What's Wrong with Indispensability? (Or, the Case for Recreational Mathematics)

• Published in: Synthese (Dordrecht) Vol. 131; no. 3; pp. 395 - 417
• Main Author: Leng, Mary
• Format: Journal Article
• Language: English
• Published: Dordrecht Kluwer Academic Publishers 01.06.2002; Springer; Springer Nature B.V
• Subjects: 20th century; Axioms; Catastrophe theory; History; History of science and technology; Holism; Indispensability argument; Mathematical models; Mathematical objects; Mathematical realism; Mathematical sciences and techniques; Mathematical set theory; Mathematicians; Mathematics; Naturalism; Philosophy; Realism; Recreation; Science; Scientists; Theory; Holism; Platonism; Quine (W. V. O.); Realism; Practice; Science; Mathematics; Naturalism; Confirmation; Arithmetic
• ISSN: 0039-7857; 1573-0964
• DOI: 10.1023/A:1016141509719

For many philosophers not automatically inclined to Platonism, the indispensability argument for the existence of mathematical objects has provided the best (and perhaps only) evidence for mathematical realism. Recently, however, this argument has been subject to attack, most notably by Penelope Maddy (1992, 1997), on the grounds that its conclusions do not sit well with mathematical practice. I offer a diagnosis of what has gone wrong with the indispensability argument (I claim that mathematics is indispensable in the wrong way), and, taking my cue from Mark Colyvan's (1998) attempt to provide a Quinean account of unapplied mathematics as 'recreational', suggest that, if one approaches the problem from a Quinean naturalist starting point, one must conclude that all mathematics is recreational in this way.