A Revealing Flaw in Colyvan's Indispensability Argument.

Pincock, Christopher

Mark Colyvan uses applications of mathematics to argue that mathematical entities exist. I claim that his argument is invalid based on the assumption that a certain way of thinking about applications, called 'the mapping account,' is correct. My main contention is that successful applications depend only on there being appropriate structural relations between physical situations and the mathematical domain. As a variety of non-realist interpretations of mathematics deliver these structural relations, indispensability arguments are invalid.

MATHEMATICAL functions; MATHEMATICAL programming; CYBERNETICS; STATISTICS; COLYVAN, Mark; MATHEMATICAL mappings

Philosophy of Science, 2004, Vol 71, Issue 1, p61

0031-8248

Academic Journal

10.1086/381413