An Ontological Argument from Pure Actuality

Informal Argument

D1. God is the being of pure actuality.
P1. For all x, if x exists in the intellect but not in reality, then there is a y such that x is causally dependent on y.
P2. For all x, if x is purely actual, then there is not a y such that x is causally dependent on y.
P3. God is in the intellect.
C. God is in reality

Defense of Definitions and Premises

It should be noted, at the outset that this argument is in Free Logic. As such, the existential quantifier carries no existential import in the argument. This prevents any inference of the existence of God from the definition alone.

D1: A being of pure actuality is simply a being that lacks any potentiality. Such a being has, as Aquinas argues, the divine attributes of omnipotence, omniscience, immutability, eternity, immateriality, and uniqueness. It is this last feature, uniqueness, that justifies the use of a definite description, since there can be only one such being. Instead, existential claims are made by the predicate “R” in the formal argument below, which means that something exists in sense of being real, as opposed to existing in a fictitious or imaginary way.

P1: This premise is motivated by the fact that if something exists in the intellect alone, then its existence is causally dependent on some mind.

P2: A being of pure actuality exists a se, and uncaused, as Thomas proves in his five ways.

P3: Every Thomist who contemplates the implications of a being of pure actuality has the Thomistic conception of God in mind.

The Formal Proof

Let,

Ix ≝ x is in intellectu
Rx ≝ x is in re
Dxy ≝ x is is causally dependent on y
Ax ≝ x is purely actual
g ≝ (ɿx)Ax

1. (∀x)[(Ix ∧ ~Rx) → (∃y)Dxy] (premise)
2. (∀x)(Ax → ~(∃y)Dxy) (premise)
3. Ig (premise)
4. (Ig ∧ ~Rg) (IP)
5. (Ig ∧ ~Rg) → (∃y)Dgy (1 UI)
6. (∃y)Dgy (4,5 MP)
7. Dgμ (6 EI)
8. (∃x){[Ax ∧ (∀y)[Ay → (y = x)]] ∧ Dxμ} (7 theory of descriptions)
9. [Aν ∧ (∀y)[Ay → (y = ν)]] ∧ Dνμ (8 EI)
10. Aν ∧ (∀y)[Ay → (y = ν)] (9 Simp)
11. Aν (10 Simp)
12. Aν → ~(∃y)Dνy (2 UI)
13. ~(∃y)Dνy (11,12 MP)
14. (∀y)~Dνy (13 QN)
15. ~Dνμ (14 UI)
16. Dνμ (9 Simp)
17. Dνμ ∧ ~Dνμ (15,16 Conj)
18. ~(Ig ∧ ~Rg) (4-17 IP)
19. ~Ig ∨ ~~Rg (18 DeM)
20. ~~Rg (3,19 DS)
21. Rg (20 DN)

QED

Posted on October 8, 2019, in Arguments for God and tagged , , . Bookmark the permalink. 5 Comments.

  1. Hey Daniel! I am a huge fan of yours.

    I have recently been puzzling over how to derive certain attributes of God from the notion of a purely actual being.

    Suppose we have a demonstration of the existence of a Purely Actual being. I am curious, though, how we derive:

    (A) the uniqueness of such a being;

    (B) that in such a being existence and essence are identical;

    and

    (C) that such a being is absolutely simple (i.e. without parts, physical or metaphysical) (SIDE NOTE: I can actually see how (B) entails (C) quite easily, but I am wondering if there is a more direct way from pure actuality to absolute simplicity).

    One avenue some thomists have taken in deriving (A) from the concept of Pure Actuality is that in order to have two or more of something, there must be some principle of individuation that distinguishes them (i.e. some feature that one has but that the other lacks). This, the Thomist may argue, would entail that one such being has a potentially that the other lacks. But if such a being has potentiality, then it cannot be purely actual. Hence, no such principle of individuation could exist, in which case there could not possibly be more than one such being.

    One initial worry for this is that surely two things could be distinguished by their differing *actual* features instead of their differing potencies. It seems, then, that the inference from having an individuating feature to having potentiality may be a non-sequitur.

    The avenue one would presumably take to demonstrate (B) would be a modus tollens argument proceeding roughly as follows:

    P1) Any being in whom essence and existence are distinct has potency.

    P2) A Purely Actual being has no potency.

    C) Therefore, a Purely Actual is such that its essence and existence are not distinct.

    There may be other avenues, but this seems like a suitably general one that roughly details the procedure. But my question now is: what is the justification for P1?

    One may argue that essence is a principle of potentiality and stands in potency to esse as an actualizing principle, but I am really trying to find a justification for P1 that does not presuppose certain substantive Thomistic metaphysical commitments like this sort of justification.

    The avenue some take in relation to (C) is to point out that anything of Pure Actuality cannot be composed of act and potency and hence is simple. But why couldn’t there be a being which is a composite not of act and potency, but of different actual and really distinct parts, all of which are equally and necessarily actual?

    Thanks in advance. Keep up what you are doing — you inspire others!!!

  2. Hi MOR,

    These are great questions, and some that I return to from time to time, so I am not sure that I have anything like a definitive reply. However, I will share some of my thoughts:

    With respect to the Thomistic defense of (A), one way to think about this is by sortals, or things of the same sort. If pure actuality were a sort or a kind, which would have to be the case when there is more than one instance, then I think you could run an argument like this:

    1) Both x and y are the same sort of thing, i.e. a being of pure actuality.
    2) F is an actuality x has.
    3) If F is an actuality x has, then F is an actuality predicated of the sort of thing x is.
    4) But, F is an actuality that is not predicated of y.
    5) If F is an actuality not predicated of y, and F is an actuality predicated of the sort of thing y is, then F is potentially predicated of y.

    Given 2 and 3, we can conclude that F is an actuality predicated of the sort of thing x is. Since y is the same sort of thing, F is an actuality predicated of the sort of thing y is. Since, in this case, F is an actuality that is not predicated of y, it follows that F is potentially predicated of y. Since y is purely actual, i.e. has nothing potentially predicated of it, and also has something potentially predicated of it, we must reject (1), and conclude that a being of pure actuality is necessarily unique.

    As for your subsequent argument, I think P1 is best defended by Thomas in De Ente. I would simply say that whatever has a distinct existence from its essence could exist necessarily, but it does not seem to have necessity in itself (the Third way). In other words, there does not seem to be an metaphysical reason to think a being whose existence is distinct from its essence happens to exist in every possible world, or something like that, but that necessity does not appear to be self-explanatory in the way the Thomistic God is self-explanatory. It would seem, then, to have a lower grade of necessity, or a conditional necessity where the antecedent explanation (that which is necessary in itself) must ground its existence. It is there, in the antecedent of that conditional necessity that I think you will find potency, even among “necessary beings”.

    Lastly, what explains that these actual parts cohere in a unified individual being? I think we could go in a Neo-Platonic direction and wonder if a purely actual composite being, composed of purely actual parts, is the first principle of explanation. There would be some sense in which the whole is explained by the parts, and so the necessity of the whole would, once again, be derived by whatever necessitates the parts or that the parts should compose a unity. Since the whole is not self-explanatory, but must appeal to what is explanatorily prior, its necessity is once again conditional. If it were unconditionally necessary, then it would also be self-explanatory, and so there is room for potential in the whole precisely in its explanatory dependence on its parts.

    I will have to give it more thought though.

    My best,

    Daniel

    • Aw man, I just saw this right now! Thank you so much for the response, and I apologize for my untimely rejoinder.

      You present an interesting argument from the sort or kind of thing a purely actual thing is to the uniqueness of such a being. Your argument proceeds as follows:

      1) Both x and y are the same sort of thing, i.e. a being of pure actuality.
      2) F is an actuality x has.
      3) If F is an actuality x has, then F is an actuality predicated of the sort of thing x is.
      4) But, F is an actuality that is not predicated of y.
      5) If F is an actuality not predicated of y, and F is an actuality predicated of the sort of thing y is, then F is potentially predicated of y.

      But it seems there may be parody arguments that display perhaps an underlying difficulty with this argument. Consider the following argument:

      6) Both my dog and me are the same sort of thing, i.e. animals.
      7) Being merely sentient is an actuality my dog has (where something is merely sentient provided that it is essentially sentient and arational, meaning that, necessarily, its highest causal powers are the sensitive causal powers).
      8) If being merely sentient is an actuality my dog has, then being merely sentient is an actuality predicated of the sort of thing my dog is.
      9) But, being merely sentient is an actuality that is not predicated of me.
      10) If being merely sentient is an actuality not predicated of me, and being merely sentient is an actuality predicated of the sort of thing I am, then being merely sentient is potentially predicated of me.

      But 10 is clearly absurd, since I am not potentially merely sentient. I am essentially and necessarily not merely sentient, since I am essentially and necessarily rational.

      There are a few ways to see underlying problems. For starters, suppose you hypothetically reject (6), arguing that dogs are clearly not the same sort of thing as humans — they are different natural kinds! By same sort, then, you (in this hypothetical scenario) must mean that the x and y share the same essence. In other words, we could only compare things like Socrates and me, since Socrates and I are of the same essence (humanity) and hence of the same sort. But now P1 of the original argument seems question-begging, since it presupposes that that, necessarily, two purely actual beings share the same essence — and since two essences can only be individuated by accidental properties, but yet accidental properties entail the potentiality for change, it follows that purely actual things could only have essential properties (I’m understanding cambridge properties not as real properties), in which case they couldn’t be individuated, in which case there can only be one — it follows that this very assumption in and of itself already entails that there could only be one purely actual thing. But that is the very thing that needs to be demonstrated, and no dialectical opponent would ever grant in this dialectical context that two purely actual beings must share in one essence (per this hypothetical objection). And the reason is, again, because this very claim cannot be true unless the conclusion is true.

      But suppose you don’t mean “of the same sort” as sharing the same essence. But then we seem to be able to criticize the argument on other grounds, since sorts/kinds are hierarchically ordered, in which case there can be two things falling under one natural kind, but where such things do not share in common their lowest, most specific, most fine-grained natural kind. Instead, they simply share a more encompassing natural kind. But this means they are essentially different, i.e. one has some feature F that the other could not possibly have without undergoing substantial change. The differentiating F in this case, then, would not entail the potentiality for F on the part of one of the two purely actual beings, since it would be necessarily not-F and hence lack the potential for F. Hence, on this supposition, the argument seems to fail. And this is the case of my parody argument with me and my dog.

      But now we have a dilemma: Either P1 means the lowest, most specific, most fine-grained kind/sort (i.e. essence); or P1 means some higher, less specific, more coarse-grained kind/sort. If it is the former, then the argument seems question begging in this dialectical context. If it is the latter, then the argument fails (per the hierarchical nature of natural kinds and the parody argument captured in 6-10). Either way, though, the argument seems to be unsuccessful.

      What do you think?

      With regard to your second major paragraph, I thank you for your thoughts. I’m really trying to find a demonstration that does not have certain controversial Thomistic elements. Personally, I’m not (as yet) on board with the notion of necessary in itself (perhaps this is due to my upbringing in analytic philosophy where we mainly only discuss metaphysical necessity i.e. cannot fail to exist). I also personally do not see a reason to think, even if we could grant the distinction between necessity in itself vs necessity from another, that it must be the case that, for something S which exists necessarily but that still has an essence/existence distinction, S cannot be self-explanatory (or at least cannot be sufficiently self-explanatory). Speaking from my own sight, I guess I currently just do not see reasons for this.

      Finally, you ask: “Lastly, what explains that these actual parts cohere in a unified individual being?”. This is a wonderful question. It is something I’ve been puzzling over, and I have no definitive answer. For starters, it is unclear to me that necessary things need explanations. Pruss gives some principled reasons for restricting the PSR and other demands for explanation solely to contingent things in his book on the PSR. But even if I granted necessary things must have explanations, I guess I don’t see why we need to appeal to anything beyond the metaphysical impossibility of their non-existence. In other words, their existence is explained by the necessity of their own nature. Why do they exist, or why are their parts unified? Because it is metaphysically impossible for them not to be. I guess I do not see a reason to appeal to anything beyond this. It seems that a reasonable thing to say in response to your question is: Well, either (i) it doesn’t seem we need a further explanation since their cohesion into a unified whole is (ex hypothesi) a necessary truth; but even if (i) weren’t the case, surely the explanation for why the parts cohere into a unified whole is the fact that they are metaphysically necessarily together in the way they are and united into the whole they are — they cannot possibly be otherwise (again, ex hypothesi).

      Finally, it is unclear to me that wholes are explanatorily dependent upon their parts. Under some versions of Aristotelianism, whole substances are actually more fundamental than and explanatorily prior to the parts that compose them,. So, my humanity is more fundamental than the particles that compose me, or the plurality of my limbs and torso and head, and so on. Second,even if I granted that wholes explanatorily depend upon their parts, it is unclear to me that explanatory dependence implies potentiality in that which depends on another. For there are different forms of dependence, not all of which are causal. So, the whole’s existence could be grounded in its parts and thereby explanatorily dependent upon them, but it is unclear that when x is grounded by y, x stands in potency to y. I don’t see why x holding (non-causally) in virtue of y entails that x has potentials of some sort.

      Once again, thank you for your time, effort, and for being awesome. I’m looking forward to your thoughts!

  3. Hi MOR:

    Hmm. I think there is something fishy about the “actuality” of “mere sentience”. Of course, since dogs are sentient by virtue of their genus-membership (to which we belong), there is no real issue in supposing both the dog and I share the actuality of sentience. However, “mere sentience” is actually a limiting or privative predication intended to deny rationality to the dog. Can we say that a dog is essentially arational? This actually relates to my dissertation, and the question of whether and when we can essentially predicate of privative terms like arationality. I am inclined to say that we should not do this, or if we do, we must realize we are on shaky metaphysical ground. For example, I think it makes sense to say that the sheet of paper is not white, therefore it is a non-white sheet of paper. However, I am not inclined to accept that since the number 7 is not white, 7 has non-whiteness, as it suggests that it is the sort of thing that can receive some quality of color, and just happens to be deprived of white. Likewise, I think we can say that dog is not rational, but I am less certain we can say that dogs have arationality, and even less certain that it makes sense to say they have arationality essentially and actually (as this seems to treat the fact that something essentially lacks a feature as a true actuality, and I don’t think it is), but I would like to set these worries aside.

    So either the sortal is of the species-form, i.e. sharing the same essence, which leads to problems of introducing potency to individuate. So let’s close that horn off to you as unacceptable. What of the other horn? Can we say that “Pure Actuality” is a kind of genus that, itself, has the potential to admit of various differentiae? Thomas argues that the differentia is related to that which the genus is dervied as actuality is to potentiality. So, if there are differentia that is generative of a multitude of species in the genus “pure actuality” then whatever is generative of the genus “pure actuality”, itself, will stand as potency to the actuality of the differentiae, which is unacceptable (ST I.3.5).

    So the only way out would be to suppose that there is no species or genus for “pure actuality”, which is to say that “pure actuality” is no sort of thing at all.

    As for your concerns about being necessary in itself, I would simply suggest this: if there are other ways for being self-necessary, certainly the Thomistic doctrine of simplicity is one on offer. I don’t really know of other theories, They tend to be brute or conditional, e.g. Plantinga’s maximally great God, or the idea that if 7 exists as a Platonic object, then it would necessarily exist…

    I guess my concern about the appeal to “metaphysical necessity” is that it is not always clear what is less than logically necessary, but more than physically necessary. Sometimes it seems just like an insistence–a begging of the question. Frankly, if the question is “why do those parts cohere” and you answer that it is metaphysically necessary that they cohere, then I would point to the following: I asked for a “why” and I got a “that”. It may be that there is nothing deeper, right? But then I think there is something deeper in the Thomistic conception, and that would make Thomism more appealing, all else equal.

    You mention the Aristotelian route of noting that the whole is explanatorily prior to the parts. This is true, in the sense that the whole contains the essential form that unifies those parts, but it is not absolutely true.

    Thanks for the reply. I am sorry that I am slow with my responses. Mid-semester is busy.

    Best,

    Daniel

    • Thanks for the response!

      As for predicating privations of things, I have a couple notes. First, you are likely much more knowledgeable on the difficulties with this, since it relates (at least in part) to your dissertation. Second, with the aforementioned caveat out of the way, it seems that at least some privative terms can be and are legitimately predicated of things. Speaking at least of my metaphysical “seemings”, it seems that 7 is essentially and necessarily non-white, precisely because it is the wrong category of thing to even be colored in the first place. And it is unclear to me why saying that something is necessarily and essentially non-white would suggest or indicate that it is the sort, category, or kind of thing to which colors could apply. Saying something is essentially non-white seems indeterminate with respect to that further suggestion. Nevertheless, and this is my third point, we can set these issues aside if you like given your last sentence of the first paragraph. My fourth and final point is that this may be a quirk of the example I chose for my parody argument — it seems we may be able to construct a parody argument that demonstrates the same thing as I had originally intended but that avoids this privative predication.

      I apologize, but I do not sufficiently understand the argument you are presenting here:

      “Can we say that “Pure Actuality” is a kind of genus that, itself, has the potential to admit of various differentiae? Thomas argues that the differentia is related to that which the genus is dervied as actuality is to potentiality. So, if there are differentia that is generative of a multitude of species in the genus “pure actuality” then whatever is generative of the genus “pure actuality”, itself, will stand as potency to the actuality of the differentiae, which is unacceptable (ST I.3.5).”

      I would humbly ask that you please explain this to me again, good sir, if you will!

      Is the argument essentially to the effect that, on this horn of the dilemma (namely, treating purely actual as a genus), we run into an absurdity since genuses stand in potency to the specific differences (differentia) contained within the genus, in which case “pure actuality” would have potency, which is impossible?

      I have a few notes on this (admittedly probably misunderstood) construal argument.

      First, we must be careful to avoid equivocating between “purely actual” qua genus and “purely actual” qua a concrete, individual, unchangeable being. It seems that “purely actual” qua genus is really just a property of sorts: “the property of being purely actual”. But notice that this *property* can stand in potency to further specific differences without *pure actuality itself* standing in potency to further specific differences. It seems to me that all the argument would warrant is the claim that has potencies — but this is crucially different from and does not by itself entail that pure actuality *itself* would have potencies. It seems that the argument, then, under this construal/understanding (and I admit that this is likely a misunderstanding), equivocates between the *property* of being purely actual and actually *being* a purely actual, unchangeable being.

      Second, it is unclear to me what sorts of extramental realities “genus” and “specific difference//differentia” could fall under. This, again, is likely due to my lack of in-depth study, but are we sure the genus and specific difference reflect anything in extramental reality apart from our classificatory schemes? Maybe you just see them as determinable and determinate universals of sorts, or properties of sorts. But it is at least initially unclear why these extend beyond our classificatory schema. But if that is true, then “pure actuality” would only stand in potency to the actuality of specific differences//differentia *in thought*, which is no guarantee that pure actuality stand in such a relation of potency in extramental reality.

      You then state that: “So the only way out would be to suppose that there is no species or genus for “pure actuality”, which is to say that “pure actuality” is no sort of thing at all.”

      I am curious: how can this allow us to infer there could only be one purely actual thing given that “pure actuality” would transcend, as it were, any genus or category of being?

      Perhaps the reason is that, in order for there to be two purely actual things, they must ipso facto be of the same sort or kind or participate in one essence/universal, which (provided that pure actuality is not a category or genus) would be absurd since such things are kinds of categories/genuses.

      You then state that “it is not always clear what is less than logically necessary, but more than physically necessary.” This is a very good point. From my understanding, a logically necessary truth is one that must be the case (i.e. must be true) given all logical truths (such as LNC, LEM, and so on). A physically necessary truth is one that must be the case (i.e. must be true) given the actual laws of nature.

      To see how metaphysical possibility fits in, it may be useful to consider an example. Take the proposition that “prime numbers cannot produce prime ministers.” Now, it seems clear that this cannot be derived from logical axioms (indeed, given Gödelian incompleteness, the very consistency of the logical axioms cannot be derived from the logical axioms). But it seems equally implausible that there is some law of physics (or collection of laws of physics) which disallows for prim numbers to produce prime ministers. This seems, then, to be a further species of necessary truth — metaphysical necessity.

      You then state:

      “Frankly, if the question is “why do those parts cohere” and you answer that it is metaphysically necessary that they cohere, then I would point to the following: I asked for a “why” and I got a “that”. It may be that there is nothing deeper, right? But then I think there is something deeper in the Thomistic conception, and that would make Thomism more appealing, all else equal.”

      This is a fascinating point! Ultimately, we face brute necessity no matter what we have as our ultimate explanation of reality or of composite things. Sure, when you ask “why do those parts cohere”, I may ultimately have to get to a fundamental, necessary foundation layer of reality which has its parts cohering of metaphysical necessity. But it seems equally the case that I can ask “why does God exist?”. And the answer seems ultimately to be that it is necessary that God exists. You may instead say that God exists because his very essence is identical to the very act of existence. But then I could ask, “but why is his essence and existence identical?”. And note this isn’t a “why” in the sense of “why are we rationally justified in believing this,” but rather a question as to the metaphysical explanation of it. And it seems that the explanation is just that “well, that’s how he is” or “it’s necessarily the case”. It seems that any account must posit brute necessity at the foundation of reality (or, if it isn’t brute, its simply explained solely in terms of its very necessity). Either way, I think your point is not unique to my position but plagues any worldview, including Thomistic ones.

      Once again, thank you so much for your patience, kindness, and willingness to probe reality with me. You are special and awesome.

      Thank you so much,

      MOR

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