Monday, February 28, 2011

Argument for the existence of coincident objects?

In a previous post, I mentioned that I believe in coincident objects. Here is another argument for their existence. It seems very likely that impure sets exist. Impure sets are even more plausible than the pure sets of mathematics which are either the null set or sets built up from the null set by certain (mental operations or otherwise) "operations." Thus you seem to get everything in the mathematical world out of nothing, ex nihilo. That may seem counter intuitive. But impure sets are sets that contain concrete objects such as the set containing president Obama and the world's largest potato. If any sets exist, impure sets must exist. A set is just a collection of objects. And surely, collections of individual objects exist as much as individual objects exists.

Now consider the set containing you, the person. Now consider another: the set containing all your cells. These are clearly two different sets as one has as its sole element, you, and the other contains more than a trillion elements. But it seems that both these sets occupy the same space-time region. (Also consider the set containing you as another example).

Some may object by saying that since all sets are abstract including impure sets, they don't really occupy any region of space-time even if all their elements do and thus, the two sets don't really coincide. I'm not sure what to say about this. I'm not sure of its coherence to say that a set (which by definition is just the collection of its elements) is not instantiated in space-time but all its elements are. A corollary of this is that some abstract objects really occupy regions of space-time such as impure sets as weird as that sounds.