Fifty years after Locke the Scottish philosopher David Hume dissected the self and argued that it, like all enduring substance, was a perceptual illusion. In his Treatise on Human Nature he argues the self is an illusion created by the contiguity of sense perceptions and thoughts. The self is merely a “…a bundle or collection of different perceptions which succeed one another with an inconceivable rapidity and are in perpetual flux and movement” (Hume, 1739).While lighter, you might also be interested in this New Yorker profile of the philosopher Derek Parfit, who is mentioned in Hughes' post.
While for Locke memory was the core of personal identity, knitting together past and present selves, for Hume memory created the illusion that there was some kind continuity between past and present mental states. The contradiction between the Enlightenment’s foundational concept of Lockeian selfhood and the Humeian, empiricist recognition that the self is a fiction lay dormant until the twentieth century when neuroscience, another product of the Enlightenment, revived the debate. As neuroscientists collected accounts of patients with localized lesions and degenerative diseases - men who mistook their wives for hats, or who could form no long term memories and were persistently in the last ten minutes, or were certain they were in the wrong body - they began to create an empirical model of the ways that the brain creates the ongoing narrative of the self, and illustrate just how malleable and fragile that narrative is.
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On the nature of identity
J. Hughes examines the debate over the existence of a 'persistent self':