Pleas against Balaguer’s superplatonism
DOI:
https://doi.org/10.4013/fsu.2016.171.05Abstract
Mark Balaguer has developed a quirky brand of mathematical plat onism – called ‘full-blooded platonism’ or ‘FBP’ – in order to solve Benacerraf’s problem about the inaccessibility of abstract entities. According to FBP, every mathematical object that can consistently be characterized thereby exists, although contingently so. In this paper I would like to show that ontological plenitude and modal contingency cannot converge into a philosophically respectable theory of mathematical objects. To achieve this, I argue that FBP does not cover some basic factors of epistemic reliability and that it involves a criterion of plenitude both mathematically and metaphysically implausible.
Keywords: Balaguer, Benacerraf, consistency, contingency, superplatonism.
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