Furthermore, if our thoughts exist, then don't we also exist? Our body might not be real, but our thoughts are, which means that - 'I think, therefore I exist'. To quote Descartes: "I am, I exist". If this were to be put in a proper argument form, then it would be:
- Everything that thinks exists.
- I am thinking.
- I am existing.
(In the meditations Descartes never says: "I think therefore I am", but he says it in a response to a criticism). Now Descartes has the foundations for existence, and can begin to build up everything else that must be true, based from the cogito.
So if some wannabe philosopher - after having watched the matrix - asks in a nasally voice: "How can you be sure that you even exist?" Simply reply: "I just think that I do".