Mathematical explanation and indispensability arguments

Philosophical Quarterly

Volumn 59, Issue 237, 2009, Pages 641-658

  Daly, Chris ^a   Langford, Simon ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 73949148929     PISSN: 00318094     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9213.2008.601.x     Document Type: Review

References (14)

1. This premise can be and has been contested, but we shall not engage with arguments on this issue here. See H. Field, Science without Numbers (Oxford: Blackwell, 1980), for an attempt to dispense with mathematics
2. See W.V. Quine, 'Two Dogmas of Empiricism', Philosophical Review, 60 (1951), pp. 20-43
3. §VI, and H. Putnam, Philosophy of Logic (New York: Harper & Row, 1971), §VIII, for early statements of this style of argument
4. J. Melia, 'Weaseling Away the Indispensability Argument', Mind, 109 (2000), pp. 455-79
5. Similar arguments have since been offered by M. Leng, 'What's Wrong with Indispensability?', Synthese, 131 (2002), pp. 395-417
6. §§5-6, who speaks of mathematics as merely modelling concrete facts, and C. Pincock, 'A Revealing Flaw in Colyvan's Indispensability Argument', Philosophy of Science, 71 (2004), pp. 61-79, §3, who speaks of mathematics as merely mapping onto concrete facts
7. M. Colyvan, The Indispensability of Mathematics, henceforth IM (Oxford UP, 2001), and 'Mathematics and Aesthetic Considerations in Science', henceforth MACS, Mind, 111 (2002), pp. 69-74
8. A. Baker, 'Are There Genuine Mathematical Explanations of Physical Facts?', Mind, 114 (2005), pp. 223-38
9. C. Swoyer, 'Structural Representation and Surrogative Reasoning', Synthese, 87 (1991), pp. 449-508, at pp. 451-2
10. See, for example, C. Mortensen, 'Arguing for Universals', Revue Internationale de Philosophie, 160 (1987), pp. 97-111, at p. 105
11. Melia, 'Response to Colyvan', Mind, 111 (2002),pp. 75-9, at p. 76
12. Colyvan, IM, p. 83. Colyvan's example is also discussed by Pincock, §5
13. See F. Jackson and P. Pettit, 'Functionalism and Broad Content', Mind, 107 (1988), pp. 381-400, at pp. 391-7
14. A referee rightly pointed out that it is contentious at best to classify a duration as a concrete phenomenon. Many philosophers would count a duration as abstract. This raises the pertinent but vexed issue of how the abstract/concrete distinction is to be drawn. It also recalls a familiar criticism of Hartry Field's philosophy of mathematics. Although Field avowedly posits only concrete objects, he posits space-time points. Yet some philosophers would count a space-time point as abstract: cf. the discussion in M.D. Resnik, review of Field's Science without Numbers, Noûs, 17 (1983), pp. 514-19, at p. 516. Our working definition of 'concrete object' is that x is a concrete object if and only if x stands in a space-time relation to another object, and x has causal powers. By this definition, durations and space-time points arguably both count as concrete objects