What is the epistemological argument against mathematical Platonism?

The epistemological argument against mathematical Platonism centers on the difficulty of explaining how humans, who exist entirely within space-time, can acquire knowledge of abstract objects that are, by definition, nonspatiotemporal and noncausal.12

The argument is structured as follows:
* (1) Humans exist entirely within space-time.
* (2) If abstract objects exist, they exist entirely outside of space-time.
* (3) Therefore, humans cannot acquire knowledge of abstract objects.1

Platonists have proposed several strategies to address this challenge:
* Rejecting (1): Some argue the human mind is not entirely physical and can forge contact with abstract objects, such as through Plato’s theory of recollection or Kurt Gödel’s faculty of mathematical intuition.1
* Rejecting (2): Penelope Maddy suggested that certain abstracta, like sets of physical objects, are spatiotemporally located and thus perceivable.1
* Accepting (1) and (2): Others argue knowledge is acquired through pattern recognition, empirical scientific evidence, or full-blooded Platonism, which posits that internally consistent axiom systems describe parts of the mathematical realm.1