Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Many philosophers claim to be naturalists, but there is no common understanding of what naturalism is. Maddy proposes an austere form of naturalism called 'Second Philosophy', using the persona of an idealized inquirer, and she puts this method into practice in illuminating reflections on logical truth, philosophy of mathematics, and metaphysics.

Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of (...) the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments. (shrink)

The Logical Must is an examination of Wittgenstein's philosophy of logic, early and late, from an austere naturalistic perspective called "Second Philosophy.".

Pragmatists have traditionally been enemies of representationalism but friends of naturalism, when naturalism is understood to pertain to human subjects, in the sense of Hume and Nietzsche. In this volume Huw Price presents his distinctive version of this traditional combination, as delivered in his René Descartes Lectures at Tilburg University in 2008. Price contrasts his view with other contemporary forms of philosophical naturalism, comparing it with other pragmatist and neo-pragmatist views such as those of Robert Brandom and Simon Blackburn. (...) Linking their different 'expressivist' programmes, Price argues for a radical global expressivism that combines key elements from both. With Paul Horwich and Michael Williams, Brandom and Blackburn respond to Price in new essays. Price replies in the closing essay, emphasising links between his views and those of Wilfrid Sellars. The volume will be of great interest to advanced students of philosophy of language and metaphysics. (shrink)

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.

The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners (...) approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth. (shrink)

What Do Philosophers Do? takes up the leading arguments for radical skepticism from an everyday point of view. A range of philosophical methods are examined and employed, for a revealing portrait of what philosophers do, and perhaps a quiet suggestion for what they should do, for what they do best.

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...) She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

This is a very short introduction to ethics. It divides into three parts: first, introducing and discussing reasons for skepticism about ethics; second introducing themes of birth, death, happiness, desire and freedom to show how deeply our lives are interwoven with ethics; third, introducing attempts to found ethics, due to Aristotle, Kant, and the contractarian tradition.

From political scandals at the highest levels to inflated repair bills at the local garage, we are seemingly surrounded with unethical behavior, so why should we behave any differently? Why should we go through life anchored down by rules no one else seems to follow? Writing with wit and elegance, Simon Blackburn tackles such questions in this lively look at ethics, highlighting the complications and doubts and troubling issues that spring from the very simple question of how we ought (...) to live. Blackburn dissects many common reasons why we are skeptical about ethics. Drawing on all-too-familiar examples from history, politics, religion and everyday personal experience, he shows how cynicism and self-consciousness can paralyze us into considering ethics a hopeless pursuit. But ethics is neither futile nor irrelevant, he assures us, but an intimate part of the nitty gritty issues of living--of birth, death, happiness, desire, freedom, pleasure, justice. Indeed, from moral dilemmas about abortion and euthanasia, to our obsession with personal rights, to our longing for a sense of meaning in life, our everyday struggles are rife with ethical issues, whether we notice it or not. Blackburn distills the arguments of Hume, Kant and Aristotle down to their essences, to underscore the timeless relevance of our voice of conscience, the pitfalls of complacency, and our concerns about truth, knowledge and human progress. Blackburn's rare combination of depth, rigor and sparkling prose, and his distinguished ranking among contemporary philosophers, mark Being Good as an important statement on our current disenchantment with ethics. It challenges us to take a more thoughtful reading of our ethical climate and to ponder more carefully our own standards of behavior. (shrink)

Mathematical axioms have traditionally been thought of as obvious or self-evident truths, but current set theoretic work in the search for new axioms belies this conception. This raises epistemological questions about what other forms of justification are possible, and how they should be judged.

This best-selling dictionary is written by one of the most famous philosophers of our time, and it is widely recognized as the best dictionary of its kind. Comprehensive and authoritative, it covers every aspect of philosophy from Aristotle to Zen. With clear and concise definitions, it provides lively and accessible coverage of not only Western philosophical traditions, but also themes from Chinese, Indian, Islamic, and Jewish philosophy. Entries include over 500 biographies of famous and influential philosophers, in-depth analysis of philosophical (...) terms and concepts, and a chronology of philosophical events stretching from 10,000 BC to the present day. The first edition of this dictionary became a market-leader and a standard work of reference, selling over 100,000 copies. Now the author, Professor Simon Blackburn, has revised it to include web links which provide up-to-date and valuable extra information via the Dictionary of Philosophy companion website. Fully cross-referenced and containing over 3,000 alphabetical entries, it is the ideal introduction to philosophy for anyone with an interest in the subject, and it is an indispensable work of reference for students and teachers. (shrink)

Hybrid languages are expansions of propositional modal languages which can refer to worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work has focussed on a more constrained system called $\mathscr{H}$. We show in detail that $\mathscr{H}$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations and a syntactic characterization. The key result to emerge is that $\mathscr{H}$ corresponds to the fragment of first-order logic which is invariant for generated (...) submodels. We then show that $\mathscr{H}$ enjoys interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage $\mathscr{H}$. Finally, we provide complexity results for $\mathscr{H}$ and other fragments and variants, and sharpen known undecidability results for $\mathscr{H}$. (shrink)

The tenor of much recent work in the philosophy of mathematics has been dictated by the popular assumption that Platonism is defunct. Some embrace that assumption and look for alternatives, others deny it and attempt to revive Platonism, but either way it is the starting point. The fate of Platonism took center stage with the appearance of Paul Benacerraf’s “Mathematical truth”, but a decade has passed since then, and the philosophical climate has changed. Most important, the quarter from which Platonism (...) was to receive its mortal wound—epistemology—has developed considerably; the epistemological theory presupposed by Benacerraf is no longer popular. This makes it difficult to assess the value of work in the philosophy of mathematics done under the influence of Benacerraf’s formulation. (shrink)

Lust, says Simon Blackburn, is furtive, headlong, always sizing up opportunities. It is a trail of clothing in the hallway, the trashy cousin of love. But be that as it may, the aim of this delightful book is to rescue lust "from the denunciations of old men of the deserts, to deliver it from the pallid and envious confessor and the stocks and pillories of the Puritans, to drag it from the category of sin to that of virtue." (...) class='Hi'>Blackburn, author of such popular philosophy books as Think and Being Good, here offers a sharp-edged probe into the heart of lust, blending together insight from some of the world's greatest thinkers on sex, human nature, and our common cultural foibles. Blackburn takes a wide ranging, historical approach, discussing lust as viewed by Aristophanes and Plato, lust in the light of the Stoic mistrust of emotion, and the Christian fear of the flesh that catapulted lust to the level of deadly sin. He describes how philosophical pessimists like Schopenhauer and Sartre contributed to our thinking about lust and explores the false starts in understanding lust represented by Freud, Kinsey, and modern "evolutionary psychology." But most important, Blackburn reminds us that lust is also life-affirming, invigorating, fun. He points to the work of David Hume who saw lust not only as a sensual delight but also "a joy of the mind." Written by one of the most eminent living philosophers, attractively illustrated and colourfully packaged, Lust is a book that anyone would lust over. (shrink)

Though many working mathematicians embrace a rough and ready form of Platonism, that venerable position has suffered a checkered philosophical career. Indeed the three schools of thought with which most of us began our official philosophizing about mathematics—Intuitionism, Formalism, and Logicism—all stand in fundamental disagreement with Platonism. Nevertheless, various versions of Platonistic thinking survive in contemporary philosophical circles. The aim of this paper is to describe these views, and, as my title suggests, to trace their roots.I'll begin with some preliminary (...) remarks about the big three schools. This seems a reasonable approach to the issues both because most observers are familiar, at least in a general way, with the tenets of Intuitionism, Formalism, and Logicism, and because it is in reaction to these that contemporary Platonism has taken shape. (shrink)

Practical philosophy and ethics -- Practical tortise raising -- Truth, beauty, and goodness -- Dilemmas: dithering, plumping, and grief -- Group minds and expressive harm -- Trust, cooperation, and human psychology -- Must we weep for sentimentalism? -- Through thick and thin -- Perspectives, fictions, errors, play -- The steps from doing to saying -- Success semantics -- Wittgenstein's irrealism -- Circles, finks, smells, and biconditionals -- The absolute conception: Putnam vs. Williams -- Julius Caesar and George Berkeley play leapfrog (...) -- The majesty of reason -- Fiction and conviction. (shrink)

The effort to fit simple logical truths–like `if it's either red or green and it's not red, then it must be green'–into Kant's account of knowledge turns up a position more subtle and intriguing than might be expected at first glance.

This paper explores women's accounts of prostitution in terms of the lived experience of the body, drawing on life story narratives and arts images created by women in the sex industry. These narratives show that women's experiences of prostitution constitute a spectrum of (dis)embodiment that is inflected, not determined, by settings and contexts. Theoretical approaches to embodiment were sought that acknowledged tensions between violation and a sense of empowerment. Therefore, the ontology of selling sex, and associated experiences such as violence, (...) drug use and self-harm are explored using feminist applications of Merleau-Ponty's notion of the `habit body'. A key focus is how the body is constituted by embodied experiences of abuse (e.g. the work of Parkins and of Weiss), and how women negotiate ownership of the body within commercial sex transactions. This highlights the process of repositioning the body by selling sex, in accordance with the accumulated experiences of the habit body. Thus, to borrow from Wendy Parkins, women perceive that they are acting meaningfully through the body, even when reproducing dynamics of objectification and dissociation. (shrink)