First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

Henry E. Allison presents a comprehensive commentary on Kant's Groundwork for the Metaphysics of Morals. Allison pays special attention to the structure of the work and its historical and intellectual context. He argues that, despite its relative brevity, the Groundwork is the single most important work in modern moral philosophy.

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)

Born in 1838, Mach was a pioneer in the field of physics, having even made an impression on Einstein in his younger life who credited him with being the "Philosophical forerunner of relativity theory." His name is also associated with the speed of sound (as in traveling at Mach "insert-number-here") as well as the Doppler effect. Throughout his career, he was particularly interested in the biological and sensory relationship to physics and science, and naturally, this interest expanded to that of (...) the world of psychological perception and physiological psychology as well as philosophy. The Analysis of Sensations is about just that, the nature of the relationship of physics and the physical sciences to psychological phenomena of sense and perception. It's a fascinating read for anyone looking to expand their knowledge of how the two sides of the same coin meld harmoniously. (shrink)

This paper distinguishes revolutionary fictionalism from other forms of fictionalism and also from other philosophical views. The paper takes fictionalism about mathematical objects and fictionalism about scientific unobservables as illustrations. The paper evaluates arguments that purport to show that this form of fictionalism is incoherent on the grounds that there is no tenable distinction between believing a sentence and taking the fictionalist's distinctive attitude to that sentence. The argument that fictionalism about mathematics is ‘comically immodest’ is also evaluated. In place (...) of those arguments, an argument against fictionalism about abstract objects of any kind is presented in the last section. This argument takes the form of a trilemma against the fictionalist. (shrink)

The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.

Mark Balaguer has written a provocative and original book. The book is as ambitious as a work of philosophy of mathematics could be. It defends both of the dominant views concerning the ontology of mathematics, Platonism and Anti-Platonism, and then closes with an argument that there is no fact of the matter which is right.

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument (...) for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct. (shrink)

This book does three main things. First, it defends mathematical platonism against the main objections to that view (most notably, the epistemological objection and the multiple-reductions objection). Second, it defends anti-platonism (in particular, fictionalism) against the main objections to that view (most notably, the Quine-Putnam indispensability objection and the objection from objectivity). Third, it argues that there is no fact of the matter whether abstract mathematical objects exist and, hence, no fact of the matter whether platonism or anti-platonism is true.

Ogden spent over forty years attempting "to deal... with the whole of the linguistic problem." This study gives his work an enduring quality which is of particular relevance to late twentieth century linguistics.

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. (shrink)

Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

Fictionalism in ontology is a mixed bag. Here I focus on three main variants—which I label after the names of Pascal, Berkeley, and Hume—and consider their relative strengths and weaknesses. The first variant is just a version of the epistemic Wager, applied across the board. The second variant builds instead on the fact that ordinary language is not ontologically transparent; we speak with the vulgar, but deep down we think with the learned. Finally, on the Humean variant it’s the structure (...) of the ontological inventory, not its content, that may turn out to involve fictional elements. That is, for the Humean the fiction lies, not in the reality of common-sense ontology, but in the laws—of unity, identity, causation, etc.—in terms of which we articulate our experience of that reality. In the end, this is the kind of fictionalism that I find most interesting, sensible, and tenable. And I argue that it is even compatible with the sort of “naive” realism we have all come to appreciate in the work of Paolo Bozzi, to whom the paper is dedicated. (shrink)