An argument that organisms aren't wholly material

Here’s an argument for non-materialism about all organisms.

Start with these premises:

1. Organisms exist.

2. If organisms exist, it is possible to have two organisms that have all their matter in common.

3. Antisymmetry of parthood: Two distinct things can’t each be a part of the other.

4. Strong supplementation: If y isn’t a part of x, then y has a part that doesn’t overlap x.

Now suppose that x and y are two organisms that have all their matter in common. By antisymmetry of parthood, they can’t both be mutual parts of each other. Swapping labels if necessary, suppose y isn’t a part of x. Then by strong supplementation, y has a part z that doesn’t overlap x. But any material part of y is a material part of x by (2). Thus, y has a part that isn’t a material part. Hence:

5. It is possible to have an organism with a non-material part.

But this is weak in two ways. First, it doesn’t show that any actual organism has a non-material part. Second, even if we showed that, that wouldn’t show that all organisms have non-material parts. Moreover, I have given no argument for premise 2.

I will fix all these problems together. In a recent post, I gave a plausible construction of a world where there is a dog-like organism and a cat-like organism with all their matter in common. The same construction would give the following conclusion: there is a world where there is a mushroom-like organism and a grass-like organism thathave all their matter in common. Plugging that into the above argument yields:

5. Possibly a mushroom-like or a grass-like organism has a non-material part.

The likeness here is functional: the way of life of the organism is like that of mushroom or a grass plant. Then add:

6. If possibly a mushroom-like organism has a non-material part, all organisms have non-material parts.

7. If possibly a grass-like organism has a non-material part, all organisms have non-material parts.

From 5-7, we get:

8. All organisms have non-material parts.

Why believe 6 and 7? Here’s a thought. You might think that conscious animals have to have souls or something like that. But if a mushroom- or grass-like organism can have a non-material part, probably it actually does, and if it has a non-material part, probably all organisms do.

There is a lot in this argument that doesn’t personally convince me. In fact, I am skeptical of premises 2 and 4, and my main reason for accepting 6 and 7 is that I already accept anti-materialism about all organisms. But I think the argument has some force.