Metaphysics/Epistemology

This book presents an expanded edition of the author's exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, the book engages with issues across philosophical borders, from the historical to the modern, from Eastern to Western, and from the continental to the analytic. This edition of the text includes new chapters on European and Indian philosophy, and reflections on responses to the previous edition of the book.

This book provides a presentation of views on the relations between metaphysics and logic from Aristotle through twentieth century philosophers who contributed to the return of metaphysics in the analytic tradition. The collection combines interest in logic and its history with interest in analytical metaphysics and the history of metaphysical thought. The focus is on metaphysica generalis, or the systematic study of the most general categories of being. The volume aims at historical coverage of certain influential figures and themes. As the tradition is very rich, some choices between important philosophers and topics cannot be avoided. The volume seeks for a balance between different periods; still, early modern, modern and twentieth century metaphysics are more extensively studied than the pre-modern tradition. Thinkers discussed include Aristotle, Avicenna, Thomas Aquinas, Duns Scotus, William Ockham, Gottfried Wilhelm Leibniz, Immanuel Kant, Georg Wilhelm Friedrich Hegel, Bernard Bolzano, Charles Sanders Peirce, Georg Cantor, Gottlob Frege, Alexius Meinong, Edmund Husserl, Bertrand Russell, G. E. Moore, C. I. Lewis, Martin Heidegger, Ludwig Wittgenstein, Rudolf Carnap, Willard Van Orman Quine, Wilfrid Sellars, Peter F. Strawson, Ruth Barcan Marcus, David Armstrong, Saul Kripke, and David Lewis. Not all of these have a chapter of their own, however, for some figure only in connection with other thinkers and specific themes related with their work. The individual chapters seek to cover more than one philosopher's thought and also to take notice of other periods in the history than what is their main focus.

This account of rational belief revision explains how a rational agent ought to proceed when adopting a new belief — a difficult matter if the new belief contradicts the agent’s old beliefs. Belief systems are modeled as finite dependency networks. So one can attend not only to what the agent believes, but also to the variety of reasons the agent has for so believing. The computational complexity of the revision problem is characterized. Algorithms for belief revision are formulated, and implemented in Prolog. The implementation tests well on a range of simple belief‐revision problems that pose a variety of challenges for any account of belief‐revision. The notion of ‘minimal mutilation’ of a belief system is explicated precisely. The proposed revision methods are invariant across different global justificatory structures (foundationalist, coherentist, etc.). They respect the intuition that, when revising one's beliefs, one should not hold on to any belief that has lost all its former justifications. The limitation to finite dependency networks is shown not to compromise theoretical generality. This account affords a novel way to argue that there is an inviolable core of logical principles. These principles, which form the system of Core Logic, cannot be given up, on pain of not being able to carry out the reasoning involved in rationally revising beliefs. The book ends by comparing and contrasting the new account with some major representatives of earlier alternative approaches, from the fields of formal epistemology, artificial intelligence and mathematical logic.

Vagueness is a familiar but deeply puzzling aspect of the relation between language and the world. It is highly controversial what the nature of vagueness is; a feature of the way we represent reality in language, or rather a feature of reality itself? Assuming standard logical principles, Sorites' arguments suggest that vague terms are either inconsistent or have a sharp boundary. The account we give of such paradoxes plays a pivotal role for our understanding of natural languages. If our reasoning involves any vague concepts, is it safe from contradiction? Do vague concepts really lack any sharp boundary? If not, why are we reluctant to accept the existence of any sharp boundary for them? And what rules of inference can we validly apply, if we reason in vague terms? This book presents the latest work towards a clearer understanding of these old puzzles about the nature and logic of vagueness. The collection offers a stimulating series of original chapters on these and related issues by some of the world's leading experts.

Mathematics depends on proofs, and proofs have to begin somewhere, from some fundamental assumptions. Chapter I traces the historical rise of pure mathematics and the development of set theory, eventually axiomatic set theory, to play this foundational role for contemporary classical mathematics. Here the Euclidean ideal of postulates that are simply obvious or self-evident can't be the whole story, which raises two basic questions: what are the proper methods for defending set-theoretic axioms? And, why are these the proper methods? Chapter II introduces the meta-philosophical perspective, called Second Philosophy, from which the inquiry into these questions will take place, and identifies straightforward mathematical answers to the first question. Addressing the second requires engagement with the troublesome ontological and epistemological issues that have dogged the philosophy of mathematics from its beginnings. Chapters III and IV describe and explore two apparently conflicting stands on these issues—called Thin Realism and Arealism—not so much to recommend either one, but with an eye to suggesting that the question of which is correct has less bite than it might appear. In the end, the hope is to shift attention away from these elusive matters of truth and existence, and to direct it toward the distinctive type of mathematical objectivity emphasized in the opening section of Chapter V. The concluding sections of chapter V return, at last, to the question of set-theoretic method and draw some concrete morals for the project of defending the axioms.

This book offers a defence of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focused on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. This book, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.

The philosophy of modality investigates necessity and possibility, and related notions — are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This book presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the chapters address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal logic and its relations to necessary existence and to counterfactual reasoning. The general introduction locates the individual contributions in the wider context of the contemporary discussion of the metaphysics and epistemology of modality.

The relationship of part to whole is one of the most fundamental there is. This book shows that mereology, the formal theory of part and whole, is essential to ontology. This book surveys and criticises previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. This has far-reaching consequences for our understanding of such classical philosophical concepts as identity, individual, class, substance and accident, matter, form, essence, dependence, and integral whole. The book offers new solutions to long-standing problems surrounding these concepts, such as the Ship of Theseus Problem and the issue of mereological essentialism. The book shows by its use of formal techniques that classical philosophical problems are amenable to rigorous treatment, and the book represents a synthesis of issues and methods from the analytical tradition and from the older continental realist tradition of Franz Brentano and the early Edmund Husserl.

This book contains a collection of twelve metaphysical chapters that address a range of first-order topics, including identity, coincidence, essence, causation, and properties. Some first-order debates are not worth pursuing, the book argues; there is nothing at issue in them. Several of the chapters explore the metaontology of abstract objects, and more generally of objects that are ‘preconceived’, their principal features being settled already by their job-descriptions. The book rejects standard forms of fictionalism, opting ultimately for a view that puts presupposition in the role normally played by pretense.