On the Scope and Force of Indispensability Arguments
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:456 - 464 (1992)
| Abstract | Three questions are highlighted concerning the scope and force of indispensability arguments supporting classical, infinitistic mathematics. The first concerns the need for non-constructive reasoning for scientifically applicable mathematics; the second concerns the need for impredicative set existence principles for finitistic and scientifically applicable mathematics, respectively; and the third concerns the general status of such arguments in light of recent work in mathematical logic, especially that of Friedman et al. and Feferman et al. Some recent results (of Pour-El and Richards and of the author) are then presented bearing on the first question on the need for non-constructive analysis, especially for quantum physics. Despite the impressive work of Bishop et al. in constructive analysis, Hilbert's objection to intuitionism still carries significant force, and may be decisive depending in part on one's conception of "physics". | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | No categories specified (fix it) | |||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,679 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesSolomon Feferman (1992). Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:442 - 455.
Richard Pettigrew (forthcoming). Indispensability Arguments and Instrumental Nominalism. Review of Symbolic Logic.
Otávio Bueno (2010). Quine's Double Standard: Undermining the Indispensability Argument Via the Indeterminacy of Reference. Principia 7 (1-2):17-39.
David Liggins (2008). Quine, Putnam, and the 'Quine-Putnam' Indispensability Argument. Erkenntnis 68 (1):113 - 127.
Anne Newstead & James Franklin (2012). Indispensability Without Platonism. In Alexander Bird, Brian Ellis & Howard Sankey (eds.), Properties, Powers and Structures. Routledge.
Pieranna Garavaso (2005). On Frege's Alleged Indispensability Argument. Philosophia Mathematica 13 (2):160-173.
Lieven Decock (2002). Quine's Weak and Strong Indispensability Argument. Journal for General Philosophy of Science 33 (2):231-250.
Geoffrey Hellman (1997). Quantum Mechanical Unbounded Operators and Constructive Mathematics – a Rejoinder to Bridges. Journal of Philosophical Logic 26 (2):121-127.
Helen Billinge (2003). Did Bishop Have a Philosophy of Mathematics? Philosophia Mathematica 11 (2):176-194.
H. Billinge (2000). Applied Constructive Mathematics: On Hellman's 'Mathematical Constructivism in Spacetime'. British Journal for the Philosophy of Science 51 (2):299-318.
Chris Pincock (2007). A Role for Mathematics in the Physical Sciences. Noûs 41 (2):253 - 275.
C. Juhl (2012). On the Indispensability of the Distinctively Mathematical. Philosophia Mathematica 20 (3):324-338.
Mark Colyvan (1998). In Defence of Indispensability. Philosophia Mathematica 6 (1):39-62.
Analytics
Monthly downloads
Sorry, there are not enough data points to plot this chart.
|
Added to index2011-05-29Total downloads0Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
