The Buddhist theory of "Pratityasamutpada" and the Scottish philosopher David Hume's (1711-1776) "Bundle theory" & "Causation theory" have an interesting parallel, both lead to the impermanence of the Soul or individual self.
This is a radical shift from what appears to commonsense and that held by most religions of the world. Be it the dualistic traditions of everyday religion or the monist spirituality of mysticism (sufism, advaita, Christian mysticism); almost every one of them assumes the continuity and identity of the Self/Soul.
Both "Pratityasamutpada" and Hume's "Bundle theory", implies that the individual Self/Soul is nothing more than a series of connected sensations, and its the combination of "memory" & "imagination" creates the illusion of a permanent Self/Soul.
The credit should go to great Buddhist thinkers like Nagarjuna (2nd or 3rd century AD) who developed the original Buddhist theory of "impermanence" to an formidable philosophical argument. Though Hume' got the same ideas centuries later, he still deserves a great deal of respect for coming up with these ideas independently and for being the first in the Western world to popularize these ideas.
This perspective looks more probable than that of a permanent self/soul. In fact the possibility of an impermanent Soul/Self is the more scientific viewpoint, as it does away with the "Ghost in the machine" hypothesis of Soul. Soul/Self is no more a non-material "ghost" residing in the material "machine" of the body; but rather its an after effect or by product of the material body in its material environment.
Ego has a central place to play in all human action, and ego is rooted in the concept of I/Self/Soul. But if the very concept of Self is nothing more than the totality of one's experiences and sensations projected through the prism of imagination, what we call as "I" or "Self" loses its subjective nature and becomes objectified.
One major implication of this thought process is that there is no Soul in the usual sense in which we use the term. "No Soul" implies that no part of us survives our physical bodily death. This further implies the improbability of life-after-death, heaven/hell, Moksha, etc.
The Buddhist view point however still holds on to reincarnation in the sense that a set of actions/sensations/thoughts in a particular birth can act as causes to a set of effects in some other birth, thereby maintaining the continuity of Karma. This however is not scientifically possible.