Objectivity in Mathematics, Without Mathematical Objects†

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