Skip to content
Narrow screen resolution Wide screen resolution Auto adjust screen size Increase font size Decrease font size Default font size

Philosophia Verlag GmbH

Home arrow Philosophia Contributions to Philosophy arrow Can Set Theory Be Nominalized?
Info: Your browser does not accept cookies. If you want to put products into your cart and purchase them you need to enable cookies.


 


Otávio Bueno

Can Set Theory Be Nominalized?

A Fictionalist Response

ISBN: 978-3-88405-512-0

Price: €18.00 (including 19 % tax)


Abstract

A
number of nominalist approaches to mathematics have been developed: Field’s [1980] conservative nominalism, Hellman’s [1989] modal-structuralism, Lewis’ [1990] megethology (under a certain interpretation), and Azzouni’s [2004] deflationary nominalism. In this paper, Bueno argues that all of these approaches face a serious problem: they fail to provide an adequate nominalization strategy for set theory. Field’s approach ultimately presupposes such a nominalization, but B. argues that it is unable to provide one. It is part of Hellman’s approach to offer tentatively a nominalist reformulation of set theory. However, the approach faces difficulties with the interpretation of the second-order quantifier and the modal operators introduced. Lewis’ proposal - under a certain interpretation - also attempts to provide a nominalization of set theory. However, if the nominalization were to be carried out, it would make set theory contingent upon the size of reality, which conflicts with the way in which the theory is typically conceived. Finally, Azzouni’s proposal faces some tensions that emerge from the alleged ontological independence of sets. I conclude that set theory becomes the crucial area in which nominalists should concentrate their efforts if nominalism is to become a plausible account. I then sketch a fictionalist alternative that does not face the difficulties above.

About the Author

Otávio Bueno is Professor of Philosophy at the University of Miami. He has held visiting professorships or fellowships at Princeton University, University of York (in the
UK), University of Leeds, and at the University of São Paulo. His research concentrates in philosophy of science, philosophy of mathematics, and philosophy of logic. He has published widely in journals and collections, including: Noûs, Mind, Philosophy of Science, Synthese, Journal of Philosophical Logic, Studies in History and Philosophy of Science, British Journal for the Philosophy of Science, Analysis, Erkenntnis, History and Philosophy of Logic, and Logique et Analyse. He is the author of two books, Constructive Empiricism: A Restatement and Defense (CLE, 1999), and Elements of Paraconsistent Set Theory (CLE, 1998; with Newton da Costa and Jean-Yves Béziau). And he edited New Waves in Philosophy of Mathematics (Palgrave-Macmillan, 2009; with Øystein Linnebo).

e-mail: otaviobueno@mac.com

http://web.me.com/otaviobuno/Site/Otavio_Bueno.html




 





new publications

Cosmetics and Makeup
Cosmetics and Makeup
€9.80
Add to Cart

The Virtue Analysis of Inner Beauty: Inner Beauty as Moral, Eudaimonistic, or Relational Virtueness
The Virtue Analysis of Inner Beauty: Inner Beauty as Moral, Eudaimonistic, or Relational Virtueness
€14.80
Add to Cart

The Beauty of Landscape
The Beauty of Landscape
€9.80
Add to Cart

Aesthetic Experience and the Experience of Poetry
Aesthetic Experience and the Experience of Poetry
€14.80
Add to Cart

An Aesthetics of Insight
An Aesthetics of Insight
€14.80
Add to Cart

The Case Against Beauty
The Case Against Beauty
€14.80
Add to Cart

The Beauty of Doing: Remarks on the Appreciation of Conceptual Art
The Beauty of Doing: Remarks on the Appreciation of Conceptual Art
€14.80
Add to Cart

The Value of Art: On Meaning and Aesthetic Experience in Difficult Modern Art
The Value of  Art: On Meaning and Aesthetic Experience in Difficult Modern Art
€9.80
Add to Cart

Art, Beauty, and Criticism
Art, Beauty, and Criticism
€9.80
Add to Cart

Beauty and Bell’s Aesthetic Emotion
Beauty and Bell’s Aesthetic Emotion
€14.80
Add to Cart