For simplicity, say there were only two unmoved movers, β & ψ. They would each be an actus purus, by definition. They would both likewise be necessary and eternal.
Neither of them could influence the other, obviously. So, they couldn’t do or know anything about each other, and would not therefore be either omnipotent or omniscient. Nor could either one of them be properly understood as ultimate, because by the definition of ‘ultimate,’ there can be only one ultimate. So neither of them could be God (that’s why I didn’t label them α & ω).
In order both to exist, β & ψ need to be somehow different from each other. There must be at least one property that they do not both equally share. This is Leibniz’ Principle of the Identity of Indiscernibles: if the referent of “A” and the referent of “B” have exactly the same properties, then both “A” and “B” refer to the same entity (e.g., “3” and “4 – 1” refer to the same quantity). Put another way, you can’t have more than one being that exists in exactly the same way.
Simplifying again, say that β & ψ each have only two properties: the property of necessity, and either p or ~p. They are both necessary, but β is p, while ψ is ~p. Here’s the question: is it possible for β to be ~p?
Yes: if a necessary being like ψ can be ~p, then it is possible for an otherwise identical necessary being such as β to be ~p – after all, ψ has managed it – and β could therefore possibly be ~p. But this means that β is not necessarily p. And this means that β is not entirely necessary, but rather partially contingent. But a partially contingent being *just is* a contingent being.
The same goes for ψ: if β can be p, so can ψ; so ψ is only contingently ~p, and is therefore not a necessary being, but rather a contingent being.
Contingencies require causes other than themselves to be just the things that they are (when, of course, they might possibly have been otherwise). So, they cannot be unmoved movers.
Thus there can be at most one unmoved mover.
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I love it when you try this stuff, but I do have a question: don’t you set up a bit of a logical straw man by labeling both movers as “necessary” from the get-go, when we already know that ‘necessary’ can apply to only one? The conclusion you reach is correct because it is preordained, built into the premises, so to speak.
(nota bene, I’m out of my depth on this)
This is so for all valid deductive arguments. “Socrates is mortal” is built into the premises that Socrates is a man and that all men are mortal.
The question then is whether the premises of the argument are well-formed and true. The premise in question is that an unmoved mover must be necessary. It must. A being that is not necessary is contingent by definition, and contingent beings can come into being only if moved by some other mover. So if you’ve got an unmoved mover, you know you’ve got a necessary being. Likewise if you’ve got two unmoved movers: they have to be necessary.
The argument did not start with the premise that there can be only one necessary being who is an unmoved mover. It started by stipulating to two. But since it shows that there can be no more than one necessary being, it shows also that there can be only one unmoved mover.
I guess I just don’t understand why the argument begins the way it does. That Socrates is a man and that all men are mortal is true – self-evidently so, that’s why they work as premises – whereas “two unmoved movers” (who are necessary and eternal while lacking omniscience and omnipotence) sounds like a contradiction in terms. ‘Unmoved mover’ is part of any commonly accepted theory about, or definition of, God, and only about God. That is, *if* God exists, this would be part of the description we apply to him.
The premise in question is that an unmoved mover must be necessary.
Is this what your argument is intending to establish, that such a mover actually exists? Or is it that *if* such a mover exists, there can be only one? Because (fwiw) I think you are successful at the latter, but not the former.
And then there’s the possibility that I don’t understand what you’re up to at all.
Well, the argument begins the way it does because in writing what ended up as the post I was actually responding to a correspondent who asked why there could not be two unmoved movers, both necessary, both eternal, etc.; i.e., two Gods. So I started out by supposing for the sake of argument that there were two such beings, and asking what would be the consequences of that state of affairs.
That “… two unmoved movers” [who are necessary and eternal] sounds like a contradiction in terms” to you, and that you feel that “we already know that ‘necessary’ can apply to only one,” suggests that you were already convinced of the argument’s conclusion before you first considered it. Nothing wrong with that; I was in the same boat. But then my correspondent asked the question, and I thought, “OK, let’s *show* why it’s a contradiction in terms.” My position was like that of number theorists who set out to prove that 1 + 1 = 2, when anyone can *just see* that they must.
I’m certain that St. Thomas proves the same thing somewhere – I think in Summa Contra Gentiles – but it was literally easier to make up a proof of my own than to locate his. Having been a blogger for a while now, I find my attention span and memory are not what they were. Easy to blame the internet, right? Couldn’t be age …
If our premise that an unmoved mover must be necessary is true – as it seems it must be, by definition – then no non-necessary being (i.e., no contingent being – no being that might have been otherwise in respect to some property p) could be an unmoved mover.
The other main premise of the argument is Leibniz’s Principle of the Identity of Indiscernibles. If there are two unmoved movers, then by that Principle, they must be discernible in some respect. They cannot be exactly alike, for if they were, then they would be just the same thing. They must differ, somehow.
Say that their only difference is that one of them is red, the other black. Could the red one have been black, or vice versa? Well, why not? If β & ψ are exactly alike in every respect except their color, then one of the ways that they are exactly alike is that they both *might have been* either red or black. But this means that both of them are partly non-necessary. And a partly non-necessary being is not necessary *at all*: it is contingent. And contingent beings can’t be unmoved, because unmoved beings cannot be otherwise than they are. An unmoved mover can’t possibly be either red or black, depending on how things turn out. On the contrary, it can’t depend on anything.
The argument does not show that an unmoved mover exists. It shows only a bit about what an unmoved mover must be like, if it does exist.
the argument begins the way it does because in writing what ended up as the post I was actually responding to a correspondent who asked why there could not be two unmoved movers
This is uncanny. I actually referred your post to a philosopher friend who somehow intuited that that’s probably what you were up to. Must be psychic in addition to really smart. The information in your last comment would have made a useful preface to the post. I withdraw my reservations.
Paul refers to the beings that are not the Unmoved Mover as “powers.” There can be many “powers” but there can be only one Power.