I was reading over a book titled, "Philosophy demystified" and it presented this argument found in one of Plato's writings:

P1. Look around you: nothing moves by itself.
P2. Anything you see always needs another thing to move it.
P3. Natural things are no different from human-made things in that they need to be moved by something else.
P4. Just like anything else, the bodies of living things can’t move by themselves.
Therefore, there has to be something else, other than the body, that moves a body, and this we can call a soul (or psyche in Greek).

The author of the book then critiques this argument with this reply:

"This argument can be critiqued by pointing out that, while it may be true that nothing moves by itself, we need not jump to the conclusion that there must be something wholly other than a part of the body (or something material in the bodily realm), like some soul, that is responsible for moving the body. Bodies can be broken down into parts, and when seen in this way, we can imagine one part of the body moving another part (or parts) of the body. Plato and many of the Greek philosophers did not seem to consider this as a viable option."

What I am having difficulty understanding is how does the fact that the body is composed of parts (and may be moved by these parts) defeat the argument given by Plato?

Wouldn't plato then reply by stating that premise 4 should be read as "the parts of living things can't move by themselves?" I don't mean to suggest that I believe Plato's argument is successful, but I just find it hard to see how introducing parts, or stating that a whole is composed of parts and that parts may be what moves the whole, defeats Plato's argument.

If I were to rewrite Plato's argument to accommodate the relation between parts and wholes and the possibility that the parts move the whole, then this is what I think Plato would argue:

Nothing can move by itself.
If nothing can move by itself, then parts that compose wholes cannot move by itself.
if parts that compose wholes cannot move by itself, then something else must be responsible for the movement of parts.

All things that are moved, because of something else, are causally impotent.
All things that are their own source of movemnent are causally potent.

If that something else is moved by another something else, then the source of movement of such a sequence of movers is found in something that is its own source of movement.
The body is not its own source of movement.
Therefore, the body is moved by something that is its own source of movement.
This is the soul.

I am not a logician at all, and I figure that I presented this argument's logical structure poorly, but if any of you can try to interpret this argument, then I think that you can see that Plato would argue that parts aren't exempt from premise 1.

However, the reason I think that Plato's argument fails (as it was presented in Philosphy demystified) is because premise 1 seems to contradict the conclusion. If nothing moves itself, then a soul can't move itself. So the soul's movement must be the product of some other thing and so on. Even if it is accepted that whatever is moved, because of something else, is itself causally impotent and whatever is its own source of movement is causally potent, we are left wondering if premise 1 is compatible with the notion that some things are their own source of motion. If somethings are their own source of motion, then it seems that some things can move by itself and premise 1 is false.

Another issue with the argument is how it looks at causal relations. Why suppose that causal occurances are assymetrical relationships between a causally inert thing and a casually potent thing? Perhaps, causal occurances are between things of equal causal potency? Think of how paper and a comb are attracted to each other with static electricity or how magnets attrack each other or how the mass of two things affect each other as examples of how, in nature, there doesn't seem parts of reality that are causally inert and other parts that are causally potent.

Or perhaps movement occurs as the result of the way that thing X affects thing Y and how thing Y affects thing X? So we can agree that no single thing can move itself, but it does not follow that because no single thing can move itself, that the collection of individual things must be moved by something that is not contained within the set of individual things. In this case, movement occurs because individual things move each other simultaneously and we are still able to agree that nothing moves itself.

Again, I don't want to argue that the alternatives I give of how movement occurs is correct, but it seem to me that there are other reasons for why one would be skeptical of Plato's argument that go beyond the way that parts and wholes affect each other.

I welcome any one that can help me understand why the parts/wholes reply would defeat the argument and for any help with understand if premise 1 is compatible with the soul being responsible for the movement of the body without itself being moved by something else.