Saturday, March 12, 2011
In another post I argued that there seems to be some reason to think that some abstract objects occupy physical space. A (impure) set containing some material object(s) for example.
There are classes of problems in philosophy that this conclusion may be related. Consider the causal theory of knowledge (I believe first proposed by Alvin Goldman). One of the objections to this theory of knowledge is that it can't seem to explain how we come to have knowledge about abstract objects like sets and numbers. But if coincident objects (say, a set containing a car as only element and the car itself) can be thought as two objects which completely overlap spatio-temporally, then can't we think of these two objects as affecting other objects (physical or abstract) when they interact with them? In other words, if some abstract objects occupy space (compare the Cartesian concept of "res extens") like physical objects do, can't they also interact with physical objects? Doesn't it make sense to say that both the car caused the accident or, (albeit awkwardly) that the car's singleton caused the accident?
If so then at least some abstract objects can cause effects in the physical world. But if it makes sense to say that some sets may cause effects in the physical world, why not all? Other problems with dualism which asks how the mind, if it is not material, can cause physical effects by controlling the body, etc may also be less problematic once this once thought problematic issue is not thought so problematic. Relatedly, the ancient Nyaya philosophers of mind, as far as I know, had no problems with abstracta being extended in space or time such as their conceptions of the mind. That may be why they didn't seem to have much problems with mind-body causation despite being dualists.