A charitable interpreter who has read some medieval philosophy may be able to see how scholastics use this claim and identify certain inferences from this claim as being valid and others not. But it'd be nice if we had a more precise characterization of what it means to say God is 'pure actuality', so that we can see if all that Aquinas says follows actually does follow from this claim. Moreover, once we have a precise characterization of what Aquinas is even asserting, we can begin to more clearly assess the plausibility of the claim itself and whether Aquinas has established it. I propose the following definition:
- x is pure actuality if and only if for all (intrinsic) P, if x is P then x is actually P.
For completeness and wider scope of application, I also propose the following definitions of a thing's being 'composed of' or 'having' actuality and potentiality:
- x is composed of potentiality if and only if for some (intrinsic) P, x is P and x is potentially P
- x is composed of actuality if and only if for some (intrinsic) P, x is P and x is actually P.
Here P is taken to range over all and only intrinsic properties, i.e. properties which in some sense have to do only with the being in question, as it is "in itself". So it does not include so-called extrinsic properties, such as being smaller than Socrates or being Socrates's father. It does include properties such as weighing 50 grams, having an intellect, being round, etc.
As far as what being actually P means, this is in contrast with being potentially P. These phrases clearly modify predicates -- e.g. something can be actually hot or potentially hot -- but there probably isn't a precise definition to be given of them because they are such basic and fundamental concepts. It is better to look at indubitable examples to see what sort of feature of the world these terms pick out.
Suppose I am about to boil some water, but have not yet done so. I put the water in my pan and turn on the heat. At this point it is merely potentially boiling. Once the water reaches a certain temperature and bubbles start to appear the water is now actually boiling. Another example: Suppose I am asleep. I am not at that very moment conscious, though I am potentially conscious. When I wake up and start realizing what's going on around me, at that point I have become actually conscious. This is all clear enough.
As an aside, I think it is consistent with the duality of actuality and potentiality that some things be neither actually nor potentially P (though they cannot be both). Sherlock Holmes is neither potentially alive nor actually alive. Whatever else they are, non-existents are neither potentially nor actually anything. (We sometimes say that merely possible entities potentially exist, but I think this is just a roundabout way of saying they possibly exist.) I would also argue that the only things which are actually or potentially anything are present entities. Maybe this is all contentious and more work needs to be done here, but it seems right to me. Regardless, the important point is that we have some grasp on the distinction between something's having a feature potentially and something's having it actually.
Now let us test our definition. Let's see whether some of Aquinas's claims about God actually do follow from his being pure actuality. Consider the discussion on immutability:
"First, because it was shown above that there is some first being, whom we call God; and that this first being must be pure act, without the admixture of any potentiality, for the reason that, absolutely, potentiality is posterior to act. Now everything which is in any way changed, is in some way in potentiality. Hence it is evident that it is impossible for God to be in any way changeable." (ST Ia Q.9 a.1)
Aquinas's talk about potentiality being posterior to act is supposed to be justification for his claim that the 'first being' must be pure actuality. Let's assume simply for the sake of argument that this justification is right; then his first premise is that there exists a being (God) which is pure actuality. So, applying the definition I gave: for all P, if God is P then God is actually P. But, second premise: if something x changes, then for some P, x is potentially P. But this clearly would contradict the first premise. So we can indeed conclude that God does not change.
The problem is that Aquinas appears to make a further inference here, that it is impossible for God to change. But the argument can be amended. Suppose God is possibly changing with respect to some intrinsic property P. Then, since God is pure actuality, God actually exists and is possibly changing with respect to P. But, I would argue, if something actual can be changed with respect to P, then there exists something actual which has the potentiality to bring about such a change. But x has the potentiality to bring about a change in y with respect to P only if y is potentially P. So God is potentially P for some P, contradicting the thesis that God is pure actuality. Hence, God is not possibly changing with respect to any property P. So God cannot change.
Let us consider another case, where Aquinas argues God cannot be composed of matter:
"First, because matter is in potentiality. But we have shown that God is pure act, without any potentiality. Hence it is impossible that God should be composed of matter and form." (ST Ia Q.3 A.2)
This argument is simple. Using the definitions earlier, the first premise is that anything which is material or has matter is potentially P for some (intrinsic) P. God is not potentially P for any intrinsic P. So God is not material. Whether the premises work or not, the validity of the argument is clear under our interpretation.
My purpose in this post has not been to defend Aquinas's arguments. I merely hope to have made slightly more clear the meaning of claims involving potentiality and actuality. If the definitions I've given above help to make Aquinas's arguments seem more clearly sound, then this supports them as accurately representing what claims of potentiality and actuality are supposed to mean in the hands of medieval philosophers. And even if the soundness of these arguments remains contentious, on the above interpretation of potentiality and actuality I would argue it is at least easier to see why the arguments are formulated as they are.
There still remains a ton of work to be done on the logic and semantics of potentiality and actuality, and much to be done on the metaphysics of it. Nevertheless, taking the predicate modifier status of 'potentially' and 'actually' as basic and defining other phrases in terms of them seems to me to be a promising framework. Since the examples are so incontrovertible, these definitions provide powerful tools for rebutting the claims of those who feign incomprehension whenever arguments involving these terms are brought forward.