ABSTRACT
This chapter investigates the distinction between the abstract and the concrete, which is of fundamental importance for the nominalist–platonist debate. Platonism requires both the ontological thesis that entities like numbers exist as well as the categoreal thesis that such entities are abstract rather than concrete. The standard view incorporates various widespread assumptions about the abstract–concrete distinction. The formal features of the standard view suggest that the abstract–concrete distinction is a remarkably well-behaved divide in reality, separating entities into two exhaustive, disjoint ontological categories. Primitivists and reductionists agree that the abstract–concrete distinction has a place within the best metaphysical theories. According to the Way of Causation, abstract entities are distinguished precisely by their conspicuous absence from the causal order of the world. Numbers, propositions, and properties are perhaps the least contentious examples of necessary existents. According to the Way of Indiscernibility, it is possible that, for any concrete entity, there is some entity qualitatively indiscernible from it.
