I judge that I'm thinking and that if I think I am. Also, I know I'm CL. So, among other things, I judge that CL now thinks and thus CL now exists. That's what I think to myself now. Does that belief constitute knowledge?
Between now and later, I'll be kidnapped and my brain split into two. Each half is placed into a new body. Upon waking, I'll remember everything I now know but I won't then be able to say knowingly 'Earlier I judged that CL thought and thus must have existed' because I wouldn't know this to be true. I won't later know it because I won't then believe it. I won't then believe it because I don't know whether I can say truthfully that I, CL, existed earlier given that I don't know how to describe splitting cases. Thus, because I won't later know whether I, CL, existed previously when someone named 'CL' formulated the cogito I don't now know that it's true that I judge that I, CL, think and thus must exist.
The crucial assumption appears to be this one: if S knows that p at t1, and if (at some later time) t2, S remembers everything S knew at t1, then S knows p at t2. It seems at t1 that I know I exist at this time. It seems I later remember everything I knew prior to the surgery but it seems that after the surgery I do not know whether I existed before that surgery. It seems that either my cogito judgment does not constitute knowledge now or the principle is false. I tend not to side with Descartes, but this time I might.