Descartes and Buddhism

I find it interesting that one of the central ideas in Buddhism is the non-existence of the self.  This is in direct contrast with Descartes' famous 'cogito ergo sum' idea, which states that the existence of the self is the only thing that one can be certain of.  I wonder how a Buddhist would respond to Descartes' reasoning - would they say that the apparent self is actually just a collection of attributes which can under certain circumstance break apart?  Would they say that the consciousness perceiving the (possibly illusionary, by both theories) world is not the self, but a universal consciousness that is simply manifested in parts?

Not being sufficiently well-versed in Buddhist doctrine myself, I cannot make any assertions about the answer with any confidence.  If anyone would like to suggest ideas, I would very much appreciate it!