Objectivity in Mathematics, Without Mathematical Objects†

Philosophia Mathematica 29 (3):318-352 (2021)
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Abstract

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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Markus Pantsar
Aachen University of Technology

References found in this work

The origin of concepts.Susan Carey - 2009 - New York: Oxford University Press.
A System of Logic.John Stuart Mill - 1829/2002 - Longman.
Truth and objectivity.Crispin Wright - 1992 - Cambridge, Mass.: Harvard University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.

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