, '..... and then there were none' grew from conversations and arguments about mortality, our technologically mired existence and the degradation of the environment. Collaboration in a real sense, Harvey Benge, Jon Carapiet, Haru Sameshima, Stu Sontier, breaks out of conventional authorship (...) based story-telling, to play out their anxieties and doubts about the world they see, as one visual voice. The author Lloyd Jones adds his contribution of trenchant narrative texts of two scenes of slaughter and one execution. All addicted to travels, the project triggered its own version of flygskam [the feeling of climate guilt associated with airline travel] or the collaborators, conflicted by the international travel that made many of the photographs and the writing possible and tainted by knowing the greater price to be paid. Narratives included from such travels are drenched in sordid human histories that recall the myriad pathways that have led us to now, and to what comes next. The nod to mortality echoing through the book is rendered stark by the recent death of Benge, adding a sense of urgency to the title of the book - not just for the remaining collaborators, but for us all."--Publisher. (shrink)

Ostensibly a discussion about love, the debate in the Phaedrus also encompasses the art of rhetoric and how it should be practised. This new edition contains an introductory essay outlining the argument of the dialogue as a whole and Plato's arguments about rhetoric and eros in particular. The Introduction also considers Plato's style and offers an account of the reception of the dialogue from its composition to the twentieth century. A new Greek text of the dialogue is accompanied by a (...) select textual apparatus. The greater part of the book consists of a Commentary, which elucidates the text and makes clear how Plato achieves his philosophical and literary objectives. Primarily intended for advanced undergraduates and graduate students of ancient Greek literature and philosophy, it will also benefit scholars who want an up-to-date account of how to understand the text, argument, style and background of the work. (shrink)

The first full-length critical introduction in English to Nietzsche's lifelong obsession with Wagner, and why it matters for understanding Nietzsche's philosophy as a whole.

Skepticism, Relativism, and Religious Knowledge shows where responses to skepticism and relativism by Karl Barth and Reformed epistemology have led to impasses, and reconstructs their insights in a more robust response that does not depend on making excessive claims about our epistemic capacities. This response is based on a more nuanced conception of the relationship between trust, doubt, faith, and reason, and a Kierkegaardian perspective on religious knowledge that stresses the role of the will and the intellectual and theological virtues.

Thought-provoking explorations of the relationship between psychoanalysis and Judaism.

‘Argument’ has multiple meanings and referents in contemporary argumentation theory. Theorists are well aware of this but often fail to acknowledge it in their theories. In what follows, I distinguish several senses of ‘argument’ and argue that some highly visible theories are largely correct about some senses of the term but not others. In doing so, I hope to show that apparent theoretical rivals are better seen as collaborators or partners, rather than rivals, in the multi-disciplinary effort to understand ‘argument,’ (...) arguments, and argumentation in all their varieties. I argue as well for a pluralistic approach to argument evaluation and argumentative norms, since arguments and argumentation can be legitimately evaluated along several dimensions, but urge that epistemic norms enjoy conceptual priority. (shrink)

(1) Is the rational person _eo ipso_ intellectually virtuous? (2) Is the intellectually virtuous person _eo ipso_ rational? In what follows I answer both questions in the negative.

Some people commonly know a proposition just in case they all know it, they all know that they all know it, they all know that they all know that they all know it, and so on. They commonly believe a proposition just in case they all believe it, they all believe that they all believe it, they all believe that they all believe that they all believe it, and so on. A long tradition in economic theory, theoretical computer science, linguistics (...) and philosophy has held that people have some approximation of common knowledge or common belief in a range of circumstances, for example, when they are looking at an object together, or when they have just discussed something explicitly in conversation. In this paper, I argue that people do not have any approximation of common knowledge or common belief in these circumstances. The argument suggests that people never have any approximation of common knowledge or common belief. (shrink)

(1) Is the rational person _eo ipso_ intellectually virtuous? (2) Is the intellectually virtuous person _eo ipso_ rational? In what follows I answer both questions in the negative.

André Padoux was among a small number of scholars, including Harvey P. Alper and Lilian Silburn, who introduced the study of Tantra to Western scholars. He authored such important works as Vāc: The Concept of the Word in Selected Hindu Tantras and Tantric Mantras: Studies on Mantrasastra. Padoux's 2017 Hindu Tantric World: An Overview is a significant revision of his 2010 Comprendre le tantrisme: Les sources hindoues.Padoux seeks to discover what constitutes Tantric Hinduism by investigating its essential notions (...) and its numberless practices. These are bound together, "since there is no practice without a theory that gives it meaning and explains it". He discusses the Tantric body, as it "is a... (shrink)

The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to do (...) by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

Current work in language models (LMs) helps us speed up or even skip thinking by accelerating and automating cognitive work. But can LMs help us with critical thinking -- thinking in deeper, more reflective ways which challenge assumptions, clarify ideas, and engineer new concepts? We treat philosophy as a case study in critical thinking, and interview 21 professional philosophers about how they engage in critical thinking and on their experiences with LMs. We find that philosophers do not find LMs to (...) be useful because they lack a sense of selfhood (memory, beliefs, consistency) and initiative (curiosity, proactivity). We propose the selfhood-initiative model for critical thinking tools to characterize this gap. Using the model, we formulate three roles LMs could play as critical thinking tools: the Interlocutor, the Monitor, and the Respondent. We hope that our work inspires LM researchers to further develop LMs as critical thinking tools and philosophers and other 'critical thinkers' to imagine intellectually substantive uses of LMs. (shrink)

Robert Aumann presents his Agreement Theorem as the key conditional: “if two people have the same priors and their posteriors for an event A are common knowledge, then these posteriors are equal” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s proof but are not explicit in the key conditional: (1) that agents commonly know, of some prior μ, that it is the common prior; (2) that agents commonly know that each of them updates (...) on the prior by conditionalization; (3) that agents commonly know that if an agent knows a proposition, she knows that she knows that proposition (the “K K” principle); (4) that agents commonly know that they each update only on true propositions. It is shown that natural weakenings of any one of these strong assumptions can lead to countermodels to Aumann’s key conditional. Examples are given in which agents who have a common prior and commonly know what probability they each assign to a proposition nevertheless assign that proposition unequal probabilities. To alter Aumann’s famous slogan: people can “agree to disagree”, even if they share a common prior. The epistemological significance of these examples is presented in terms of their role in a defense of the Uniqueness Thesis: If an agent whose total evidence is E is fully rational in taking doxastic attitude D to P, then necessarily, any subject with total evidence E who takes a different attitude to P is less than fully rational. (shrink)