Platonic Semantics

Justin Clarke-Doane (Monash University)

A common view in metaphysics is that whatever costs platonism about an area may incur by way of ontological extravagance or epistemological mystery, it allows us to “take the semantic appearances atface-value”.  In this talk, I will argue that this common view is mistaken.  Although the platonist can allow that the logical form of
sentences from a relevant area mirrors the syntax of those sentences, she can only do this at the cost of reinterpreting the corresponding predicates.  To take a simple example, the mathematical platonist can hold that the sentence “The Triangle has three sides” is true, and of the logical form “a is F” (or “there is exactly one G that is F”).  However, she cannot do this if she takes the predicate at face value, to express the property of having three sides.  As an abstract object, The Triangle cannot literally have any sides.  Similar points apply to
sentences apparently about other sorts of object which are commonly thought to be abstract, such as fictional objects, natural kinds, and works of art.  One upshot of the discussion is that abstract objects have no unique explanatory capacities. Slices of a table would serve
their purpose equally.  Another upshot is that we should rethink our methodology in metaphysics.