Here is the argument we discussed today:
1. If M is a material object, then M is identical to the sum S of material particles that compose M at time t.
2. If M is identical to the sum S of material particles that compose M at t, then M is always distinct from any sum S* that is distinct from S.
3. So, if M is a material object, then M is always distinct from any sum S* that is distinct from S.
4. If M is always distinct from any sum S* that is distinct from S, then M never survives the gain or loss of any parts.
5. So, if M is a material object, then M never survives the gain or loss of any parts.
Here is some support for its premises:
Support for 1. Assume M is material. Then it seems the only option for M is for it to be (identical to) some (hunk of or sum of) matter. So (1) is true.
Support for 2. Assume the antecedent. The consequent then follows provided strict identity is not temporary: if ever x = y, then always x = y (or at least whenever x or y exist). This may sound surprising, but I don’t think it should. Recall strict identity is governed by Leibniz’s Law. Now suppose x used to be distinct from y, but later on will not be. Then x has the following property: it used to be distinct from y. But y lacks that property. But LL says if x = y, then Fx iff Fy. Since they differ in their properties, it cannot be the case that they are strictly identical. So identity is not temporary. So 2 is true.
Support for 3. Subconclusion.
Support for 4. Assume antecedent. Suppose M gained or lost a part. Then we would be considering another sum S* that is distinct from S. M can’t be S* since M is identical to S. So 4 is true.
Finally, here's what we said about identity:
Identical: Strict, literal identity. Not like “identical” twins. Like 4 is identical to the sum of 2 and 2. Identity is a two-place logical relation governed by Leibniz’s Law: if x = y, then Fx iff Fy (x and y have all of the same properties).
Some good suggestions came up in class concerning where things might be going wrong. Other thoughts?