Rene Descartes' theory of the separation between soul and flesh.
Many fictions draw on this theme, especially in the cyberpunk genre. Blade Runner explored replicant robots that were gifted with memories and were otherwise indistinguishable from humans; Armitage III and Ghost in the Shell are two anime treatments of the same basic plot. The Matrix explores Descartes' hypothesis more closely; what if we're merely being subjected to an incredibly detailed simulation of "reality?"
Descartes thus asked himself, "How can I prove that I really exist, if everything may just be an artificial illusion around me?" His answer, "I think, therefore I am."
His point being, the soul is the identity; the body and its senses are irrelevant.