This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the "algebraic" approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a "foundation", (...) or turning meta-mathematical analyses of logical concepts into "philosophical" ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be structuralists all the way down. (shrink)

Feferman argues that category theory cannot stand on its own as a structuralist foundation for mathematics: he claims that, because the notions of operation and collection are both epistemically and logically prior, we require a background theory of operations and collections. Recently [2011], I have argued that in rationally reconstructing Hilbert’s organizational use of the axiomatic method, we can construct an algebraic version of category-theoretic structuralism. That is, in reply to Shapiro, we can be structuralists all the way down (...) ; we do not have to appeal to some background theory to guarantee the truth of our axioms. In this paper, I again turn to Hilbert; I borrow his distinction between the genetic method and the axiomatic method to argue that even if the genetic method requires the notions of operation and collection, the axiomatic method does not. Even if the genetic method is in some sense epistemically or logically prior, the axiomatic method stands alone. Thus, if the claim that category theory can act as a structuralist foundation for mathematics arises from the organizational use of the axiomatic method, then it does not depend on the prior notions of operation or collection, and so we can be structuralists all the way up. (shrink)

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall2007, Beall2009, Field2008, Field2009). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated---so that they can be said to jointly entail a given conclusion---is appropriately understood. In addition, we briefly rehearse (...) some reasons for restricting structural contraction. (shrink)

Embodied cognition is one of the foremost areas of study and research in philosophy of mind, philosophy of psychology and cognitive science. The Routledge Handbook of Embodied Cognition is an outstanding guide and reference source to the key philosophers, topics and debates in this exciting subject and essential reading for any student and scholar of philosophy of mind and cognitive science. Comprising over thirty chapters by a team of international contributors, the Handbook is divided into six parts: Historical Underpinnings Perspectives (...) on Embodied Cognition Applied Embodied Cognition: Perception, Language and Reasoning Applied Embodied Cognition: Social and Moral Cognition and Emotion Applied Embodied Cognition: Memory, Attention and Group Cognition Meta-Topics. The early chapters of the Handbook cover empirical and philosophical foundations of embodied cognition, focusing on Gibsonian, phenomenological and cybernetic approaches. Subsequent chapters cover additional, important themes common to work in embodied cognition, incuding embedded , extended and enactive cognition as well as chapters on embodied cognition and empirical research in perception, language, reasoning, social and moral cognition, emotion, consciousness, memory and learning and development. (shrink)

Part philosophical meditation, part cultural critique, The Body in Pain is a profoundly original study that has already stirred excitement in a wide range of intellectual circles. The book is an analysis of physical suffering and its relation to the numerous vacabularies and cultural forces--literary, political, philosophical, medical, religious--that confront it. Elaine Scarry bases her study on a wide range of sources: literature and art, medical case histories, documents on torture compiled by Amnesty International, legal transcripts of personal injury (...) trials, and military and strategic writings by such figures as Clausewitz, Churchill, Liddell Hart, and Kissinger, She weaves these into her discussion with an eloquence, humanity, and insight that recall the writings of Hannah Arendt and Jean-Paul Sartre. Scarry begins with the fact of pain's inexpressibility. Not only is physical pain enormously difficult to describe in words--confronted with it, Virginia Woolf once noted, "language runs dry"--it also actively destroys language, reducing sufferers in the most extreme instances to an inatriculate state of cries and moans. Scarry analyzes the political ramifications of deliberately inflicted pain, specifically in the cases of torture and warfare, and shows how to be fictive. From these actions of "unmaking" Scarry turns finally to the actions of "making"--the examples of artistic and cultural creation that work against pain and the debased uses that are made of it. Challenging and inventive, The Body in Pain is landmark work that promises to spark widespread debate. About the Author: Elaine Scarry is Associate Professor of English at the University of Pennsylvania. (shrink)

Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language is, or corresponds to, a part of a natural language like English or Greek. The deductive system is to capture, codify, or simply record which inferences are correct for the given language, and the semantics is to capture, codify, or record the meanings, or truth-conditions, or possible truth conditions, for at least part of the language.

Part philosophical meditation, part cultural critique, The Body in Pain is a profoundly original study that has already stirred excitement in a wide range of intellectual circles. The book is an analysis of physical suffering and its relation to the numerous vocabularies and cultural forces--literary, political, philosophical, medical, religious--that confront it.Elaine Scarry bases her study on a wide range of sources: literature and art, medical case histories, documents on torture compiled by Amnesty International, legal transcripts of personal injury trials, (...) and military and strategic writings by such figures as Clausewitz, Churchill, Liddell Hart, and Kissinger, She weaves these into her discussion with an eloquence, humanity, and insight that recall the writings of Hannah Arendt and Jean-Paul Sartre.Scarry begins with the fact of pain's inexpressibility. Not only is physical pain enormously difficult to describe in words--confronted with it, Virginia Woolf once noted, "language runs dry"--it also actively destroys language, reducing sufferers in the most extreme instances to an inarticulate state of cries and moans. Scarry analyzes the political ramifications of deliberately inflicted pain, specifically in the cases of torture and warfare, and shows how to be fictive. From these actions of "unmaking" Scarry turns finally to the actions of "making"--the examples of artistic and cultural creation that work against pain and the debased uses that are made of it. Challenging and inventive, The Body in Pain is landmark work that promises to spark widespread debate. (shrink)

Introduction: Losing our heads -- Kristeva and Benjamin: melancholy and the allegorical imagination -- Kenotic art: negativity, iconoclasm, inscription -- To be and remain foreign: tarrying with l'inquietante etrangete alongside Arendt -- And Kafka -- Sublimating maman: experience, time, and the re-erotization of existence in -- Kristeva's reading of Marcel Proust -- The "Orestes Complex": thinking hatred, forgiveness, Greek tragedy, and the -- Cinema of the "thought specular" with Hegel, Freud, and Klein -- Conclusion: forging a/head.

In The Phenomenology of Religious Belief, the renowned philosopher Michael J. Shapiro investigates how art - and in particular literature and film - can impact upon both traditional interpretations and critical studies of religious beliefs and experiences. In doing so, he examines the work of prolific and award-winning writers such as Toni Morrison, Philip K. Dick and Robert Coover. By placing their work in conjunction with critical analyses of media by the likes of Ingmar Bergman and Pier Paolo Pasolini (...) and combining it with the work of groundbreaking thinkers such as George Canguilhem, Giorgio Agamben and Slavoj Žižek, Shapiro takes a truly interdisciplinary approach to the question of how life should be lived. His assessment of phenomenological subjectivity also leads him to question the nature of political theology and extend the criticism of Pauline theology. (shrink)

Assesses Irish republicanism's strategic process of moderation, from violence to peace and power.

Holding life and death in their hands -- Is this for me? -- The intensive care unit. Personnel ; Rhythms ; Economics -- Actors. Patients ; Friends, family, and significant others ; Health care professionals -- Decisions. Informed consent ; Venues ; Affect ; Conflict -- Prognosis. Evidence ; Timing ; Mixed messages ; Negotiation ; Accuracy ; Prognostic framing -- Decision-making scripts. The legal script ; Cognitive scripts ; Conflicts of interest ; Law at the bedside -- Improvisation: decisions (...) in the real world. The patient should decide ; Reprising patient instructions ; Standing in the patient's shoes ; Beneficence ; It's God's decision ; What we want ; Denial, opting out -- Making a difference? The role of physicians ; Opting for a trajectory ; Outcomes ; I thought the law would take care of this ; Does any of this matter? -- The end. Implications ; Before it's too late ; When it's too late ; When "this" happens to me. (shrink)

ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.

"--J.M.Coetzee "Here is a writer almost magically summoning up the world through words and ideas, in a new way, and so guiding the reader, lovingly, to receive the treasures and accept the pleasures of this book as naturally as breathing.

Perceptions of Medieval Manuscripts takes as its starting point an understanding that a medieval book is a whole object at every point of its long history. As such, medieval books can be studied most profitably in a holistic manner as objects-in-the-world. This means readers might profitably account for all aspects of the manuscript in their observations, from the main texts that dominate the codex to the marginal notes, glosses, names, and interventions made through time. This holistic approach allows us to (...) tell the story of the book's life from the moment of its production to its use, collection, breaking-up, and digitization--all aspects of what can be termed 'dynamic architextuality'. The ten chapters include detailed readings of texts that explain the processes of manuscript manufacture and writing, taking in invisible components of the book that show the joy and delight clearly felt by producers and consumers. Chapters investigate the filling of manuscripts' blank spaces, presenting some texts never examined before, and assessing how books were conceived and understood to function. Manuscripts' heft and solidness can be seen, too, in the depictions of miniature books in medieval illustrations. Early manuscripts thus become archives and witnesses to individual and collective memories, best read as 'relics of existence', as Maurice Merleau-Ponty describes things. As such, it is urgent that practices fragmenting the manuscript through book-breaking or digital display are understood in the context of the book's wholeness. Readers of this study will find chapters on multiple aspects of medieval bookness in the distant past, the present, and in the assurance of the future continuity of this most fascinating of cultural artefacts. (shrink)

_A spirited defense of the Enlightenment against assaults from both the left and the right that explains its urgent implications for our contemporary politics_ Ours is an age when optimism about politics is hard to come by. Ian Shapiro explains why this is so and, without minimizing the daunting challenges, spells out an appropriate response. Written in the indomitable spirit exemplified by Tom Paine, _Uncommon Sense_ is a rich source of insight and inspiration in dark political times. The Enlightenment (...) commitments to reason and science are under assault from the Postmodern Left and the Authoritarian Right. Shapiro explains why the attacks are misguided and politically destructive. He agrees with the critics that there are no universal principles of justice that transcend political battles and no fair, impartial rules to govern the distribution of income, wealth, rights, or opportunities. But abandoning the search for them as futile does not mean junking the Enlightenment’s core political goal: to deploy the tools of reason and science to fight domination. Democracy is essential to vindicating that goal, yet citizens in many democracies are profoundly alienated and many democracies are in danger of failing. Shapiro explains what has gone wrong, debunks ill-considered remedies, and spells out better ones—deepening and extending his previous writing on political theory and democratic politics. (shrink)

This chapter wades into the growing discussion surrounding embodied cognition and predictive processing. After surveying a recent debate between Jakob Hohwy and Andy Clark, it articulates two outstanding issues facing discussions of compatibility. It argues that headway on these issues can be made by drawing on the resources of philosophy of science.

A consideration of how segments of Orthodox society rewrite the past by eliminating that which does not fit in with their contemporary world-view. This wide-ranging and original review of how this policy is applied in practice adds a new perspective to Jewish intellectual history and to the understanding of the contemporary Jewish world.

This philosophical game changer looks critically at the Golden Rule in the context of game theory to see where it works and where it doesn’t, when it is applicable and when it isn’t. It shows you why knowing the difference can offer you a powerful way to transform your life from one driven by fear to one driven by love.

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between (...) the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. (shrink)

We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...) full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory. (shrink)

This chapter contains sections titled: Introduction The Dissertation Proposal Shift to the Critique of Teleology Kant's Organicism and Critique of Teleological Judgment Goethe's Aesthetic Philosophy of Nature Multiple Purposivenesses Individuation Rationality and Purposiveness The Legacy of the Dissertation Project in Nietzsche's Later Work.

Behind the dramas and conflicts, there exists a quiet inner place where meditation and mindfulness can help us reside. This book shares personal insights from visionary leaders -- the Dalai Lama, Jon Kabat-Zinn, and Marianne Williamson among them -- who discuss their methods of maintaining mental health and happiness. Their teaching can help you transform your life from the inside out and discover innate strength, kindness, and courage.

Shapiro knows there are totalitarians on the political Right. But statistically, they represent a fringe movement with little institutional clout. The authoritarian Left, meanwhile, is ascendant in nearly every area of American life. A small number of college-educated, coastal, and uncompromising leftists have not just taken over the Democratic Party but our corporations, our universities, our scientific establishment, our cultural institutions. And they have used their newfound power to silence their opposition. Shapiro lays bare the intolerance and rigidity (...) creeping into all American ideology, and prescribes the solution to ending the authoritarianism that threatens our future. -- adapted from jacket. (shrink)

Much has been said about intuitionistic and classical logical systems since Gentzen’s seminal work. Recently, Prawitz and others have been discussing how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system. We call Prawitz’ proposal the Ecumenical System, following the terminology introduced by Pereira and Rodriguez. In this work we present an Ecumenical sequent calculus, as opposed to the original natural deduction version, and state some proof theoretical properties of the system. We reason that (...) sequent calculi are more amenable to extensive investigation using the tools of proof theory, such as cut-elimination and rule invertibility, hence allowing a full analysis of the notion of Ecumenical entailment. We then present some extensions of the Ecumenical sequent system and show that interesting systems arise when restricting such calculi to specific fragments. This approach of a unified system enabling both classical and intuitionistic features sheds some light not only on the logics themselves, but also on their semantical interpretations as well as on the proof theoretical properties that can arise from combining logical systems. (shrink)

Next SectionIntensification of poverty and degradation of health infrastructure over recent decades in countries most affected by HIV/AIDS present formidable challenges to clinical research. This paper addresses the overall standard of health care (SOC) that should be provided to research participants in developing countries, rather than the narrow definition of SOC that has characterised the international debate on standards of health care. It argues that contributing to sustainable improvements in health by progressively ratcheting the standard of care upwards for research (...) participants and their communities is an ethical obligation of those in resource-rich countries who sponsor and implement research in poorer ones. (shrink)

"--Robert Fagles, translator of Homer's "Iliad" "I finished "Dreaming by the Book" feeling that fundamental aspects of the nature of consciousness had been peeled open and exposed to view."--Stephen M. Kosslyn, author of "Image and Brain".