This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed (...) by human activity in a manner similar to the constitutive construction of the US Supreme Court by certain legal and political activities. Finally, I outline some of the philosophical merits of metaphysical interpretations of mathematical theories of this type. (shrink)

This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...) and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism. (shrink)

This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), (...) the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy. (shrink)

I argue that Monique Wittig's view that lesbians are not women neglects the complexities involved in the composition of the category "woman." I develop an articulation of the concept "woman" in the contemporary United States, with thirteen distinct defining characteristics, none of which are necessary nor sufficient. I argue that Wittig's emphasis on the material production of "woman" through the political regime of heterosexuality, however, is enormously fruitful for feminist and queer strategizing.

Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given (...) axioms. Moreover, all the evidence suggests that all practitioners work with the same ontology. (My number 7 is exactly the same as yours.) How can we reconcile the notion that people construct mathematics, with this apparent choice-free, predetermined objectivity? I believe the answer is to be found by examining what mathematical thinking is (as a mental activity) and the way the human brain acquired the capacity for mathematical thinking. (shrink)

Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)

Essays cover historical, sociological, psychological and anthropological approaches, ethics and politics, and the policy implications of the real and perceived differences between the sexes.

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

This book of sixteen original essays is the first to explore this range of new developments in the philosophy of mathematics, in a language accessible to ...

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic (...) problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians. (shrink)

Especially troublesome in this dispute is the status of the natural sciences, and this is where Hacking finds some of his most telling cases, from the conflict ...

White supremacy is the unnamed political system that has made the modern world what it is today. You will not find this term in introductory, or even advanced, texts in political theory. A standard undergraduate philosophy course will start off with plato and Aristotle, perhaps say something about Augustine, Aquinas, and Machiavelli, move on to Hobbes, Locke, Mill, and Marx, and then wind up with Rawls and Nozick. It will introduce you to notions of aristocracy, democracy, absolutism, liberalism, representative government, (...) socialism, welfare capitalism, andlibertarianism. But though it covers more than two thousand years of Western political thought and runs the ostensible gamut of political systems, there will be no mention of the basic political system that has shaped the world for the past several hundred years. And this omission is not accidental. Rather, it reflects the fact that standard textbooks and courses have for the most part been written and designed by whites, who take their racial privilege so much for granted that they do not even see it as political, as a form of domination. Ironically, the most important political system of recent global history-the system of domination by which white people have historically ruled over and, in certain important ways, continue to rule over nonwhite people-is not seen as a political system at all. It is just taken for granted; it is the background against which other systems, which we are to see as political are highlighted. This book is an attempt to redirect your vision, to make you see what, in a sense, has been there all along. (shrink)

John Searle began to discuss his recently published book `The Construction of Social Reality' with Anthony Freeman, and they ended up talking about God. The book itself and part of their conversation are introduced and briefly reflected upon by Anthony Freeman. Many familiar social facts -- like money and marriage and monarchy -- are only facts by human agreement. They exist only because we believe them to exist. That is the thesis, at once startling yet obvious, that philosopher John Searle (...) explores in The Construction of Social Reality. (shrink)

I discuss social constructivism in the philosophy of mathematics and argue for a novel variety of social constructivism that I call Practice-Dependent Realism.