ABSTRACT
This chapter surveys arguments against platonism that turn on the non-causal nature of abstract entities. It examines arguments for nominalism stemming from the alleged causal inactivity, and the resulting lack of epistemic, semantic, or cognitive access, to abstract entities. According to Eleatics, causal activity is a prerequisite for existence. So, if abstract entities are indeed causally inactive, Eleaticism entails that there are no abstract entities. The causal constraint also faces a range of putative counter examples that are independent of concerns about mathematical knowledge. Epistemic access arguments proceed from the plausible observation that causal relations structure our cognitive and epistemic life. The primitivist approach provides a response to the cognitive access problem. It also furnishes platonists with an important resource for addressing the epistemic and semantic access problems. If mathematical platonism is true, the reliable connection between abstract mathematical entities and mathematicians' beliefs about mathematics must be, in principle, explicable.
