Amanda Jackson5 said:Lacan touched on something pretty similar when he suggested, "I think where I am not, therefore I am where I do not think," referring to that fundamental split within the subject. Basically, the unconscious is doing the thinking in the places where the ego isn't present. Or, looking at it from the other side, the "I"—that conscious, linguistic ego—exists exactly where the "it," the unconscious subject, isn't thinking.
From what I’ve gathered through various interpretations—rather than reading Lacan directly—for him, this represents the very locus of self-awareness. It goes so far as to suggest that self-awareness itself is marked as an external object, or perhaps the *objet petit a* (that elusive object of human desire, the phantasmatic goal we can never quite grasp).
To that extent, this "point cast out from the center"—self-awareness—serves to mark and represent the existence of distance; after all, if there were no distance (which self-awareness itself produces), how could one "think where they are not, yet be where they do not think"? If it were possible to come to a standstill, to finally reach that point and collapse the distance, we would exist precisely where we think, but aren't we always positioned as being against, towards, or in opposition to the reality and the world we perceive?
Is it possible that this distance is dissolved during sleep?
Regardless, I am not entirely sure how all of this correlates with the philosopher's claim in the opening post—the idea that he does not exist?
He wouldn't exist if he were one with the world (though one has to wonder if the world as we see it exists without the relationship established by that distance) or, more simply, if self-awareness did not exist.
And so, Descartes is everywhere: "I think, therefore I am."
I intentionally avoided saying "I think, therefore I *am*" because of that peculiar Copernican shift suggested by Lacan above.
What conclusions can we draw by weighing Descartes against Lacan?
One cannot really derive from Lacan's claim that "being" and "existing" are identical, though existence remains a necessary and unquestionable condition. The question is merely where one is, or is not. It is much like sitting in a social circle and "listening" absentmindedly to someone speaking while your mind is drifting somewhere else entirely. Then, noticing your distraction, the person asks, "Hey, where did you go just now?"
So, the argued claim by that certain philosopher mentioned earlier might, as I see it, relate to what Jonathan Brooks8 suggested: that there is no single answer to the question "who am I?" Or perhaps that the "I" is indeterminate (emerging instead as a defining element within a relation or interaction), which, if I recall correctly, traces back to Jung.