Philosophia Mathematica:nkab010 (forthcoming)

Markus Pantsar
University of Helsinki
I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects.
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DOI 10.1093/philmat/nkab010
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References found in this work BETA

The Origin of Concepts.Susan Carey - 2009 - Oxford University Press.
Truth and Objectivity.Crispin Wright - 1992 - Harvard University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.

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