MICHAEL DUMMETT, Elements of intuitionism. With the assistance of Robert Minio. Oxford: Oxford University Press, 1977. xii + 466 pp. No price stated.

Menachem Butler. Bibliography: Mark Steiner’s main works, pp. 3–7.

The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical philosophy, (...) and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant. (shrink)

Robert C. Scharff has written what we might call, after Nietzsche, a timely meditation. It is timely in that it is aimed at our particular time , and it is a meditation on timeliness, on what it means to do philosophy within time and history . These two topics meet in his depiction of our time as one that is either not fully aware of or that actively suppresses its own timeliness, its own determination by its time and historical (...) context, due largely to analytic philosophy’s remaining caught in the vestigial grips of positivism and the dominance of science. We may be “After Positivism,” but we are not wholly past positivism. Scharff considers this ahistorical approach untenable because, as he informs us in the book’s second sentence, all meditations are timely: time and historical context inescapably determine how and what we meditate on, especially the attempts to escape them.Scharff identifies our place in history as “after posi .. (shrink)

It is argued that the tensed theory of the creative subject provides a natural formulation of the logic underlying Brouwer's notion of unextendable order and explains the link between that notion and virtual order. The tensed theory of the creative subject is also shown to be a useful tool for interpreting recent evidence about the stages of Brouwer's thinking concerning these two notions of order.

The abstract structure of inquiry - the process of acquiring and changing beliefs about the world - is the focus of this book which takes the position that the "pragmatic" rather than the "linguistic" approach better solves the philosophical problems about the nature of mental representation, and better accounts for the phenomena of thought and speech. It discusses propositions and propositional attitudes (the cluster of activities that constitute inquiry) in general and takes up the way beliefs change in response to (...) potential new information, suggesting that conditional propositions should be understood as projections of epistemic policies onto the world.Robert C. Stalnaker is a professor in the Sage School of Philosophy at Cornell University. A Bradford Book. (shrink)

Winner of the 1975 National Book Award, this brilliant and widely acclaimed book is a powerful philosophical challenge to the most widely held political and social positions of our age--liberal, socialist, and conservative.

Winner of the Los Angeles Times Book Prize With a new preface by the author In his most powerful and important book, renowned psychiatrist Robert Jay Lifton presents a brilliant analysis of the crucial role that German doctors played in the Nazi genocide. Now updated with a new preface, The Nazi Doctors remains the definitive work on the Nazi medical atrocities, a chilling exposé of the banality of evil at its epitome, and a sobering reminder of the darkest side (...) of human nature. (shrink)

This paper revisits some foundational questions concerning the abstract representation of a discourse context. The context of a conversation is represented by a body of information that is presumed to be shared by the participants in the conversation – the information that the speaker presupposes a point at which a speech act is interpreted. This notion is designed to represent both the information on which context-dependent speech acts depend, and the situation that speech acts are designed to affect, and so (...) to be a representation of context that is appropriate for explaining the interaction of context and the contents expressed in them. After reviewing the motivating ideas and the outlines of the apparatus, the paper responds to a criticism of the framework, and considers the way it can help to clarify some phenomena concerning pronouns with indefinite antecedents. (shrink)

ABSTRACT This paper aims to show that intuitionistic Kripke models are a powerful tool for interpreting Kant’s ‘Critical Philosophy’. Part I reviews some old work of mine that applies these models to provide a reading of Kant’s second antinomy about the divisibility of matter and to answer several attacks on Kant’s antinomies. But it also points out three shortcomings of that original application. First, the reading fails to account for Kant’s second antinomy claim that matter is divisible ‘ad infinitum’ and (...) his first antinomy claim that empirical space extends only ‘ad indefinitum’. Secondly, in conformity with the ‘assertability’ heuristics for Kripke models, it attributes an assertability semantics to Kant. In fact, it attributes a pair of assertability semantics to Kant, but neither of these accords with modern assertabilism. And finally, one must wonder the propriety of using contemporary assertability and contemporary formal logic to save an eighteenth-century text. Part II goes historical to solve the problems about assertability. It outlines the Descartes–Leibniz dialectic about the infinite/indefinite distinction and demonstrates how each position reflects larger philosophical positions. It then demonstrates that Kant’s two versions of assertability and his version of the infinite/indefinite dichotomy emerge naturally from his attempts to resolve a tension in Leibniz’s philosophy. In light of this demonstration, Part III adapts the Kripke model interpretation so that it does reflect that dichotomy. It then refines the Kripke semantics in order to model some of Kant’s signature critical doctrines, and it shows how Kant’s critical version of the infinite/indefinite distinction differs from all those of his predecessors and from his own pre-critical version. It also addresses the question of using contemporary logical machinery to interpret Kant. Part IV turns the tables and uses what we have learned about Kant and modern semantics in order to address a pair of issues in the contemporary critical foundations of logic. (shrink)

I thank the editors for inviting me to contribute to this issue on critical views of logic. Kant invented the critical philosophy. He fashioned its doctrines (Understanding versus Reason, synthetic...

Though my title speaks of Kant’s mathematical realism, I want in this essay to explore Kant’s relation to a famous mathematical anti-realist. Specifically, I want to discuss Kant’s influence on L. E. J. Brouwer, the 20th-century Dutch mathematician who built a contemporary philosophy of mathematics on constructivist themes which were quite explicitly Kantian. Brouwer’s theory is perhaps most notable for its belief that constructivism requires us to abandon the traditional logic of mathematical reasoning in favor of different canon of reasoning, (...) called intuitionistic logic. Brouwer thought that classical logic is intrinsically bound up with a nonconstructive view of mathematics. This means that, according to Brouwer, when we do mathematics we must give up bivalence, we must no longer use such familiar logical laws as excluded middle, and we must sometimes forebear from the classic method of reductio ad absurdum. All of these are intuitionistically invalid classical principles. (shrink)

After sketching the essentials of L. E. J. Brouwer’s intuitionistic mathematics—separable mathematics, choice sequences, the uniform continuity theorem, and the intuitionistic continuum—this chapter outlines the main philosophical tenets that go hand in hand with Brouwer’s technical achievements. It presents his views about general and mathematical phenomenology and shows how these views ground his positive epistemological and ontological positions and his stinging criticisms of classical mathematics and logic. The chapter then turns to intuitionistic logic and its philosophical side. It first sets (...) out the basic meta-logical technical results, then discusses the relevant philosophical views—those of Arend Heyting and Michael Dummett. It concludes by tracing intuitionism’s philosophical and technical roots in Aristotle and Kant. (shrink)

Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. (...) It also includes the most important recent work on Kant's philosophy of mathematics. The essays bring to bear a wealth of detailed Kantian scholarship, together with powerful new interpretative tools drawn from modern mathematics, logic and philosophy. The cumulative effect of this collection upon the reader will be a deeper understanding of the centrality of mathematics in all aspects of Kant's thought and a renewed respect for the power of Kant's thinking about mathematics. The essays contained in this volume will set the agenda for further work on Kant's philosophy of mathematics for some time to come. (shrink)

_A moving meditation on recent geopolitical crises, viewed through the lens of ancient and modern tragedy__ “Spare, elegant and poignant.... If there is a single contemporary book that should be pressed into the hands of those who decide issues of war and peace, this is it.”—John Gray, _New Statesman_ “It is tragic that Robert D. Kaplan’s luminous _The Tragic Mind_ is so urgently needed.”—George F. Will_ Some books emerge from a lifetime of hard-won knowledge. Robert D. Kaplan has (...) learned, from a career spent reporting on wars, revolutions, and international politics in Europe, the Middle East, and East Asia, that the essence of geopolitics is tragedy. In _The Tragic Mind_, he employs the works of ancient Greek dramatists, Shakespeare, German philosophers, and the modern classics to explore the central subjects of international politics: order, disorder, rebellion, ambition, loyalty to family and state, violence, and the mistakes of power. The great dilemmas of international politics, he argues, are not posed by good versus evil—a clear and easy choice—but by contests of good versus good, where the choices are often searing, incompatible, and fraught with consequences. A deeply learned and deeply felt meditation on the importance of lived experience in conducting international relations, this is a book for everyone who wants a profound understanding of the tragic politics of our time. (shrink)

What kind of mental state is episodic memory? I defend the claim that it is, in key part, imagining the past, where the imagining in question is experiential imagining. To remember a past episode is to experientially imagine how things were, in a way controlled by one’s past experience of that episode. Call this the Inclusion View. I motive this view by appeal both to patterns of compatibilities and incompatibilities between various states, and to phenomenology. The bulk of the paper (...) defends the account against four objections. Imagining and remembering seem to differ in whether they are active or passive, in the forms of singular content they involve, in their relations to observation and in their relations to belief. I argue that these differences can be accommodated, and some even explained, once we flesh out what else is involved in episodic memory, in addition to imagining the past. (shrink)

Mark Jay Steiner, a brilliant and influential philosopher of mathematics, whose interests and accomplishments extended beyond that field as well, passed away on.

L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation (...) for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth. (shrink)

It is almost unanimously accepted that Kant denies resultant moral luck—that is, he denies that the lucky consequence of a person’s action can affect how much praise or blame she deserves. Philosophers often point to the famous good will passage at the beginning of the Groundwork to justify this claim. I argue, however, that this passage does not support Kant’s denial of resultant moral luck. Subsequently, I argue that Kant allows agents to be morally responsible for certain kinds of lucky (...) consequences. Even so, I argue that it is unclear whether Kant ultimately endorses resultant moral luck. The reason is that Kant does not write enough on moral responsibility for consequences to determine definitively whether he thinks that the lucky consequence for which an agent is morally responsible can add to her degree of praiseworthiness or blameworthiness. The clear upshot, however, is that Kant does not deny resultant moral luck. (shrink)

IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).

Our primary focus is on analysis of the concept of voluntariness, with a secondary focus on the implications of our analysis for the concept and the requirements of voluntary informed consent. We propose that two necessary and jointly sufficient conditions must be satisfied for an action to be voluntary: intentionality, and substantial freedom from controlling influences. We reject authenticity as a necessary condition of voluntary action, and we note that constraining situations may or may not undermine voluntariness, depending on the (...) circumstances and the psychological capacities of agents. We compare and evaluate several accounts of voluntariness and argue that our view, unlike other treatments in bioethics, is not a value-laden theory. We also discuss the empirical assessment of individuals? perceptions of the degrees of noncontrol and self-control. We propose use of a particular Decision Making Control Instrument. Empirical research using this instrument can provide data that will help establish appropriate policies and procedures for obtaining voluntary consent to research. (shrink)

Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’. And he rests these upon consistently opposite grounds. In the Antinomy we are told that we can have (...) no intuitive grasp of an infinite space, and in the Aesthetic he says that our grasp of infinite space is precisely intuitive. (shrink)

In the Western world it is usually taken as given that we all want happiness, and our educational arrangements tacitly acknowledge this. Happiness, Hope, and Despair argues, however, that education has an important role to play in deepening our understanding of suffering and despair as well as happiness and joy. Education can be uncomfortable, unpredictable, and unsettling; it can lead to greater uncertainty and unhappiness. Drawing on the work of Søren Kierkegaard, Miguel de Unamuno, Fyodor Dostoevsky, Simone Weil, Paulo Freire, (...) and others, Peter Roberts shows why these features of educational life need not be feared; to the contrary, they can be seen as a source of hope and human fulfilment. After years of negotiating an education system dominated by the language of competition, performance, and economic advancement, students and teachers often long for something different; they seek not just measurable success but also opportunities to ask searching questions of themselves and the world they encounter. Happiness, Hope, and Despair makes an important contribution toward meeting this need. It fosters a rethinking of the nature, purpose, and value of education, and opens up possibilities for further scholarly and professional inquiry. (shrink)

This paper provides an overview of the history of the notion of essence in 20th century analytic philosophy, focusing on views held by influential analytic philosophers who discussed, or relied on essence or cognate notions in their works. It in particular covers Russell and Moore’s different approaches to essence before and after breaking with British idealism, the (pre- and post-)logical positivists’ critique of metaphysics and rejection of essence (Wittgenstein, Carnap, Schlick, Stebbing), the tendency to loosen the notion of logical necessity (...) to accommodate certain metaphysical truths in Wittgenstein and others, Quine’s logical rehabilitation of metaphysics and criticism of de re modality, the modal view of essence promoted by the development of quantified modal logic (C. I. Lewis, Barcan Marcus, Kripke) and direct reference theory (Barcan Marcus, Kripke, Putnam), and the emergence of the notion of metaphysical necessity (Kneale, Kripke), and finally Fine’s re-establishment of a Neo-Aristotelian, hyperintensional notion of essence in contemporary metaphysics. (shrink)

Philosophers often consider problems of free will and moral luck in isolation from one another, but both are about control and moral responsibility. One problem of free will concerns the difficult task of specifying the kind of control over our actions that is necessary and sufficient to act freely. One problem of moral luck refers to the puzzling task of explaining whether and how people can be morally responsible for actions permeated by factors beyond their control. This chapter explicates and (...) assesses skeptical, compatibilist, and libertarian approaches to moral luck. First, I argue that what makes the above problems of free will and moral luck distinct is largely their emphasis on different kinds of luck. Second, I describe and evaluate skeptical arguments from constitutive and circumstantial luck that it is impossible to act freely. Third, I explicate and assess various support and implication relationships between various kinds of compatibilism and libertarianism, on the one hand, and causal, constitutive, circumstantial, and resultant moral luck, on the other. (shrink)

Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’ (A25/B39). And he rests these upon consistently opposite grounds. In the Antinomy we are told that we can (...) have no intuitive grasp of an infinite space, and in the Aesthetic he says that our grasp of infinite space is precisely intuitive. (shrink)

In this essay I sketch some vices of virtue ethics, draw on inference about the philosophical source of the vices, and conclude with a recommendation concerning future efforts in moral theory construction. The source of the vices, I argue, lies in a mononomic or single-principle strategy within normative theory construction, a reductionist conceptual scheme which distorts certain integral aspects of our moral experience. My recommendation is that this strategy be abandoned, for the moral field is not unitary -- mononomic methods (...) are not the best tools for moral theorists. (shrink)

Robert C. Stalnaker presents a set of essays on the structure of inquiry. First he focuses on the concepts of knowledge, belief, and partial belief, and on the rules and procedures we ought to use to determine what to believe. Then he explores the relations between conditionals and causal and explanatory concepts.

In Pascal Boyer’s book Religion Explained inference systems are made to do a lot of work in his attempts to explain cognition in religion. These inference systems are systems in the brain that produces inferences when they are activated by things we perceive in our environment. According to Boyer they perceive things, produce explanations, and perform calculations. However, if Wittgenstein’s observation, that “only of a living human being and what resembles (behaves like) a living human being can one say: it (...) has sensations; it sees; is blind; hears; is deaf; is conscious or unconscious” is correct then it seems that Boyer’s talk of inference systems perceiving and inferring is confused. (shrink)

Abstract I distinguish various ways in which human life may be thought to be meaningful and present an account of what might be called existential meaningfulness. The account is neutral with respect to both theism and naturalism, but each is addressed in several places and the paper's main points are harmonious with certain versions of both. A number of important criteria for existential meaningfulness are examined, and special emphasis is placed on criteria centering on creativity and excellence, on contributing to (...) the well-being of persons, and on human relationships, particularly those pervaded by love. In the light of a conception of intrinsic goodness, the good life is compared with the meaningful life, and the relation between the two notions is explored. I argue that goodness in a life counts towards its meaningfulness and that the goodness of a life is sufficient for an important kind of meaningfulness. I also suggest that the overall notion of rewarding elements in a life-intrinsically good elements that are typically but not necessarily pleasurable-is a significant unifying concept that helps both in understanding existential meaningfulness and in integrating the various kinds of constituents in a life that conduce to its meaningfulness. (shrink)

Benacerraf’s Problem about mathematical truth displays a tension, indeed a seemingly unbridgeable gap, between Platonist foundations for mathematics on the one hand and Hilbert’s ‘finitary standpoint’ on the other. While that standpoint evinces an admirable philosophical unity, it is ultimately an effete rival to Platonism: It leaves mathematical practice untouched, even the highly non-constructive axiom of choice. Brouwer’s intuitionism is a more potent finitist rival, for it engenders significant deviation from standard (classical) mathematics. The essay illustrates three sorts of intuitionistic (...) deviations (weakening, refinement and outright contradiction), and goes on to sketch the technical tools and arguments that engender those clashes with classical mathematics and the philosophical principles underlying those arguments. Those philosophical principles coalesce into a “standpoint” no less unified and no less finitary that Hilbert’s. This intuitionistic standpoint is sufficiently detailed that it itself provides a benchmark for comparing all the rival positions; and it is sufficiently robust that it dissolves the Benacerrafian dichotomy. However, the intuitionistic refutation of the axiom of choice reveals two distinct sub-streams within that intuitionistic standpoint. Distinguishing these streams suggests perhaps that in spite of that robustness, intuitionism has an internal dichotomy parallel to the Benacerrafian split. The Benacerrafian split is a crack in the foundations of mathematics. But I shall argue that this internal intuitionistic dichotomy is not at all a foundational gap; it is rather a special insight about the nature of mathematical thought. (shrink)

Friedrich Nietzsche is one of the most popular and controversial philosophers of the last 150 years. Narcissistic, idiosyncratic, hyperbolic, irreverent--never has a philosopher been appropriated, deconstructed, and scrutinized by such a disparate array of groups, movements, and schools of thought. Adored by many for his passionate ideas and iconoclastic style, he is also vilified for his lack of rigor, apparent cruelty, and disdain for moral decency. In Living with Nietzsche, Solomon suggests that we read Nietzsche from a very different point (...) of view, as a provocative writer who means to transform the way we view our lives. This means taking Nietzsche personally. Rather than focus on the "true" Nietzsche or trying to determine "what Nietzsche really meant" by his seemingly random and often contradictory pronouncements about "the Big Questions" of philosophy, Solomon reminds us that Nietzsche is not a philosopher of abstract ideas but rather of the dazzling personal insight, the provocative challenge, the incisive personal probe. He does not try to reveal the eternal verities but he does powerfully affect his readers, goading them to see themselves in new and different ways. It is Nietzsche's compelling invitation to self-scrutiny that fascinates us, engages us, and guides us to a "rich inner life." Ultimately, Solomon argues, Nietzsche is an example as well as a promulgator of "passionate inwardness," a life distinguished by its rich passions, exquisite taste, and a sense of personal elegance and excellence. (shrink)

The second edition of Doing Ethics in Media continues its mission of providing an accessible but comprehensive introduction to media ethics, with a theoretical grounding in moral philosophy, to help students think clearly and systematically about dilemmas in the rapidly changing media environment. Each chapter highlights specific considerations, cases, and practical applications for the fields of journalism, advertising, digital media, entertainment, public relations, and social media. Six fundamental decision-making questions - the "5Ws and H" around which the book is organized (...) - provide a path for students to articulate the issues; understand applicable law and ethics codes; consider the needs of stakeholders; work through conflicting values; integrate philosophic principles; and pose a "test of publicity." Students are challenged to be active ethical thinkers through the authors' reader-friendly style and use of critical early-career examples. While most people will change careers several times during their lives, all of us are life-long media consumers, and Doing Ethics in Media prepares readers for that task. Doing Ethics in Media is aimed at undergraduate and graduate students studying media ethics in mass media, journalism, and media studies. It also serves students in rhetoric, popular culture, communication studies, and interdisciplinary social sciences. The book's companion website-doingethicsin.media, or www.doingmediaethics.com-provides continuously updated real-world media ethics examples and collections of essays from experts and students. The site also hosts ancillary materials for students and for instructors, including a test bank and instructor's manual. (shrink)