Something about my translation has bothered me since I originally posted my question (which follows below). It concerns what Bertrand Russell wrote in "On Denoting". Ryno indicated a circularity with the way I originally reformulated Cogito ergo sum. But upon rereading Russell I'm wondering if the following isn't a more accurate formulation:
- There exists an x such that x is Descartes.
- For any y that is Descartes, x and y are identical.
- For any z, if z is a time at which Dx thinks, then at z, Dx exists.
Why is it important? Because it would lend weight to the identity component of my original question. I appreciate any comments anyone might have.
Suppose we were to reformulate Cogito ergo sum to read: "For any I, if at some instant in time I thinks, then at that instant I exists."
EDIT: Please feel free to substitute "at some instant in time" with "over some unspecified range of time straddling some instant."
Wouldn't Descartes have to establish the identity of the subject I for any two distinct instants in (or ranges over) time at which the statement is true? What I have in mind is Leibniz's law, which states that entities x and y are identical only if each has exactly the same properties -- and in what sense can the I at times t1 and t2 be said to have exactly the same properties?
I know relevant questions of personal identity have been addressed by Derek Parfit, but I suppose the essence of my question concerns what implications there are (if there are any) for Cognito ergo sum should we accept Leibniz's law.
If Descartes doesn't have to establish the identity of I at times t1 and t2, then what does that say about the kind of thing Descartes' I is?