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.

A plea for natural philosophy --On the question of realism --Hume and Reid --Moore's hands --Wittgenstein on hinges --A note on truth and reference --The philosophy of logic --A Second Philosophy of logic --Psychology and the a priori sciences --Do numbers exist? --Enhanced if-thenism.

Cambridge professor Simon Blackburn is best known to the general public as the author of several books of popular philosophy such as  ink, Being Good andTruth: a Guide for the Perplexed. Academic philosophers also know him as the author of one of the most important books of contemporary moral philosophy, Ruling Passions, and as a former editor of the leading journal Mind.

Simon Blackburn puts forward a compelling original philosophy of human motivation and morality. He maintains that we cannot get clear about ethics until we get clear about human nature. So these are the sorts of questions he addresses: Why do we behave as we do? Can we improve? Is our ethics at war with our passions, or is it an upshot of those passions? Blackburn seeks the answers in an exploration of guilt, shame, disgust, and other moral emotions; (...) he draws also on game theory and cognitive science in his account of the structures of human motivation. Many philosophers have wanted a naturalistic ethics a theory that integrates our understanding of human morality with the rest of our understanding of the world we live in. What is special about Blackburn's naturalistic ethics is that it does not debunk the ethical by reducing it to the non-ethical. At the same time he banishes the spectres of scepticism and relativism that have haunted recent moral philosophy. Ruling Passions sets ethics in the context of human nature: it offers a solution to the puzzle of how ethics can maintain its authority even though it is rooted in the very emotions and motivations that it exists to control. (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)

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.

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 goal of this paper is to sketch a distinctive version of naturalism in the philosophy of science, both by tracing historical antecedents and by addressing contemporary objections.

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)

The ageing society has profound consequences for accumulation in each state and region because pensions represent a claim on future income and output. Today's United States and United Kingdom pension crisis stems from a failing private sector with excessive costs and risk. Public provision using pay-asyou-go payroll taxes has, by contrast, proved highly cost-effective and equitable. However, aging and unequal cohorts create a need for extra resources. Retirement incomes should total 12 to 14 percent of gross domestic product if older (...) people's relative incomes are to be maintained. Raising such a sum solely from payroll taxes would generate the unemployment seen in continental Europe. The alternative is to redistribute capital to a regional network of social funds by requiring each corporation to issue shares equivalent to 10 percent of their profits annually to those funds. The share levy does not subtract from the corporation's cash flow and therefore protects employment and investment, but it does dilute the value of shareholding each year by a small amount. The social funds would not sell their shares but would keep them to generate income for future pensions. The social funds would supply a universal second pension; they could establish criteria of socially responsible governance in their use of shareholder power, and they would be subject to expert and democratic audit. (shrink)

Juliette Kennedy’s new book brims with intriguing ideas. I don’t understand all of them, and I’m not convinced that the ones I do understand all fit together, b.

For some time now, academic philosophers of mathematics have concentrated on intramural debates, the most conspicuous of which has centered on Benacerraf's epistemological challenge. By the late 1980s, something of a consensus had developed on how best to respond to this challenge. But answering Benacerraf leaves untouched the more advanced epistemological question of how the axioms are justified, a question that bears on actual practice in the foundations of set theory. I suggest that the time is ripe for philosophers of (...) mathematics to turn outward, to take on a problem of real importance for mathematics itself. (shrink)

It’s often said that set theory provides a foundation for classical mathematics because every classical mathematical object can be modeled as a set and every classical mathematical theorem can be proved from the axioms of set theory. This is obviously a remarkable mathematical fact, but it isn’t obvious what makes it ‘foundational’. This paper begins with a taxonomy of the jobs set theory does that might reasonably be regarded as foundational. It then moves on to category-theoretic and univalent foundations, exploring (...) to what extent they do these same jobs, and to what extent they might do other jobs also reasonably regarded as foundational. (shrink)

In this article I argue that we do not need a strict definition of naturalism, but can satisfactorily describe the naturalistic stance or attitude in terms of hostility to seeing human beings as subject to powers or forces or laws of nature that go beyond those governing the rest of the empirical world. We are to be explained as the evolutionary products of natural processes. I argue that we should see our concepts as well in this light, and explore some (...) examples of the way this attitude can illuminate questions of meaning. (shrink)

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)

The early sections describe the pre‐theoretic realism of the mathematician, survey the basic forms of realism in philosophy, and attempt to disentangle the issues of realism from debates over the nature of truth. The final section begins by laying out traditional Platonism, intuitionism, and formalism. Quine's famous critique of Carnap's conventionalism then leads to Quine's realism, and Putnam's developments thereof, while a different sort of mathematical realism is found in Gödel's writings. Set theoretic realism emerges as an effort to build (...) on the strengths of Quine's and Gödel's realisms, while avoiding their weaknesses and filling in their lacunae. (shrink)

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

Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the Sofia school , the method remains little known. In our view this has deprived temporal logic of a valuable tool.The aim of the paper is to explain why hybridization is useful in temporal logic. We make two major points, the first technical, the second conceptual. First, we show that hybridization gives rise to well-behaved (...) logics that exhibit an interesting synergy between modal and classical ideas. This synergy, obvious for hybrid languages with full first-order expressive strength, is demonstrated for a weaker local language capable of defining the Until operator; we provide a minimal axiomatization, and show that in a wide range of temporally interesting cases extended completeness results can be obtained automatically. Second, we argue that the idea of sorted atomic symbols which underpins the hybrid enterprise can be developed further. To illustrate this, we discuss the advantages and disadvantages of a simple hybrid language which can quantify over paths. (shrink)

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

A modal logic is developed to deal with finite ordered binary trees a they are used in linguistics. A modal language is introduced with operators for the ‘mother of’, ‘first daughter of’ and ‘second daughter of’ relations together with their transitive reflexive closures. The relevant class of tree models is defined and three linguistic applications of this language are discussed: context free grammars, command relations, and trees decorated with feature structures. An axiomatic proof system is given for which completeness is (...) shown with respect to the class of finite ordered binary trees. A number of decidability results follow. (shrink)

An original study of the philosophical problems associated with inductive reasoning. Like most of the main questions in epistemology, the classical problem of induction arises from doubts about a mode of inference used to justify some of our most familiar and pervasive beliefs. The experience of each individual is limited and fragmentary, yet the scope of our beliefs is much wider; and it is the relation between belief and experience, in particular the belief that the future will in some respects (...) resemble the past and the unobserved the observed, which forms the subject of this book. Dr Blackburn's first aim is to state the problem of induction properly, to show that there does exist a genuine problem immune to the solutions in vogue at present, yet no tin principle insoluble. He gives an extended and original account of the concept of a reason and goes on to discuss prediction. In the end Dr Blackburn produces a rationale for belief in certain short-term predictions based on his reinterpretation of the classical principle of indifference. He claims that a justification for induction can be found along the lines he has suggested and must indeed be found there if anywhere. (shrink)

This volume collects some influential essays in which Simon Blackburn, one of our leading philosophers, explores one of the most profound and fertile of philosophical problems: the way in which our judgments relate to the world. This debate has centered on realism, or the view that what we say is validated by the way things stand in the world, and a variety of oppositions to it. Prominent among the latter are expressive and projective theories, but also a relaxed pluralism (...) that discourages the view that there are substantial issues at stake. The figure of the "quasi-realist" dramatizes the difficulty of conducting these debates. Typically philosophers thinking of themselves as realists will believe that they alone can give a proper or literal account of some of our attachments--to truth, to facts, to the independent world, to knowledge and certainty. The quasi-realist challenge, developed by Blackburn in this volume, is that we can have those attachments without any metaphysic that deserves to be called realism, so that the metaphysical picture that goes with our practices is quite idle. The cases treated here include the theories of value and knowledge, modality, probability, causation, intentionality and rule-following, and explanation. A substantial new introduction has been added, drawing together some of the central themes. The essays articulate a fresh alternative to a primitive realist/anti-realist opposition, and their cumulative effect is to yield a new appreciation of the delicacy of the debate in these central areas. (shrink)

My aim in this paper is to propose what seems to me a distinctive approach to set theoretic methodology. By ‘methodology’ I mean the study of the actual methods used by practitioners, the study of how these methods might be justified or reformed or extended. So, for example, when the intuitionist's philosophical analysis recommends a wholesale revision of the methods of proof used in classical mathematics, this is a piece of reformist methodology. In contrast with the intuitionist, I will focus (...) more narrowly on the methods of contemporary set theory, and, more importantly, I will certainly recommend no sweeping reforms. Rather, I begin from the assumption that the methodologist's job is to account for set theory as it is practiced, not as some philosophy would have it be. This credo lies at the very heart of the so-called ‘naturalism’ to be described here.A philosopher looking at set theoretic practice from the outside, so to speak, might notice any number of interesting methodological questions, beginning with the intuitionist's ‘why use classical logic?’, but this sort of question is not a live issue for most practicing set theorists. One central question on which the philosopher's and the practitioner's interests converge is this: what is the status of independent statements like the continuum hypothesis (CH)? A number of large questions arise in its wake: what criteria should guide the search for new axioms? For that matter, what reasons support our adoption of the old axioms? (shrink)

In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a (...) wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic. (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 talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic—what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics—Logicism, Intuitionism, Formalism, Realism—and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam (...) are among the philosophers considered along the way. (shrink)