This is the first critical study of The Logic of Sense, Gilles Deleuze's most important work on language and ethics, as well as the main source of his vital philosophy of the event.James Williams explains the originality of Deleuze's work with careful definitions of all his innovative terms and a detailed description of the complex structure he constructs. This reading makes connections to his ground-breaking work on literature, to his critical but also progressive relation to the sciences, and to (...) his controversial denial of the priority of standard logics, human values and 'meaning' in thinking.This book will open new debates and develop current ones around Deleuze's work in philosophy, politics, literature, linguistics, cultural studies and sociology. (shrink)

A revised, expanded and fully up-to-date critical introduction to Deleuze's most important work of philosophyBy critically analysing Deleuze's methods, principles and arguments, James Williams helps readers to engage with the revolutionary core of Deleuze's philosophy and take up positions for or against its most innovative and controversial ideas.

Discusses the work of G.I. Gurdjieff and his establishment of the Institute for the Harmonious Development of man, and examines the contributions of Gurdjieff's two major disciples, P.D. Ouspensky and A.R. Orage.

This book presents a comprehensive, accessible survey of Western philosophy of music from Pythagoras to the present. Its narrative traces themes and schools through history, in a sequence of five chapters that survey the ancient, medieval, early modern, modern and contemporary periods. Its wide-ranging coverage includes medieval Islamic thinkers, Continental and analytic thinkers, and neglected female thinkers such as Vernon Lee (Violet Paget). All aspects of the philosophy of music are discussed, including music and the cosmos, music's value, music's relation (...) to the other arts, the problem of opera, the origins of musical genius, music's emotional impact, the moral effects of music, the ontology of musical works, and the relevance of music's historical context. The volume will be valuable for students and scholars in philosophy and musicology, and all who are interested in the ways in which philosophers throughout history have thought about music. (shrink)

Amie Thomasson’s work provides numerous ways to rethink and improve our approach to metaphysics. This chapter is my attempt to begin to sketch why I still think the easy approach leaves room for substantive metaphysical work, and why I do not think that metaphysics need rely on any ‘epistemically metaphysical’ knowledge. After distinguishing two possible forms of deflationism, I argue that the easy ontologist needs to accept (implicitly or explicitly) that there are worldly constraints on what sorts of entities could (...) exist, and could co-exist. I argue this leaves room for a substantive role for metaphysics if (following the work of E.J. Lowe) we take metaphysics to be concerned with the possible ways that reality could be. I explain how this conception does not need to appeal to any ‘epistemically metaphysical’ knowledge, and need only make use of conceptual and/or empirical means to arrive at views on what could exist (and co-exist). Thus, the answer I propose to the question posed in the title, at least in my view, is no-one. Or, at least, no-one should be afraid of conceptual analysis. Not even metaphysicians. (shrink)

Animal behaviour and welfare research are part of a wider endeavour to optimize the health and wellbeing of humans, animals and ecosystems. As such, it is part of the One Health research agenda. This article applies ethical principles described by the One Health High Level Expert Panel to animal behaviour and welfare research. These principles entail that animal behaviour and welfare research should be valued equitably alongside other research in transdisciplinary and multisectoral collaboration. It should include and promote a multiplicity (...) of marginalized voices, including those of animals, and it should apply and describe a harmonious balance between human—animal-environment interactions. Lastly, it should describe how humans need to change behaviour, adopt sustainable solutions and recognize the importance of animal welfare and the integrity of the whole ecosystem. (shrink)

Organ donation after the circulatory determination of death requires the permanent cessation of circulation while organ donation after the brain determination of death requires the irreversible cessation of brain functions. The unified brain-based determination of death connects the brain and circulatory death criteria for circulatory death determination in organ donation as follows: permanent cessation of systemic circulation causes permanent cessation of brain circulation which causes permanent cessation of brain perfusion which causes permanent cessation of brain function. The relevant circulation that (...) must cease in circulatory death determination is that to the brain. Eliminating brain circulation from the donor ECMO organ perfusion circuit in thoracoabdominal NRP protocols satisfies the unified brain-based determination of death but only if the complete cessation of brain circulation can be proved. Despite its medical and physiologic rationale, the unified brain-based determination of death remains inconsistent with the Uniform Determination of Death Act. (shrink)

While substantial progress has been made in the field known as artificial consciousness, at the present time there is no generally accepted phenomenally conscious machine, nor even a clear route to how one might be produced should we decide to try. Here, we take the position that, from our computer science perspective, a major reason for this is a computational explanatory gap: our inability to understand/explain the implementation of high-level cognitive algorithms in terms of neurocomputational processing. We explain how addressing (...) the computational explanatory gap can identify computational correlates of consciousness. We suggest that bridging this gap is not only critical to further progress in the area of machine consciousness, but would also inform the search for neurobiological correlates of consciousness and would, with high probability, contribute to demystifying the “hard problem” of understanding the mind–brain relationship. We compile a listing of previously proposed computational correlates of consciousness and, based on the results of recent computational modeling, suggest that the gating mechanisms associated with top-down cognitive control of working memory should be added to this list. We conclude that developing neurocognitive architectures that contribute to bridging the computational explanatory gap provides a credible and achievable roadmap to understanding the ultimate prospects for a conscious machine, and to a better understanding of the mind–brain problem in general. (shrink)

This chapter provides an account of sexual ontology, grounded in and responsive to Irigaray’s philosophy, that focuses on the question of possibility. I first consider possibility in terms of the ontological negativity of sexuate beings, whereby one sex or sexuate morphology does not exhaust all that that kind of being is or can be. Second, I consider how sexual difference, as a relational structure of being, engenders possibilities for sexuate beings to develop as irreducible individuals. With particular focus on the (...) human being and the looming question of transhumanist technologies, I argue that these principles develop a sexual ontology that recognizes determinate limits between sexes while allowing for varied and creative expressions of sexuate life. (shrink)

Many people attempt to give meaning to their lives by pursuing projects that they believe will bear fruit after they have died. Knowing that their death will preclude them from protecting or promoting such projects people who draw meaning from them will often attempt to secure their continuance by securing promises from others to serve as their caretakers after they die. But those who rely on such are faced with a problem: None of the four major accounts that have been (...) developed to explain directed promissory obligation (the Authority View, the Trust View, the Assurance View, and the Reliance View) support the view that we are obligated to keep our promises to persons who are now dead. But I will provide hope for those who wish to use such promises to protect the meaning with which they have endowed their lives. I will argue that while we cannot wrong a person who is now dead by breaking a promise made to her during her life, we could wrong the living by so doing. We thus (might) have reason to keep the promises that we made to those who are now dead. (shrink)

An important question facing contemporary philosophy of science is whether the natural sciences in terms of their historical records exhibit distinguishing developmental patterns or structures. At least two philosophical stances are possible in answering this question. The first pertains to the plurality of the individual sciences. From this stance, the various sciences are analyzed individually and compared with one another in order to derive potential commonalities, if any, among them. The second stance involves a general philosophy of science in which (...) a thorough theory of the natural sciences is developed. The latter stance strives to account for more than possible commonalities among the sciences but also to provide a broad-spectrum philosophical framework to account for, or to explicate, the nature of science itself and its progress. In this paper, the second stance is taken in which an evolutionary philosophy of science is proposed. To that end, Thomas Kuhn’s evolutionary philosophy of science is initially discussed and critiqued. An evolutionary philosophy of science is then proposed based on a revision of Kuhn’s evolutionary philosophy of science in terms of George Gaylord Simpson’s various tempos and modes for biological evolution. Next, two historical case studies from the biological sciences are reconstructed to illustrate the robustness of the proposed evolutionary philosophy of science for explicating the progress of the natural sciences. A concluding section discusses the proposed evolutionary philosophy of science with respect to providing a broad-spectrum framework or general philosophy of science for understanding the nature and progress of the natural sciences. (shrink)

This article develops an interpretation and defense of Husserl’s account of the omnitemporality of idealities. I first examine why Husserl rejects the atemporality and temporal individuation of idealities on phenomenological grounds, specifically that these attributions prove countersensical in how they relate idealities to consciousness. As an alternative to these conceptions, I develop a two-sided interpretation of omnitemporality expressed in modal terms of actuality and possibility, the actual referring to appearances in time and the possible, to reactivation at any time. In (...) defense of this interpretation of omnitemporality, I consider influential criticisms against Husserl’s account of idealities as they concern time, particularly whether the historical genesis of idealities compromises their omnitemporality by binding them to time. Ultimately, I argue that the transcendental historicity of idealities, despite being relevant to the question of validity and access, proves indifferent to their omnitemporality. (shrink)

We are immersed within an odorous sea of chemical currents that we parse into individual odors with complex structures. Odors have been posited as determined by the structural relation between the molecules that compose the chemical compounds and their interactions with the receptor site. But, naturally occurring smells are parsed from gaseous odor plumes. To give a comprehensive account of the nature of odors the chemosciences must account for these large distributed entities as well. We offer a focused review of (...) what is known about the perception of odor plumes for olfactory navigation and tracking, which we then connect to what is known about the role odorants play as properties of the plume in determining odor identity with respect to odor quality. We end by motivating our central claim that more research needs to be conducted on the role that odorants play within the odor plume in determining odor identity. (shrink)

The Gifford Lectures were established in 1885 at the universities of St Andrews, Glasgow, Aberdeen and Edinburgh to promote the discussion of 'Natural Theology in the widest sense of the term - in other words, the knowledge of God', and some of the world's most influential thinkers have delivered them. The 1901–2 lectures given in Edinburgh by American philosopher William James are considered by many to be the greatest in the series. The lectures were published in book form in (...) 1902 and have been reprinted many times. James, who was educated in the United States and Europe, and spent much of his career teaching philosophy at Harvard, was very influential in the development of modern psychology, and in these twenty lectures he explores the personal experience of religion. Some of the topics include religion and neurology, 'the sick soul', saintliness, and mysticism. (shrink)

In this chapter I argue that writers on metaphor have misunderstood Aristotle on metaphor. Aristotle is not an elitist about metaphor and does not consider metaphors to be merely ornamental. Rather, Aristotle believes that metaphors are ubiquitous and believes that people can express themselves in a clearer and more attractive way through the use of metaphors and that people learn and understand things better through metaphor. He also distinguishes between the use of metaphor and the coinage of metaphor, and believes (...) that the ability to coin marvelous new metaphors is a form of literary genius, and he provided an entirely natural origin of metaphor coinage. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

A fresh explication of the Thomist justification of self-defense casts off the hobbles of the principle of double effects to find a more secure footing in the historicaldevelopment of subjective natural rights by medieval jurists, and a straight-forward application to the latent threat of death in childbirth posed by non-consensual pregnancy. By articulating the implicit Thomistic right to defensive abortion in terms of conditional rights bestowed in Creation as correlative to particular natural law duties, justly proportionate limits to defensive abortion (...) are identified, and balanced against the forfeited or reserved natural rights variously imputed to conceptus and embryo in non-consensual pregnancies. Subsequently, the varieties of involuntary consent are examined from a Thomist perspective with a view to their relevance in justifying recourse to a rehabilitated practice of defensive abortion when free and full consent to impregnation and childbirth is absent. (shrink)

This paper interprets the influential colony management simulator ‘Dwarf Fortress’ existentially, in terms of finitude, absurdity, and narrative. It applies Aarseth/Möring’s proposed method of game interpretation, adopting their definition of ‘cybermedia’ as a generalized game ontology, then providing a specialized ontology of ‘Dwarf Fortress’ which describes its genre and salient gameplay features, incorporating Ian Bogost’s concept of ‘procedural rhetoric’. It then gives an existentialist interpretation of ‘Dwarf Fortress’ which centres on ‘finitude’, ‘absurdity’, and ‘narrative’, showing that ‘Dwarf Fortress’ is a (...) game about the existential tensions involved in being human. We live knowing our lives and civilizations are finite, that there are radical limits on what we can know and do. There is no meaning inherent in the world, or in history, so it is up to us to create our own, and one of our most powerful ways of doing this is narrative. (shrink)

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

This article critically analyzes Rawls’s attitude toward envy. In A Theory of Justice, Rawls is predominantly concerned with the threat that class envy poses to political stability. Yet he also briefly discusses the kind of envy that individuals experience toward their social peers, which he calls particular envy, and which I refer to as peer envy. He quickly concludes, however, that particular envy would not present a serious risk to the stability of his just society. In this article, I contest (...) this claim by arguing that the principles that structure Rawls’s ideal society are likely to exacerbate particular envy to a politically risky extent. Section 1 reconstructs his account of envy, giving special attention to his belief that competition kindles envy between peers. Section 2 then examines the way in which Rawls often endorses rivalry within the body politic. I argue that the society governed by justice as fairness is, on account of this rivalry, likely to generate a politically problematic degree of particular envy. In Section 3, I invoke ancient Greece as an example of a society that was, as a result of its intense competitiveness, often imperiled by dangerously elevated levels of peer envy. I then survey the key institutional mechanisms by which the ancient Greeks sought to manage this hazardous emotion. It turns out, however, that most of these mechanisms would be unavailable to Rawls insofar as they starkly contravene his principles of justice. I conclude that if Rawlsians wish to establish a society that fosters rivalry, they would do well to reflect on the means by which peer envy can be effectively harnessed. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

One of the most important topics that Thomas Aquinas discusses in his extensive corpus is the love of friendship, which is a unique form of love aimed at persons. Yet Aquinas's teachings on this are perplexing, for he claims that this love always produces union between lover and beloved, and that it is always a mutual love. This implies that one's love depends on reciprocation from the beloved, which seems implausible given the possibility of phenomena such as unrequited love. A (...) common interpretation of Aquinas's account of the love of friendship maintains that it is enough that one desires union and mutuality for such love to obtain even if such desires remain unrealized, but in this paper I reject this reading and argue that achieving union and mutuality is essential to this form of love. This novel interpretation ultimately reveals that the love of friendship is an intrinsically interpersonal act. (shrink)

J. L. Schellenberg's Philosophy of Religion argues for a specific brand of sceptical religion that takes ‘Ultimism’ – the proposition that there is a metaphysically, axiologically, and soteriologically ultimate reality – to be the object to which the sceptical religionist should assent. In this article I shall argue that Ietsism – the proposition that there is merely something transcendental worth committing ourselves to religiously – is a preferable object of assent. This is for two primary reasons. First, Ietsism is far (...) more modest than Ultimism; Ietsism, in fact, is open to the truth of Ultimism, while the converse does not hold. Second, Ietsism can fulfil the same criteria that compel Schellenberg to argue for Ultimism. (shrink)

Beginning right at the start of the recently published volume II of Donner le temps, at its ‘bord’ or ‘boarding’ upon or out of a calmy oceanic surface, this essay examines the functions and movements of distinct surfaces in between Heidegger and Derrida. Confronting thus the tradition of the ‘Grund’, ‘Abgrund’, ‘Urgrund’, ‘Ungrund’, with the khôra-like surface of archi-writing and dissemination, the essay proposes an investigation of the philosophical and writerly space of Derrida/Heidegger not through their marks and letters, but (...) instead through the different surfaces of inscription and – simultaneous – effacement as the ‘proper places’ of thought and experience, of Destruktion and deconstruction. (shrink)

Newton's bucket, Einstein's elevator, Schrödinger's cat – these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking? In this revised and updated new edition of his classic text _The Laboratory of the Mind_, James Robert Brown continues to (...) defend apriorism in the physical world. This edition features two new chapters, one on “counter thought experiments” and another on the development of inertial motion. With plenty of illustrations and updated coverage of the debate between Platonic rationalism and classic empiricism, this is a lively and engaging contribution to the field of philosophy of science. (shrink)

This paper examines the philosophy of Jean-Francois Lyotard in relation to the analytic philosophy of deep disagreement. It argues not just that his work has relevance for this debate, but that it offers a challenge to the ‘epistemic paradigm’ present in its academic literature, represented by the two most prominent sets of theories within it – the ‘fundamental epistemic principle’ and ‘hinge epistemology’ views, arguably most strongly represented by Michael Lynch and Duncan Pritchard, respectively. Focussing on Lyotard’s text ‘The Differend’, (...) I show how its conceptual framework and philosophy of language locates the cause of deep disagreement not in the epistemic realm, but in things which do not fully submit to epistemic evaluation: the radically incomplete and open nature of language, and our increasingly politically pluralistic world full of incommensurable differences that do not always admit of rational resolution. Lyotard’s work calls for us to conceptualize deep disagreements as problems of politics, not epistemology, and to find new ways of dealing with disagreements that do not force a solution on them (which often comes at the cost of one party being wronged, or worse) and to create new ways of speaking so that our collective conceptual resources can be increased to better deal with specific cases of dispute. Lyotard’s relevance for the philosophy of deep disagreement is also further discussed with references to Miranda Fricker’s work on ‘epistemic injustice’, which Lyotard, in a different vocabulary, is also concerned with and analyses in ‘The Differend’. (shrink)

The developers of Red Hook Studios’ 2016 gothic horror game ‘Darkest Dungeon’ said that they wanted to ‘capture the human response to stress’. This paper analyses how the game does this with its ‘stress’, ‘affliction’ and ‘virtue’ mechanics. With reference to research literature on stress, I show how these mechanics, which could easily have been cheap gimmicks, approach the topic of stress with admirable detail, offering a complex reflection on the various aspects, positive and negative, of several possible human responses (...) to stress. They show how different responses include similar symptoms, how stress impacts the people around the stressed person, and make the case that stress can break people, but also fuel heroism. It is a fantastic example of how video game mechanics can be used to educate people about complex subjects without explicitly saying this is what they’re doing. (shrink)

If${\cal M},{\cal N}$are countable, arithmetically saturated models of Peano Arithmetic and${\rm{Aut}}\left( {\cal M} \right) \cong {\rm{Aut}}\left( {\cal N} \right)$, then the Turing-jumps of${\rm{Th}}\left( {\cal M} \right)$and${\rm{Th}}\left( {\cal N} \right)$are recursively equivalent.

As business and society is an inherently multi-disciplinary scholarly area, the book will draw from work in areas outside of business and management, such as psychology, sociology, philosophy, religious studies, economics and other related fields, as well as the natural sciences, education, and other professional areas of study.

This paper evaluates Howe and Leota/Turp's accounts of gamesmanship by examining case studies of gamesmanship from professional darts. While Leota and Turp make some substantial improvements on Howe in reconceptualizing the idea of sporting excellence, I claim that there are points of criticism that must be addressed, notably in their claims that sports do not prescribe necessary skills, and that it is impossible to distinguish between legitimate sporting strategy unaccounted for by the rules on the one hand, and gamesmanship on (...) the other. Leota and Turp criticise Howe’s account of rules for being misconceived: rather than rules prescribing necessary skills as Howe claims, rules actually proscribe skills and set limits on behaviour, rather than prescribing skills. I use darts and other sports to make the case that rules actually do both things. Elsewhere, in the phenomenon of ‘grouping’, I argue that we find a skill completely unaccounted for by the rules of darts and not a necessary skill for playing darts, which nonetheless counts as excellence for darts. This problematizes some claims from Leota and Turp on which their account of gamesmanship hinges. An aspect of Howe, Leota and Turp’s accounts on which they all agree is the importance of psychological resilience in sporting endeavours, which I discuss with reference to darts and rule changes in professional sport. The article ends with a discussion of an example from darts of a potential gamesmanship strategy, from a match between Michael van Gerwen and Darius Labanauskas, that unquestionably remains within the rules of the sport and which could not be eradicated through rule changes because it would violate the spirit of the sport. This is an interesting, controversial example for studies of the different forms of gamesmanship and their categorization, and indicates some limitations on what I say in my argument. (shrink)

Following up on his previous book, _Violence and Phenomenology_, James Dodd presents here an expanded and deepened reflection on the problem of violence. The book’s six essays are guided by a skeptical philosophical attitude about the meaning of violence that refuses to conform to the exigencies of essence and the stable patterns of lived experience. Each essay tracks a discoverable, sometimes familiar figure of violence, while at the same time questioning its limits and revealing sites of its resistance to (...) conceptualization. Dodd’s essays are readings as much as they are reflections; attempts at interpretation as much as they are attempts to push concepts of violence to their limits. They draw upon a range of different authors—Sartre, Levinas, Schelling, Scheler, and Husserl—and historical moments, but without any attempt to reduce them into a series of examples elucidating a comprehensive theory. The aim is to follow a path of distinctively episodic and provisional modes of thinking and reflection that offers a potential glimpse at how violence can be understood. (shrink)

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

In this article I respond to the constructive criticisms of my views in Markets with Limits that have been developed by Amy E. White, Roderick T. Long, and Julian Koplin. I also outline how Jason Brennan and Peter Jaworski have surreptitiously altered their position in the second edition of their book Markets Without Limits—alterations that they appear to have made in response to my criticisms. First, they have changed the view that they attribute to those they identify as anti-commodification theorists (...) in response to my claim that none of them hold the position that they attribute to them. Second, they have altered their definition of what constitutes a “semiotic” objection to markets. I argue that none of these changes successfully address my initial criticisms. By contrast, I believe that the revisions that I make to my views in response to the objections of White and Long address their concerns, and I concur with Koplin’s development of my views in the context of the use of AI. (shrink)

Conscious recollection, of the kind characterised by sensory mental imagery, is often thought to involve ‘episodically’ recalling experienced events in one’s personal past. One might wonder whether this overlooks distinctive ways in which we sometimes recall ordinary, persisting objects. Of course, one can recall an object by remembering an event in which one encountered it. But are there acts of recall which are distinctively objectual in that they are not about objects in this mediated way (i.e., by way of being (...) about events in which they featured)? This question has broad implications, not least for understanding the nature and role of imagery in remembering, the requirements of memory-based singular thought about objects, and the sense in which remembering involves ‘mental time travel’ through which one ‘relives’ past events. In this paper, I argue that we sometimes do recall objects from our past without remembering events in which they featured. The positive view of such cases I go on to propose draws on a wide body of empirical work in its support and accommodates a more nuanced picture of the role of imagery in remembering. Succinctly, remembering might essentially involve a kind of ‘re-experiencing’, but it need not involve ‘reliving’. (shrink)

Originally published in in 1893, this book contains the text of the Socratic dialogue Protagoras, which discusses a variety of Sophistic and Socratic tenets, including the teachability of virtue. The dialogue also provides an interesting view on the connection between pederasty and education in ancient Athens. Notable Plato scholars James and Adele Adams present an introduction addressing the purpose and themes of the dialogue; a biography of Protagoras and extant fragments of his works are also included. This book will (...) be of value to anyone with an interest in the Platonic, Socratic or Sophistic philosophies. (shrink)

We extend results of Bonet, Buss and Pitassi on Bondy’s Theorem and of Nozaki, Arai and Arai on Bollobás’ Theorem by proving that Frankl’s Theorem on the trace of sets has quasipolynomial size Frege proofs. For constant values of the parametert, we prove that Frankl’s Theorem has polynomial size AC0-Frege proofs from instances of the pigeonhole principle.