Imagine that ‘Sally’ (S) robs a bank (call this event R) in 1975 (t1) and is caught. However, due to various complications with the prosecution, she is not put on trial until 2011 (t2). During this time, via natural processes, various atoms that compose her body have been replaced with other ones. Now for the argument.
Let’s say that x “strictly survives” some occurrence if x exists before that occurrence and x exists after that occurrence.
1. A person can be morally accountable for an event iff they are numerically identical to an object that causally contributed to that event.
2. S at t1 is the only object that causally contributed to R which S at t2 could be numerically identical to.
3. From (1) and (2), S can be morally accountable for R’s occurrence at t1, even at t2, iff S at t2 is numerically identical to S at t1.
4. If S is a material object, S lost some composing parts between t1 and t2.
5. From (3) and (4), if S is a material object, S can be morally accountable for R’s occurrence at t1, even at t2, iff S strictly survives the loss of some of her parts.
6. S can be morally accountable for R’s occurrence at t1, even at t2.
7. From (5) and (6), either S is an immaterial object, or S is a material object that strictly survives the loss of some of her parts.
8. Material objects cannot strictly survive the loss of any of their parts.
9. From (7) and (8), S is an immaterial object.
Premise 8 is the most contentious one, and below is an argument to support it. The argument does not originate with me, a friend posted it on a theologyweb thread (and apparently it is well-known in the literature anyway).
“Consider your body. Name it “Body”. Consider the part of Body that consists of all of Body except your left pinky. Call that part “Body-minus”. At time t0, let’s say, Body is intact; it includes your left pinky as a part. Suppose that at t1, however, your left pinky is annihilated. Call the pinkyless, human-body-shaped, material object that remains in your vicinity after this unfortunate event “Deformed”. Note that the following argument appears to be sound:
(1) At t1, Body-minus still exists (because nothing happened to Body-minus except that something external to it was detached from it).
(2) At t1, if Body still exists, Body is identical to Deformed [What else could Body be at that time?].
(3) At t1, if Body-minus still exists, Body-minus is identical to Deformed [What else could Body-minus be then?].
(4) At t1, Body-minus is identical to Deformed [This follows from 1 and 3].
(5) At t1, if Body still exists, Body is identical to Body-minus [This follows from 2, 4 and the fact that identity is an equivalence relation].
(6) At t1, it is not the case that Body is identical to Body-minus [Note, for example, that at t1 if Body and Body-minus both exist, they have different historical properties – Body-minus used to be a proper part of Body, for example, but Body was never a proper part of Body].
(7) Therefore, at t1 it is not the case that Body still exists [5,6].”
A parallel argument could be given with respect to any material body that is said to have survived the loss of a part, so it seems that premise 8 in the first argument is true.