Introduction to Philosophy: Overhead

Parfit's Argument that I am Not One of the Survivors
(in reference to the division case)

1. Assume I am R but am not S.
2. That is, I = R, and I S (where "=" means "is literally the same thing as")
3. My relation to S is the same as my relation to R.
4. So, if I = R, then I = S.
5. So, I = S (by 4 and the first conjunct of 2 via modus ponens)
6. But, 5 contradicts the second conjunct of 2!
7. Hence, it is not the case that I am R but am not S. (by reductio from 1-6)

Switch the letters "R" and "S" in the above proof, and it proves that it is not the case that I am S but am not R.

Together these are proof of premise 3 of the overall argument.

Richard Lee, rlee@uark.edu, last modified: 25 November 2002

1.	Assume I am R but am not S.
2.	That is, I = R, and I S (where "=" means "is literally the same thing as")
3.	My relation to S is the same as my relation to R.
4.	So, if I = R, then I = S.
5.	So, I = S (by 4 and the first conjunct of 2 via modus ponens)
6.	But, 5 contradicts the second conjunct of 2!
7.	Hence, it is not the case that I am R but am not S. (by reductio from 1-6)