David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:442 - 455 (1992)
Does science justify any part of mathematics and, if so, what part? These questions are related to the so-called indispensability arguments propounded, among others, by Quine and Putnam; moreover, both were led to accept significant portions of set theory on that basis. However, set theory rests on a strong form of Platonic realism which has been variously criticized as a foundation of mathematics and is at odds with scientific realism. Recent logical results show that it is possible to directly formalize almost all, if not all, scientifically applicable mathematics in a formal system that is justified simply by Peano Arithmetic (via a proof-theoretical reduction). It is argued that this substantially vitiates the indispensability arguments
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Justin Clarke-Doane (2014). Moral Epistemology: The Mathematics Analogy. Noûs 48 (2):238-255.
Similar books and articles
Geoffrey Hellman (1992). On the Scope and Force of Indispensability Arguments. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:456 - 464.
Susan Vineberg (1996). Confirmation and the Indispensability of Mathematics to Science. Philosophy of Science 63 (3):263.
Solomon Feferman, The Development of Programs for the Foundations of Mathematics in the First Third of the 20th Century.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Stewart Shapiro (2004). Foundations of Mathematics: Metaphysics, Epistemology, Structure. Philosophical Quarterly 54 (214):16 - 37.
David Liggins (2008). Quine, Putnam, and the 'Quine-Putnam' Indispensability Argument. Erkenntnis 68 (1):113 - 127.
Stewart Shapiro (2000). Set-Theoretic Foundations. The Proceedings of the Twentieth World Congress of Philosophy 2000:183-196.
Peter Schreiber (1996). Mengenlehre—Vom Himmel Cantors Zur Theoria Prima Inter Pares. NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 4 (1):129-143.
Carlo Cellucci (2003). Review of M. Giaquinto, The Search for Certainty. [REVIEW] European Journal of Philosophy 11:420-423.
Marcus Rossberg & Daniel Cohnitz (2009). Logical Consequence for Nominalists. Theoria. An International Journal for Theory, History and Foundations of Science 24 (2):147-168.
Michael Resnik (1995). Scientific Vs. Mathematical Realism: The Indispensability Argument. Philosophia Mathematica 3 (2):166-174.
Richard Pettigrew (2012). Indispensability Arguments and Instrumental Nominalism. Review of Symbolic Logic 5 (4):687-709.
Thomas Hofweber (2000). Proof-Theoretic Reduction as a Philosopher's Tool. Erkenntnis 53 (1-2):127-146.
Added to index2010-12-22
Total downloads14 ( #113,509 of 1,100,740 )
Recent downloads (6 months)1 ( #289,271 of 1,100,740 )
How can I increase my downloads?