Abstract
Indispensablists argue that when our belief system conflicts with our experiences, we can negate a mathematical belief but we do not because if we do, we would have to make an excessive revision of our belief system. Thus, we retain a mathematical belief not because we have good evidence for it but because it is convenient to do so. I call this view ‘mathematical convenientism.’ I argue that mathematical convenientism commits the consequential fallacy and that it demolishes the Quine–Putnam indispensability argument and Baker’s enhanced indispensability argument.
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References
Baker A (2005) Are there genuine mathematical explanations of physical phenomena? Mind 114(454):223–237
Baker A (2009) Mathematical explanation in science. Br J Philos Sci 60(3):611–633
Baker A (2012) Science-driven mathematical explanation. Mind 121(482):243–267
Busch J (2012) The indispensability argument for mathematical realism and scientific realism. J Gen Philos Sci 43(1):3–9
Colyvan M (2001) The indispensability of mathematics. Oxford University Press, New York
Colyvan M (2006) Scientific realism and mathematical nominalism: a marriage made in hell. In: Cheyne C, Worrall J (eds) Rationality and reality: conversations with Alan Musgrave. Springer, Dordrecht
Deheane S (2011) The number sense: how the mind creates mathematics. Oxford University Press, Oxford
Kitcher P (1993) The advancement of science. Oxford University Press, New York
Lakoff G, Núñez RE (2001) Where mathematics comes from: how the embodied mind brings mathematics into being. Basic Books, New York
Laudan L (1981) A confutation of convergent realism. Philos Sci 48(1):19–49
Maddy P (1992) Indispensability and practice. J Philos 89(6):275–289
Parsons C (1983) Philosophy in mathematics: selected essays. Cornell University Press, Ithaca
Psillos S (1999) Scientific realism: how science tracks truth. Routledge, New York
Putnam H (1971) Philosophy of logic. Harper and Row, New York
Putnam H (1979) Philosophy of logic. Reprinted in mathematics matter and method: philosophical papers, vol 1, 2nd edn. Cambridge University Press, Cambridge
Quine WVO (1948) On what there is. Rev Metaphys 2(5):21–38
Quine WVO (1980) From a logical point of view, 2nd edn. Harvard University Press, Cambridge
Quine WVO (1992) Pursuit of truth. Harvard University Press, Cambridge
Resnik M (1997) Mathematics as a science of patterns. Clarendon Press, Oxford
Salmon M (2007) Introduction to logic and critical thinking, 5th edn. Thomson Wadsworth, Stamford
Acknowledgments
I am grateful to anonymous referees for sharp criticisms.
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Park, S. Against Mathematical Convenientism. Axiomathes 26, 115–122 (2016). https://doi.org/10.1007/s10516-015-9281-z
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DOI: https://doi.org/10.1007/s10516-015-9281-z