How do we know the unmoved mover for any given change must be singular and lack potential?

RE falsity of premise 5: The point of the proof is that if some thing 1 makes the putative first mover (thing 1') be the way it is, that thing 1 is really the first mover of whatever changes are laid to the putative first (1'). That thing 1 is the first mover really; and it cannot be made to be the way it is by some other thing 3 or else it is merely putative also.

DISTINCTION OF ACT AND POTENCY.

This distinction arose from the Parmenides objection. Let me summarise the argument why the change is not possible and then I will resolve the argument.

Proposition (Parmenides): Change is not possible.

Proof:

1. A thing either is or is not.
2. If it is, it is being; if it is not, it is non-being or nothing.
3. Change requires that something which is not, comes to be.
4. When change occurs, that which comes to be, before the change either is or it is not.
5. If it is, then it is being and if it is not then it is non-being.
6. We can not say that before the change it is (or that it is being), because that would mean that it comes to be what it already is; a thing can not come to be what it already is (that is contradictory to the whole point of change).
7. In the second case, it is also impossible that before the change it is not (or that it is non-being) because that would entail that non-being becomes being.
8. Therefore change is not possible.

However, Aristotle resolved this problem by admitting that there is the division inside being, namely, that something can be being in act or being in potency. He finds the middle ground not between being and non-being, but between being in act and non-being and this middle way is called being in potency. So the change does not require that non-being comes becomes being, but that being in potency becomes being in act. Hence we have the first Thomistic thesis:

Potency and Act divide being in such a way that whatever is, is either pure act, or of necessity it is composed of potency and act as primary and intrinsic principles.

Examples:

• A man is potentially a musician.
• A metal bar is potentially hot.
• Wood is potentially of green color (if painted in that color).

THE EXPLANATION OF THE FIRST WAY.

Terms: Change consists formally in the transition from one way of existing to the other way of existing; i.e. reduction of the potential state to the actual state. In every real change we need to distinguish three things:

1. Subject who is being changed,
2. initial state from which change occurs (terminus a quo) and the final state to which is the end of change (terminus ad quem),
3. the transition itself which itself constitutes change formally.

Example (Heating of cold metal): Subject which is being changed = the metal. Initial state = cold metal, final state: hot metal. Change = heating a metal.

Terms: In philosophical terminology we distinguish between physical changes and metaphysical changes and we distinguish between changeable being and unchangeable being and we define motion.

1. Physical changes = those changes who have one term positive (or existent), ie. those changes where the existent subject gains or loses something (like in the previous example). All substantial, accidental are physical changes (change of motion is also a physical change)
2. Metaphysical changes = those changes who have one term negative (non-existent), ie. these changes are creation or annihilation. This kind of change is not really considered a change at all, but rather creation is something different than change. Change requires that before and after the change there is something common (ie. the subject which is being changed), but when creation occurs, the initial state is nothing and the final state is something, and they do not have anything in common and that is the reason why creation is not considered to be a change at all (similarly the annihilation is also not considered to be a change).
3. Changeable (mobile, mutabile) being = every being which can go from one way of existing to another way of existing, ie. where some potential state is reduced to the actual state.
4. Unchangeable (immobile, immutabile) being = that which excludes the possibility of transition from one way of existing to another way of existing.
5. Motion = reducing being in potency to being in act.

Proposition: There exists a first unmoved mover.

Proof:

1. There is a (physical) change in the world (note that we start not from changeability of the world but from changeability in the world).
2. Whatever is moved is moved by something else.
3. That something else is either moved or unmoved.
4. If it is unmoved we have our conclusion.
5. If the mover is itself moved then we need to pose yet another mover.
6. Again if that mover is unmoved we have our conclusion and if that mover is itself again moved we need to pose yet another mover.
7. This can not go to infinity.
8. Therefore we need to pose the first unmoved mover.

I am not going to explain every step now but only if one of these steps is not clear to you (you can pose an objection in the comment section). The reason is that this part is not essential to your question.

WHY IS UNMOVED MOVER UNMOVABLE, IE. PURE ACT?

Proposition: If something is composed of act and potency then that subject can exist in different ways.

Proof:

1. If some subject X is composed of potency (more precisely: an object has an admixture of potency), that means that X is potentially existent in some other way which is different then the way it exists right now (namely in a way which includes that potency).

2. That means that there are at least two ways in which X can exist.

The point of the just now proved proposition is this: as soon as you admit potency in your subject, you have admitted different ways in which that subject can exist. We will illustrate the proposition with the following example.

Example. Say some metal bar is now cold. The metal bar has the potency to become hot. Therefore, there are at least two ways in which a metal bar can exist, it can exist as a cold metal bar, or as a hot metal bar.

Also, it is trivial to see that a reverse direction of a previous proposition is also true. For if something can exist in many different ways then it is potentially existent in that way, and potentially existent in another way, etc.

Key insight: Subject that can exist in different ways (this is true for subjects composed of potency) is in itself indifferent to existing in any particular way. For if it was not, then it would necessarily exist in one way and the other ways of existing would really not be possible for that object. The subject which is in itself indifferent for existing in any particular way must have a reason outside itself which determines to one particular way of existing. I will use an example to illustrate the point.

Example: A metal bar can be cold and hot. Metal bar by itself is indifferent to either, therefore there must be a reason outside of the metal bar which determines the metal bar for being cold or hot, namely, the temperature of the atmosphere (or whatever).

Proposition: First unmoved mover must be also a pure act (ie. unmovable).

Proof:

1. Let us suppose that an unmoved mover has some potency.
2. That means that he can exist in different ways.
3. Also, he by himself is indifferent to existing in any of these ways; for if it was otherwise he would exist in only one way which would imply that there is no potency (and that would be a contradiction with the premise).
4. Because we have concluded the existence of the first unmoved mover he exists in one particular way.
5. But because he himself is indifferent to existing in any particular way, there must be a sufficient reason which determines him to one, ie. another mover which actualizes his potency to exist in that particular way.
6. Now we have a contradiction because then the first mover is not really the first mover but needs something else to move.
7. So we can conclude that the unmoved mover is void of any potency.

So the gist of it is that an unmoved mover must be also unmovable to account for motion in the world (because first unmoved movere which is not pure act would be a contradiction as I have just shown).

I will edit my answer more later.