Tuesday, August 24, 2010

Unrolled dice and eternal stars…

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The point of this post is to differentiate between different kinds of causation and possibility as they figure in debates about God's existence.

Imagine a world that consists entirely of a die-cast mold and some plaster filling that mold. Call this world Wmp. Could such a combination (have) exist(ed) independently for all time? I suppose so. An immediate impulse is to say that a die-cast mold must have been crafted by someone, so this austere scenario seems to require a prior cause. But I'll suppress that impulse for the moment and grant this mold-plaster scenario, for argument's sake.

To make the suppression easier, consider a different world, Wd, which consists entirely of a pair of die in a small bowl. Our impulse once more is to imagine the dice had been rolled, or at least placed, in the bowl, or, at the very least pressed in a machine to make their divots and dimensions. But I don't think it's inconceivable for Wd to exist, so I'll grant it.

Now, both Wmp and Wb would be only dimly causal worlds. In Wmp the shape of the mold gives the plaster its shape, but, then again, the plaster is also what gives the mold its shape qua mold. So there's only a very weak form of mutual causation between them. Further, lacking any other entities, nothing could bring about their separation, which means, once again, causation is basically vacuous in Wmp. The same holds for Wd.

I am pondering these ponderables because of thoughts I had about Doug's presentation of the Scotist modal argument for God's existence (SMA). Here is how Doug presents the argument:

1. A First Cause possibly exists. (Premise)

2. Whatever is possible is either contingent or necessary. (Definition)

3. Whatever is contingent can be actualized. (Premise)

4. A First Cause cannot be actualized. (Premise)

5. Therefore, a First Cause is necessary. (From 1 - 4).

Doug then adds that

…atheistic philosopher William Rowe doesn't dispute any of the premises of Duns Scotus' argument. Rather, what Rowe attempts to do is demonstrate that if this argument were correct, it would lead to all kinds of absurdities:
Surely it is possible for an everlasting star to exist. The stars that exist are presumably not everlasting--for each star, let us suppose, there was a time before which it did not exist and there will be a time at which it ceases to exist. But this seems to be an empirical fact and not a matter of conceptual or logical necessity. The idea of an everlasting star does seem to be a non-contradictory idea, even if no star is in fact everlasting. Let us grant, then, that

i. it is possible for an everlasting star to exist.

Now clearly we must grant that

ii. it is impossible for an everlasting star to come into existence. (If x comes into existence then by definition x is not everlasting.)

Moreover, since if something is produced by something else then there was a time before which it did not exist, we have

iii. it is impossible for an everlasting star to be produced by something else.

[The Cosmological Argument, Fordham University Press, 1998, pp. 52-53.]

Doug responds by saying:

The problem with Rowe's counter-argument is that it assumes a type of modality not necessarily entailed by Scotus. Even a star that is everlasting is being actualized by the matter that composes it. The analogy, then, of a non-actualized everlasting star seems to be incoherent and disanalogous to the SCA. For, the First Cause that Scotus envisages is simply not actualized at all.

I agree, but also added what I think is a subtly different and perhaps even more basic rejoinder. Namely, the problem with conceiving of an everlasting star is that the definition of a star is a) that it is a collapsed planet and b) that it therefore has a finite amount of mass to expend before expiring. A star's definitional parameters for being require not only that it 'descended' or 'emerged' from a prior state of affairs, namely, a planet in collapse, but also that it have a finite amount of energy. Positing an eternal star, therefore, is as incoherent as positing an unborn son or an eternal two-week vacation. So Rowe's objection is––I can't help myself––a non-starter.

Perhaps Rowe, or a Rowe-like objector, would reformulate his position to mean that there is something––call it a star*––which we call "a star" but that is only phenomenally like a star (i.e. bright, hot, large, etc.). This star* would display all the 'behavior' of a star but would not be subject to the prior limitations on what a star actually is. Unfortunately, this only opens the way for further objections. For instance, being like a star entails that a star* pulsates at a specific radiometric frequency and that it recedes from a terrestrial observer at a specific Dopplerized velocity. As such, a star*'s phenomenal constitution intrinsically bears reference to spatiotemporal succession, at least in notion, and therefore includes contingency and change in its own notion.

Thus, while a star* could be posited ad hoc to have just "been there" from/for all time, its stellar specificities as a cosmic sub-entity render it decisively unlike what God is. An infinitely large star coextensive with the cosmos is incoherent, since a star must at least phenomenally shine against some non-star background. If Rowe and Rowesque objectors go for broke by saying the star––now call it Star!––is immobile, unchanging, infinitely powerful, timeless, purely luminiscent, devoid of any interfering or transmitting medium, etc., they will be dangerously to mounting an atheist case for God. The more this Star! takes on divine attributes, the less it enjoys properly stellar attributes, until eventually Rowe's objection just becomes a species of the "flying spaghetti monster" argument. At which point we must invoke St Thomas: "Sapientis enim est non curare de nominibus" (Wisdom does not treat of names).

Rowe's everlasting star and my everlasting Wmp and Wd are all counterintutive but nonetheless conceivable. Now here's the point I want to make about differing kinds of possibility in these arguments.

Let's say something is possible1 iff nothing in the notion of the thing entails an intrinsic contradiciton. A square circle would not be possible1.

Now let's say that something is possible2 iff it is possible1 and possible1 for it to exist with accidental variations. For example, as an American, it is possible1 for me to be a citizen of Idaho but only possible2 for me to be a citizen of Idaho after 1890 (when Idaho was admitted to the Union). It is likewise possible1 for N. and K. (the individuals who became my parents) not to have had me, but it is not possible2 for me not to have had N. and K. as my parents. Who I am intrinsically depends on my being the child of my parents. My proper parameters for being preclude an alternate parentage is possible2.

Lastly, something is possible3 iff it possible1 but not possible2. This means that a state of affairs S:a is conceivable (possible1) but it is inconceivable (~possible1) for S:a to exist in any other way, under any other circumstances, by any different means, in any other sense, with any other parameters for being, and so on.

This notation is totally provisional and may be terribly faulty, but, hey, this is a blog, so let me show how they apply to my larger point. I realize that the more conventional terms are "conceptual possibility" (possible1), "metaphysical possibility" (possible2), and "analycity" (possible3), but for some reason I want to avoid those terms in this train of thought. I would like to say that something possible1 is weakly possible, or enjoys weak possibility; something possible2 is strongly possible, or enjoys strong possibility; and something possible3 is integrally possible, or enjoys integral possibility.

Wmp is possible1 and possible2, but not possible3. Here's why: As I've granted, Wmp is possible1 but it is also possible1 for Wmp to exist in slightly different ways. For instance, imagine there were numerously variable pock marks in the surface of the plaster that allowed for 'air' to exist between the mold and the plaster. Or imagine no such gaps existed, and the interior of the plaster mold was perfectly hermetically smooth. Or imagine the many possible shades of the plaster, or what metal the mold is made of, and so on. The variables are endless, yet they don't compromise what Wmp is as a whole S:a. This is because there is nothing in the definition of a die-cast model and/or of a mass of plaster that either preclude its possible1 existence or exhaust its possible2 features. The same holds for Wd. The size, smoothness, glint, separation, etc. of the dice can vary indefinitely when considered in possible2 terms.

Now contrast this with the SMA, which argues that if an Unactualized Actualizer (UA) is possible1, such an Actualizer is necessary. (The UA is "unactualized" by virtue of not being subject to anything which essentially makes it actual. It is simply actual, not actualized.) The UA is possible1, since it is not intellectually repugnant like a square circle or a married bachelor or an unborn son. But is the UA possible2? I say it is not. For the very definition of the UA is not to be subject to variations in its conditions of existence, such variations being the way a thing is possible2. Unlike Wmp and Wd, the UA could not exist in any other way, could not be subject to any other qualifications, and still remain what it is by definition. Making the UA possible2, therefore, amounts to asserting that the UA is not possible1. By supposing the UA could be actualized based on, or according to, numerous other factors or under numerous other conditions––and could be "de-actualized" by other unsuitable factors/conditions (à la me and Idaho and 1889)––, the suppositions would subject the UA to an existential conditioning precluded by its definition (as a weakly-possible). Unlike Wmp and Wd, and like a circle, there is no way to 'tweak' how the UA exists without denying the possibility that the UA exists altogether. The UA is possible1 only in the way it is presented as being possible1, which means it is possible3. Like Wmp, the definition of the UA entails that it is possible1 but precludes that it is possible2. Insofar, therefore, as the UA is possible1 and not possible2, but is possible3, and its possibility conditions include its necessary existence, then the UA is actually existent (again, by virtue of it remaining a coherent first-order possibility).

Circular circles…

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In some cases, naming a thing necessarily entails asserting a thing's nonexistence. For example, if by W:x~W I name "the factor or set of factors which make the present state of affairs to be other than what they are at present," I am implicitly and necessarily denying the existence of W:x~W. Nothing exists or could possibly exist to make the present state of affairs other than they are at present. That's trivially true but, obviously, metaphysically complex.

Likewise, in some cases, naming a thing necessarily entails asserting a thing's existence. For example, if by W:xW I name "the factor or set of factors which make the present state of affairs to be they are at present," I am implicitly and necessarily asserting the existence of W:xW. That which makes the present state of affairs what they are at present cannot not exist. That is, again, trivially true but also metaphysically complex.

Why not see God's existence in the same way see a circle? Why not see the relationship between "deity" and "existence" in the same way we see the relationship between "circularity" and "roundness" (or "punctual equidistance")? Necessarily, either a circle is round or a circle is not possible; and, necessarily, either a necessary being exists or such a being is not possible. But the very terms involved––circle and round, necessary being and existing being––entail each other. In my view, "a necessarily existent being" is as much of a circumlocution for "God" as "a punctually equidistant set of points" is for "a circle." Something must fulfill what it is to be a circle, otherwise the term itself is incoherent; but it is not incoherent, since 'that which is circular' entails its roundness. Likewise, something must fulfill what it is to be W:xW, otherwise W is impossible; but since W is necessary, W:xW is also necessary. In the same way, something must fulfill what it is to be a necessary being, otherwise the term itself is incoherent; but it is not incoherent, since the term itself entails its own existence.

Perhaps an objector says, "But we can imagine 'deity' not existing. We can't imagine a non-round circle"?

I reply that I can imagine a non-round circle, in at least two ways. First, the circle is a thin rubber hoop. I find it jumbled into a knotted heap in a box. Nothing about it says "round" to my imagination. Yet it is round. Second, every instance of a circle we have experienced is actually not perfectly round and therefore not a circle. The imperfections in the chalk on the board, in the graphite on the paper, in the branch as it carves through the sand, etc.––in every case, a circle as we know it is just an approximation of 'what a circle is' in se. Yet I know such "circles" are circles because I, so to speak, know "what they are getting at." To deny that "the circle" is an impossible shape because we cannot present one devoid of any defects, is to fail to grasp what a circle is, not to disprove how and that circles exist. Likewise, while all arguments for (or presentations of) God may fail to capture wholly and perfectly 'what God is', yet we know "what they are getting at." Hence, to say that "the Deity" is an impossibility because we cannot articulate It devoid of any defects, is to misconceive of what the Godhead is, not to disprove how and that the Deity exists.

The objector continues, "But your conception of the Deity is just an historical accident. Had you been born in a different culture and a different time, you might have thought the Deity was born from an eternal chaos, etc."

I reply that our conception of a circle is also just an historical accident. Had our species evolved only to see straight and diagonal lines, we would have no conception of circularity. To retort that we have evolved to see circles because there really are circles in the world is but to beg the question, since there being circles in the world depends on circularity actually existing in the first place. I can just as reasonably say that we have evolved to detect the Deity in the world because the Deity really is in the world.

But the objector continues: "Ascribing a divine will to or 'behind' the world is just a massive cognitive illusion our species has developed because the illusion has tended to support survival and genetic transmission in the past. There isn't really 'the Deity' in the world; we are just programmed to think there is."

I reply that this only repeats the earlier error, which wanted to deny the existence of circles based on the fact that we don't experience perfect circles in nature. Seeing what is, at close range, a ragged trail of chalk on a board or graphite on paper and yet calling it "a circle" is just as much a cognitive 'illusion' as taking a discrete series of vibrations in air to be a coherent stream of language with a meaning. Fudging non-circles into "circles" must have tended to promote survival and reproduction, otherwise it would not have evolved (e.g. because such fudging drastically reduces computational demands and this reduces metabolic demands, or because Fudging the Forms prevents Platonic Paralysis by forestalling just pondering Circularity while Tigerness devours our Headness, etc.). We may have evolved to see what are not truly circles as circles, but this does not negate the existence of circularity per se.

It is my contention that any conception of God which admits His possible nonexistence is of the same character as a conception of circles which denies their roundness. I am well aware that St Thomas Aquinas, e.g. in SCG I, I, x–xi, admits the conceivability of the nonexistence of God, and thus I seem to be pitting myself against the Universal Doctor. As he says in capitum xi,

"For assuredly that God exists is, absolutely speaking, self-evident, since what God is is His own being. Yet, because we are not able to conceive in our minds that which God is, that God exists remains unknown in relation to us. So, too, that every whole is greater than its part is, absolutely speaking, self-evident; but it would perforce be unknown to one who could not conceive the nature of a whole. … For that He can be thought not to be does not arise either from the imperfection or the uncertainty of His own being, since this is in itself most manifest. It arises, rather, from the weakness of our intellect, which cannot behold God Himself except through His effects and which is thus led to know His existence through reasoning."

Thomas' target in these chapters is the Anselmian ontological argument and I don't think I am mounting an Anselmian ontological argument. St Anselm was arguing that a true grasp of what God is would convert the intellect into believing that God is. But as the quotation above indicates, St Thomas was more aware of the legitimate cognitive weaknesses many people have (à la illusions imbibed by our evolutionary past, as discussed above) and, thus, argued why Anselm's argument could not in itself convert the intellect to faith. I am making what I think is a more modest claim: insofar as God's essence is to exist, any argument against this notion fails to grasp what God is, and so, while this is not a rational fault of the objector, yet it is not a defeater for the notion of God as proclaimed in classical theism. A person may therefore legitimately be 'forgiven' for failing to see God's existence included in His essence and may be aided to faith by way of other (e.g. Thomistic) argumentation. Even so, this does not mean the person's failure to believe in God as necessarily existent is not an argument against God as held by the theist. By saying that St Thomas was perhaps more sensitive to humanity's endemic cognitive frailties, I do not mean to suggest St Anselm was unaware of the problem. This is why in chapter IV of Proslogium he says,

…there is more than one way in which a thing is said in the heart or conceived. For, in one sense, an object is conceived, when the word signifying it is conceived; and in another, when the very entity, which the object is, is understood.

In the former sense, then, God can be conceived not to exist; but in the latter, not at all. For no one who understands what fire and water are can conceive fire to be water, in accordance with the nature of the facts themselves, although this is possible according to the words. So, then, no one who understands what God is can conceive that God does not exist; although he says these words in his heart, either without any or with some foreign, signification. For, God is that than which a greater cannot be conceived. And he who thoroughly understands this, assuredly understands that this being so truly exists, that not even in concept can it be non-existent. Therefore, he who understands that God so exists, cannot conceive that he does not exist.


+ + +

Rough technical appendix… 

[∆ means possible, Ω means necessary, ~ means negation, : means predication]

1. It is impossible to assert the existence of a square circle (sc).
1a. ~∆P:(x:sc)

2. It is impossible to assert that a circle is not round (c~r) or that a non-circle is round (~cr).
2a. ~∆P:x(x:c•~r)•(x:~r)
2b. By 'round' I mean all points in an objects are equidistant from a single other point.

3. It is necessary to assert the circle is round.
3a. P:(x:c)ΩP:(x:r)

4. It is possible to assert the nonexistence of a square circle.
4a. ∆P:x(x:~sc)

5. It is necessary to be able to assert the nonexistence of a square circle.
5a. Ω∆P:x(x:~sc)

Monday, August 23, 2010

The Scotist-Anselmian argument for God?

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Doug says the following argument is "just for kicks," but I think it has some fertile potential. Quote:

1. There is possibly a sound ontological argument [sOA].
2. Therefore, God exists. (From 1 and S5)

Now, if you don't know, "S5" refers to an axiom in modal logic that, "If possibly p, and p necessarily, then necessarily p."

According to the Wikipedia, "The axiom is given as either

Possibly P implies Necessarily Possibly p \Diamond p \to \Box\Diamond p
Possibly Necessarily P implies Necessarily p \Diamond\Box p \to \Box p

Both of these axioms are properly called axiom 5."

Briefly stated, St. Anselm's "ontological argument" OA for the existence of God is the following:

1. God is that than which none greater can be thought. (Axiom)

1a. The very definition of God is that being which transcends any conception of Him, and therefore God is that 'being' compared to which no other 'thing' can be thought.

2. To exist actually is greater than to exist merely notionally. (Premise)

2a. A real dollar is better than the mere idea of a dollar. (Postulate)

2aa. That which does not exist has no way of enjoying, or having ascribed to it, any value or predicates whatsoever, therefore only that which actually exists can enjoy greatness and predication.

2ab. An imaginary dollar would not be money and therefore would be inferior as money to a real dollar. (From 2a and 2aa)

3. For God to exist actually is greater than for God to exist merely notionally. Insofar as the actual God would possess a greater perfection than a purely notional God, only an actual God would be that than which none greater can be conceived. (From 1 and 2)

4. Therefore God actually exists. His essence (or 'definition') necessarily includes His existence. (From 2 and 4)

I know of two standard objections. First, "existence is not a predicate," i.e. X's existing adds no content to 'what' X is. Therefore 'what God is' is trivially but decisively distinct from the proposition 'that He is'. Since the definition of a thing does not include its existence, the essence of God does not include His existence. Second, while it may be true that God's essence includes/entails His existence, this is a fact unknowable to us and therefore the ontological argument is merely suppositional. Kant is the most famous advocate of the first objection and St Thomas Aquinas is the most notable objector (besides Gaulino himself!) to the OA. It is a truism that, while everybody agrees the OA, no one agrees on why it fails. As such, it remains a tantalizing project for theists and non-theists to perfect and bury, respectively.

In this post I will not present my own thoughts on the OA--aside from saying I think a reasonable case can be made that, in some cases, existence is a predicate--, but rather will stick to considering Doug's argument above. His point is that, if in some world W there is a sound form of the OA (sOA), and since sOA delivers a necessary conclusion (viz. God exists), therefore God necessarily exists, and thus exists in our actual world AW. Here's an expansion of his argument:

1. There is possibly a sound ontological argument [sOA].
1.1 A sOA proves the necessary existence of God.
1.2 The necessary existence of God is possible.
2. Therefore, God exists. (From 1 and S5)

As I read it, this seems very much like Duns Scotus' modal argument (MA) for the existence of God, about which I have written very briefly before. Here's the argument in brief:

1. An Uncaused Producer is logically possible. (Premise)

2. Anything logically possible is either actual or potential. (Axiom)

3. A potential Uncaused Producer can only be caused (i.e. is not 'uncaused'), but a caused Uncaused Causer is a contradiction. (Postulate)

4. Hence, no Uncaused Producer is merely potential. (From 2 and 3)

5. Therefore, an Uncaused Producer is actual. (From 2 and 4)

6. This actual Uncaused Producer we call God. (Premise)

7. Therefore, God actually exists. (From 5 and 6)

Doug has written about the MA before as well, and he adds an objection by William Rowe, which I believe was dispensed with in the combox there. But again, I won't go into great detail on the argument as such, instead preferring to note the strange link between the OA and the MA. For the OA is effectively saying that it's impossible for God to be God and not exist, while the MA is saying that a necessary being is not possible unless it exists, and a necessary being is certainly possible. Hence, I'm inclined to say the OA and the MA mutually entail each other. Consider:

1. There is possibly a sound Scotist modal argument [sMA].
2. Therefore, God exists. (From 1 and S5)

Since it is possible that a necessarily true formulation of the OA exists, and the OA necessarily entails that God exists, then necessarily God exists. Likewise, since it is possible that a necessarily true formulation of the MA exists, and the MA necessarily entails that God exists, then necessarily God exists.

I suppose the rejoinder to all this would be that, since it is possible sound refutations of the OA and the MA exist, therefore God cannot exist. But I don't think that will work, since the necessity of the refutations is notionally parasitic on the arguments themselves. The only way to refute them entirely is to deny the first premise of all philosophical theology, namely, that "it is possible that God exists." I don't see how this denial could ever actually be made, so the OA and MA seem asymmetrically immune to absolute refutation. After all, the very act of mounting a decisive refutation of God admits "God" as a coherent, and therefore possible, subject of debate.


Modality of morality...

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Doug at Fides et Ratio has posted yet another pithy but stimulating entry, this time about the modality of moral commitments. I can't recommend Doug's blog highly enough, by the way. He's a very patient, lucid, devout, and thorough thinker, consistently producing mostly short, no-nonsense arguments on a wide range of topics in philosophical theology.

Anyway, here's his argument:

Suppose someone denies that there are objective moral obligations, e.g. moral obligations that persons everywhere are bound by. Imagine also that our skeptical friend is hesitant to accept the idea that something concrete could be logically necessary, but is willing to concede that propositions may be logically necessary. An example of a logically necessary proposition (one true in all possible worlds) would be this: "there are no square circles." Finally, suppose that objectivity entails logical necessity.

1. There are no objective moral obligations in the actual world. (Premise)

2. There are objective moral obligations in W. (Premise)

3. If there are objective moral obligations in W, then there are objective moral obligations in all possible worlds. (S5)

4. Therefore, there are objective moral obligations in all possible worlds. (From 2 and 3)

If you don't know, "S5" refers to an axiom in modal logic that, "If possibly p, and p necessarily, then necessarily p."

According to the Wikipedia, "The axiom is given as either

Possibly P implies Necessarily Possibly p \Diamond p \to \Box\Diamond p
Possibly Necessarily P implies Necessarily p \Diamond\Box p \to \Box p

Both of these axioms are properly called axiom 5."

The thrust of Doug's argument is that, if a necessarily true moral axiom is possible in some world, then that axiom is necessary in every world. Further, since it is obviously possible for there to be at least one such axiom in some world, it is necessarily the case in our world that there is such an axiom.

I replied to Doug by saying that I'm always a bit shaky on how S5 cashes out. For example, is it legitimate to import transworld necessity into W-indexed objectivity? Consider:

1. There are no objective moral obligations in the actual world (AW). (Premise)

2. In W it is objectively morally wrong to kill Smurfs.
(Premise)

3. It is objectively wrong in all worlds to kill Smurfs. (S5)

4. Therefore it is wrong to kill Smurfs in AW.

The problem is that there are no Smurfs in AW, so the necessary moral validity of 3. is objectively vacuous in AW.

Doug's initial response was:

I think the moral realist (myself included) would say that even if there are no Smurfs in AW, it would still be true that if there were Smurfs in AW it would be wrong to kill (murder) them. It's kind of like saying that even if there are no bachelors in W, then it would still be the case that if bachelors ever did come to exist in W, that they would have to be unmarried.

So, instead of saying that (3) is vacuous in AW, I would prefer to say that it is inapplicable, yet still meaningful in AW.

I replied that was my intuition as well, so going on from here, it seems a key gap to fill in this argument is against the objection that in AW there are no actual correspondents to fill the categories of any moral law. For example, "torturing babies is always wrong" The nihilist could equivocate forever about what "torture" means (noises too loud, nutritiously deficient food, less than angelic handling on a daily basis, etc.). Further, she might object to free will altogether and therefore evacuate the torturer's actions of malignancy. Or if we assert, "it is wrong to commit evil that good may result," she'll just deny good and evil result from anything in the first place. Of course, with an interlocutor like that, her horrid vacuity its own punishment and the quality of her voice in a moral debate would speak for itself--against her standing in nearly all other eyes.

This leaves me with two thoughts:

1. At least this argument forestalls the categorical assertion that moral absolutes are in principle impossible.

2. It might not get us practically farther than standard moral realist arguments, but it least it needn't keep reinventing the wheel about whether moral realism is possible.

It's an interesting argument, so I'm just thrashing it out to see what wheat falls from what chaff. Keep up the good work.

This is the day that the Lord has made...

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...and tomorrow is too often the day that unmakes today.

"God has promised forgiveness to your repentance, but He has not promised tomorrow to your procrastination." - St. Augustine (attribution)

HT to Doug B. at Fides et Ratio.

Reading the Summa contra gentiles

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ST. THOMAS D'AQUINO (1225–1274)

SCG I, I, xx: THAT GOD IS NOT A BODY (Quod Deus non est corpus)

[1] From the preceding remarks [in SCG I, I, xix, i.e. that in God is nothing violent or unnatural] it is also shown that God is not a body.

[2] Every body, being a continuum, is composite and has parts. But, as we have shown, God is not composite, and is, therefore, not a body.

[3] Again, everything possessed of quantity is in a certain manner in potency. For a continuum is potentially divisible to infinity, while numbers can be increased to infinity. But every body has quantity and is therefore in potency. But God is not in potency, being pure act…. Therefore, God is not a body
[Ergo Deus non est corpus].

[4] Furthermore, if God is a body, He must be some natural body, since, as the Philosopher proves, a mathematical body is not something self-existing, since dimensions are accidents. But God is not a natural body, being immobile, as we have shown, whereas every natural body is movable. God is, therefore, not a body.

[5] Again, every body is finite
[
Omne corpus finitum est],
as is proved in
De caelo I [I, 5]…. Now, we can transcend any given finite body by means of the intellect and the imagination. If, then, God is a body, our intellect and imagination can think of something greater than God. God is thus not greater than our intellect—which is awkward
[
Quodlibet autem corpus finitum intellectu et imaginatione transcendere possumus. Si igitur Deus est corpus, intellectus et imaginatio nostra aliquid maius Deo cogitare possunt. Et sic Deus non est maior intellectu nostro. Quod est inconveniens].
God is, therefore, not a body.

[6] Intellectual knowledge, moreover, is more certain than sensitive knowledge. In nature we find an object for the sense and therefore for the intellect as well. But the order and distinction of powers is according to the order of objects
[
Sed secundum ordinem obiectorum est ordo potentiarum, sicut et distinctio].
Therefore, above all sensible things there is something intelligible among things … [and] we can find something nobler above all bodies. Hence, if God is a body, He will not be the first and greatest being.


[That "the order and distinction of [cognitive] powers is according to the order of objects" [
secundum ordinem obiectorum est ordo potentiarum, sicut et distinctio], is a cornerstone of Thomistic epistemology. In Kantianism, by contrast, the order of objects––i.e. the knowable world––is according to the order and distinction of our cognitive structure.]

[7] A living thing, likewise, is nobler than any non-living body, and the life of a living body is nobler than it
[
Quolibet autem corpore vivente sua vita est nobilior],
since it is this life that gives to the living body its nobility above other bodies. Therefore, that than which nothing is nobler is not a body.


[God is the life of all things––the pure form of the world––and therefore distinct from all things by His very immanence.]


[8] Then, too, there are the arguments of the philosophers to the same effect, based on the eternity of motion
[ostendendum procedentes ex aeternitate motus].
They are as follows. In every everlasting motion, the first mover cannot be moved either through Himself or by accident…. Now, the body of the heavens is moved in a circle with an everlasting motion. Therefore, its first mover is not moved either through Himself or by accident. … Now, that to which the motion of the heavens is ultimately reduced as to its first unmoved mover is God. God is, therefore, not a body.

[This is interesting. Thomas grants
ex hypothesi the eternity of celestial motion––the analogue of which might, say, be "strings" in modern parlance––and argues further that, given the nature of local motion, God could not be a (local) body. So, even allowing for celestial eternity, Thomas notes how it would still depend on God as its First Unmoved Mover.]

[9] Again, no infinite power is a power in a magnitude. But the power of the prime mover is an infinite power. Therefore, it is not in any magnitude
[
Nulla potentia infinita est potentia in magnitudine. Potentia primi motoris est potentia infinita. Ergo non est in aliqua magnitudine. Et sic Deus, qui est primus motor, neque est corpus neque est virtus in corpore.].
Therefore, God, Who is the prime mover, is neither a body nor a power in a body.


[I love this argument. I have argued at least twice before––
here and here––that an infinite quantity is incoherent, and therefore that a key premise of naturalism (i.e. that the universe, being uncaused, is eternal, and therefore also spatiotemporally infinite), either renders the universe an object outside of scientific knowledge, thus making naturalism ultimately non-scientific; or, given the obvious measurability of the universe, scientifically refutes naturalism. Were the universe in itself of infinite power, and thus not dependent on God's infinite creative power, it would not be a magnitude, and thus would not be a body. But clearly the world is a body of a certain magnitude,ergo….

A further point I take from this argument is that, were the universe in se infinitely powerful, it would have actualized all possibilities within it, since nothing in it would be subject to (finite) potentiality. If that were the case, however, there would be no such thing as possibility per se in the world. But it's clear that this is only possibly the case and therefore possibility exists; ergo….

Additionally––and this is only a dim hunch––I think St Thomas' argument here also sheds light on the famous dispute between him and St Bonaventure (inter alii) on the possibility of the eternity of the world, i.e. on the feasibility of an actual infinitude in nature. (Cf. this page and this page for details.) St Thomas argued that we know the world is not eternal only by Divine Revelation, whereas St Bonaventure argued that it could be demonstrated an eternal world was impossible. St Thomas' De aeternitate mundi is actually (and ironically!) quite short, if you care to read it.

What strikes from this argument in SCG is that, perhaps a premise in Aquinas' argument (cf. articula v and vii, immediately above] is that the possible celestial eternity of the world does not impinge on the actual, empirical finitude of the world, whereas St Bonaventure was focusing on the temporal finitude of the world as a sensible reality. In other words, perhaps the cosmos Thomas granted could be eternal was not of the same order as the cosmos which Bonaventure insisted could only be temporal finite. They may, in other words, have been arguing equivocally about two subtly different conceptions of "the world." Might the aeviternality of the angels as cosmic powers somehow allow for a reconciliation of these views, if the former is linked to St Thomas' hypothetical conception of celestial as opposed to terrestrial eternity? Insofar, in other words, as the celestial world is beyond magnitude, it is not subject to finite (de)composition, and therefore could exist in an idealized timelessness. The terrestrial world, by contrast, is subject to magnitude and quantitative (de)composition, and therefore cannot be eternal. On the latter point I think St Thomas and St Bonaventure would agree.]


[10] The first proposition is proved thus. If the power of some magnitude is infinite, it will be the power either of a finite magnitude or an infinite one. But there is no infinite magnitude, as is proved in Physics III [5] and De caelo I [5]. But a finite magnitude cannot have an infinite power. Therefore, an infinite power cannot reside in any magnitude
[Magnitudo infinita nulla est, ut probatur in III Physic. et in I caeli et mundi. Magnitudinis autem finitae non est possibile esse potentiam infinitam. Et sic in nulla magnitudine potest esse potentia infinita.].

That an infinite power cannot reside in a finite magnitude is proved thus. A greater power produces an equal effect in a shorter time than a lesser power does in a longer time. … Therefore, by moving more swiftly, it should produce its effect in a shorter time than any finite power. Nor can it be in something lesser that still is in time. Therefore, this will be in an indivisible point of time. And thus to move, to be moved, and motion will take place in an instant—of which the contrary has been proved in Physics VI [3]
[Et sic movere et moveri et motus erunt in instanti. Cuius contrarium demonstratum est in VI physicorum.]. …

[Interesting. An infinite power would produce its effect in an infinitely small time, but this would mean motion occurs in literally no time at all, which is impossible. Thus, if the world were produced by a body of some (even, say, 'infinitely large') magnitude, its causing motion would never occur. Consequently, the cause of the motion of the world is not only not a body of any magnitude but also, for that reason, not subject to time, which allows for it to generate an infinitely powerful effect without the limitations of magnitude in time.]


[11] That the power of the first mover is infinite is proved thus. No finite power can move in an infinite time. But the power of the first mover moves in an infinite time because the first motion is endless. Therefore, the power of the prime mover is infinite.

[Now St Thomas addresses the other side of the coin, as it were. Just as no allegedly infinitely powerful finite magnitude can effect anything in a real amount of finite time, so no magnitude can effect an infinite effect in infinite time.]


… If the finite power of some body moves in an infinite time, a part of that body, having a part of the power, will move in a shorter time; for the greater the power of a mover, the more it will be able to keep up its motion in a longer time
[quia quanto aliquid est maioris potentiae, tanto in maiori tempore motum continuare poterit].
… Thus, as we add to the power of the mover, we shall always add to the time according to the same proportion
[Et sic semper, secundum quod addetur ad potentiam motoris, addetur ad tempus secundum eandem proportionem].
But after a certain addition has been made, the addition will reach the quantity of the whole or even exceed it. So, too, an addition of time will reach the quantity of time in which it moves the whole. But the time in which it moved the whole was said to be infinite. Therefore, a finite time will measure an infinite time—which is impossible.
[Ergo tempus finitum metietur tempus infinitum. Quod est impossibile.]

[12] But against this reasoning there are several objections.
[Sed contra hunc processum plures sunt obiectiones.]

[13] One objection is this. It can be assumed that the body that moves the first moved is not divisible, as is the case with a heavenly body. But the preceding proof is based on the division of the first body.

[This objection says that the foregoing argument simply begs the question about the divisibility of a first mover
as a body.]

[14] The reply to this objection is as follows. There can be a true conditional proposition whose antecedent is impossible. If there is something that destroys the truth of this conditional proposition, it is then impossible.
[Sed ad hoc dicendum quod conditionalis potest esse vera cuius antecedens est impossibile. Et si quid est quod destruat veritatem talis conditionalis, est impossibile].
For example, if someone destroys the truth of the conditional proposition, "If man flies, he has wings," it would be impossible. It is in this manner that the above proof is to be understood. For the following conditional proposition is true: "If a heavenly body is divided, a part of it will have less power than the whole." Now, the truth of this conditional proposition is taken away if it be posited that the first mover is a body; and the reason is the impossibilities that follow from it. Therefore, to posit this is impossible. A similar reply can be given if objection is made concerning the increase of finite powers. We cannot assume powers in nature according to all proportions of time to any given time. Nevertheless, the proposition required in the above proof is a true conditional proposition.

[Thomas is here saying that, were the first premise true––i.e. "the first body is indivisible"––, the objection against his argument in this chapter would stand. However, given the impossibilities that follow from such a claim, the first premise is false, and therefore the objection fails. I fear I am misconstruing something here, though.]


[15] The second objection is this. Although a body is divided, it is possible to find in a given body a power that is not divided when the body is divided
[…etsi corpus dividitur, aliqua virtus potest esse alicuius corporis quae non dividitur diviso corpore].
For example, the rational soul is not divided if the body is divided.

[16] The reply is as follows. The above argument does not prove that God is not joined to a body as the rational soul is joined to the human body; it proves that He is not a power in a body in the manner of a material power, which is divided upon the division of the body. So, too, it is said of the human intellect that it is not a body or a power in a body. However, that God is not joined to a body as the soul is, this is another issue
[
Et ad hoc est dicendum quod per processum praedictum non probatur quod non sit Deus coniunctus corpori sicut anima rationalis corpori humano: sed quod non est virtus in corpore sicut virtus materialis, quae dividitur ad divisionem corporis. Unde etiam dicitur de intellectu humano quod non est corpus neque virtus in corpore. Quod autem Deus, non sit unitus corpori sicut anima, alterius rationis est.].

[This is a very fecund rebutall and, from what I can gather, is the basic shape of Charles Taliaferro's
Consciousness and the Mind of God, a book I have wanted to read for about a decade, and which I finally have in my possession. The key point is that, even if we grant that there is some level of division at which we find a power not subject to the objections against infinite power in (finite) magnitude, this would only show that that power is not a body, which confirms the thrust of this chapter.]

[17] The third objection is this. If some given body has a finite power, as the above argument shows, and if through a finite power nothing can endure through an infinite time, it will follow that no body can endure through an infinite time. Thus, a heavenly body will of necessity be corrupted.

[See what I mean about Thomas' emphasis on celestial incorruptibility vis-à-vis the eternity of the world?]


[18] To this objection some reply that, as far as its own power is concerned, a heavenly body can fail, but it acquires an eternal duration from another being of an infinite power. Plato [Timaeus] seems to speak for this solution when he introduces God addressing the heavenly bodies as follows: “By your natures you are dissoluble, but through my will you are indissoluble; for my will is greater than your bond.”

[19] The Commentator attacks this position in Metaphysics XI. According to him, it is impossible that what can of itself not-be should acquire a perpetuity of being from another. This would mean that something corruptible becomes incorruptible, which according to him is impossible. Hence, Averroes answers the objection as follows. All the potency that is in a heavenly body is finite, but there is no reason why a heavenly body should have every potency. For, according to Aristotle in Metaphysics VIII, there is in a heavenly body potency with respect to place, but not with respect to being. Hence, a heavenly body need not have a potency to non-being.

[20] This reply of the Commentator, however, is not sufficient. Even if we should grant that in a heavenly body there is no sort of a passive potency to being, which is the potency of matter, yet there is in it a potency of an active kind, which is the power of being
[
Quia, etsi detur quod in corpore caelesti non sit potentia quasi passiva ad esse, quae est potentia materiae, est tamen in eo potentia quasi activa, quae est virtus essendi].
For Aristotle expressly says in De caelo I [I, 3] that "the heavens have the power to be forever.”

[21] Hence, it is better to reply as follows
[Et ideo melius dicendum est quod,…].

Since potency is said relatively to act, we must judge of potency according to the mode of the act. Now, according to its nature, motion has quantity and extension, and hence its infinite duration requires that the potency moving it be infinite. But being does not have any quantitative extension
[…cum potentia dicatur ad actum, oportet iudicare de potentia secundum modum actus. Motus autem de sui ratione quantitatem habet et extensionem: unde duratio eius infinita requirit quod potentia movens sit infinita. Esse autem non habet aliquam extensionem quantitatis],
especially in the case of a thing, such as the heavens, whose being is without change. Hence, the power of being need not be infinite in a finite body, even though it will endure to infinity. For it is one and the same whether through that power something will endure for an instant or for an infinite time, since its changeless being is not touched by time except by accident.

[22] The fourth objection is this. In those beings that in moving are not themselves altered, it does not seem necessary that what moves in an infinite time should have an infinite power. For such a motion consumes nothing of their power, so that after they have moved for a time they are able to move for no less a time than before. Thus, the power of the sun is finite, and because its active power is not lessened by acting, it is able, according to its nature, to act on the sublunary world during an infinite time.

[23] To this the reply is, as we have proved, that a body does not move unless it be moved. If, then, it should happen that a certain body is not moved, that body will consequently not move. But in everything that is moved there is a potency towards opposites, since the termini of motion are opposites. Therefore, of itself, every body that is moved can also not-be-moved. But what can not-be-moved is not of itself able to be moved through endless time, and hence neither to move through endless time
[Et ideo, quantum est de se, omne corpus quod movetur possibile est non moveri. Et quod possibile est non moveri, non habet de se ut perpetuo tempore moveatur. Et sic nec quod in perpetuo tempore moveat.].

[Being in motion entails being-moved. But since motion is radically subject to potency––i.e. in opposite directions––, any moving object is subject to potency as a moving object and therefore its motion lacks the necessity of an endlessly powerful mover. If it's not clear, the reason motion is radically subject to potency, is that, if a moving object were not possibly able to be moved in any other way, it would not actually be in motion, but would necessarily be in stasis, since, again, it would not be subject to any possible motion from its current (necessary) state of being. Conversely, any moving object cannot have been moving as it is from eternity, and thus cannot be an eternal mover.]


[24] The above demonstration, consequently, holds of the finite power of a finite body, which power of itself cannot move in an infinite time. But a body that of itself can be moved and not-moved, move and not-move, can acquire perpetuity of motion from another. This must be incorporeal. The first mover must, therefore, be incorporeal [Procedit ergo praedicta demonstratio de potentia finita corporis finiti, quae non potest de se movere tempore infinito. Sed corpus quod de se possibile est moveri et non moveri, movere et non movere, acquirere potest perpetuitatem motus ab aliquo. Quod oportet esse incorporeum. Et ideo oportet primum movens esse incorporeum.].

[I take this to be the linch pin of this chapter's argument.]

Thus, according to its nature, nothing prevents a finite body, which acquires from another a perpetuity in being moved, from likewise having a perpetuity in moving. For the first heavenly body itself, according to its nature, can revolve the lower heavenly bodies with a perpetual motion, according as sphere moves sphere.

[And this I take to be the linch pin to the distinction between celestial and terrestrial motion as it figures into the debate about the eternity of the world, discussed above.]

Nor, according to the Commentator, is it impossible (as it was impossible in the of perpetuity of being) that what of itself can be moved and not-moved should acquire perpetuity of motion from another. For motion is a certain flow out of the mover to the thing moved, and hence something moved can acquire from another a perpetuity of motion that it does not have of itself. To be, on the other hand, is something fixed and at rest in being, and, therefore, that which of itself is in potency to non-being cannot, as Averroes himself says [In XII Metaphysicorum], following the course of nature acquire from another a perpetuity of being [Esse autem est aliquid fixum et quietum in ente: et ideo quod de se est in potentia ad non esse, non potest, ut ipse dicit, secundum viam naturae acquirere ab alio perpetuitatem essendi].

[This is a very important point, but I don't have the time right now to exegete it at great length–not the least because it is a bit over my head! The basic point I take to be that, while motion can be granted perpetually from one mover to another, no such perpetuity can be given in the order of being as such, since the potency of a thing's actus essendi precludes it from receiving perpetual being. The heavenly bodies might, therefore, be able to move perpetually, but they can not have existed perpetually in and of themselves, since their perpetual motion depends on their being, and their being, in turn, radically depends on their reception of being from a necessary being.]

[25] The fifth objection is that, following the above reasoning, there does not seem to be a greater reason why an infinite power is not in a magnitude rather than outside a magnitude. For in either case it will follow that it moves in null time.

[26] To this the reply is that, in magnitude, time, and motion, finite and infinite are found according to one and the same notion, as is proved in Physics III [4] and VI [2, 7]. Therefore, the infinite in one of them removes a finite proportion in the others. But in beings without magnitude there is no finite or infinite except equivocally
[
Et ad hoc dicendum quod finitum et infinitum in magnitudine et tempore et motu inveniuntur secundum unam rationem, sicut probatur in III et in VI Physic.: et ideo infinitum in uno eorum aufert proportionem finitam in aliis. In his autem quae carent magnitudine, non est finitum et infinitum nisi aequivoce.].
Hence, the aforementioned method of demonstration is not applicable among such potencies.

[I understand the objection to be that, if a body cannot possess an infinite power by virtue of its having a magnitude, as was argued above, there is no probative reason to say that an infinite power is outside the order of magnitude either (viz., is not a body), since in either case, the infinite power will act in zero. Yet, the temporal nullity of an infinite effect by a body of some magnitude was argued as a disproof of infinite power being found in any body. Thomas' rejoinder seems to be, however, that insofar as magnitude, time, and motion are all linked under one metaphysical heading, a being without magnitude will not be subject to limitations by the other two categories. There is an inverse proportion between motion, time, and magnitude. An infinitely large body will have 'no where else' to go, and therefore will not move, and thus will not move at any time. By contrast, a being outside the order of magnitude altogether will not face these problems, since its infinite power is not proportionally limited by time. As such, the objection is a category mistake.

I admit this point is not totally clear to me.]


[27] There is, however, another and better answer [Aliter autem respondetur et melius]. The heavens have two movers, a proximate one with a finite power, which is responsible for the fact that they have a finite velocity, and a remote mover with an infinite power, which is responsible for the fact that their motion can be of an infinite duration. And thus it is evident that an infinite power that is not in a magnitude can move a body in time, but not immediately
[
non immediate in tempore].
But a power that is in a magnitude must move immediately, since no body moves except by being moved. Hence, if it did move, it would follow that it would move in null time
[Sed potentia quae est in magnitudine oportet quod moveat immediate: cum nullum corpus moveat nisi motum. Unde, si moveret, sequeretur quod moveret in non tempore].


[28] An even better reply is this.
[Potest adhuc melius dici quod…].
A power that is not in a magnitude is an intellect, and moves by will
[
…potentia quae non est in magnitudine est intellectus, et movet per voluntatem].
For we have proved that the intellect is not a corporeal power. Therefore, it moves according to the needs of the movable body and not the proportion of its power; whereas a power that is in a magnitude can move only through the necessity of nature.

[Potentia autem quae est in magnitudine non potest movere nisi per necessitatem naturae: quia probatum est quod intellectus non est virtus corporea.]
Thus, of necessity, it moves according to the proportion of its quantity. Hence, if it moves, it moves in an instant.

[29] Thus, with the removal of the preceding objections, we see that the argumentation of Aristotle stands
[Secundum hoc ergo, remotis praedictis obiectionibus, procedit demonstratio Aristotelis.].

[30] No motion, furthermore, which is from a corporeal mover can be continuous and regular, because in local motion a corporeal mover moves by pulling and pushing. Now, what is pulled or pushed is not uniformly disposed towards its mover from the beginning to the end of the motion, since at times it will be nearer and at other times farther away. Thus, no body can move with a continuous and regular motion. But the first motion is continuous and regular, as is proved in Physics VIII [7]. Therefore, the mover of the first motion is not a body.

[31] Again, no motion to an end that passes from potency to act can be endless, since when it reaches act the motion comes to rest. If, then, the first motion is endless, it must aim at an end that is always and in all ways in act. But such an end is not a body or a power in a body, since all such things are movable either through themselves or by accident. Therefore, the end of the first motion is neither a body nor a power in a body. But the end of the first motion is the first mover, which moves as something desired. This, however, is God. God, therefore, is neither a body nor a power in a body.

[32] However, although according to our faith it is false that the motion of the heavens is perpetual
[
Quamvis autem falsum sit, secundum fidem nostram, quod motus caeli sit perpetuus],
… yet it is true that it will not fail either through a failure of power in the mover or through the corruption of the substance in the moved; for there is no evidence that the passing of time has slowed down the motion of the heavens. Hence, the above demonstrations do not lose their force.

[33] With this demonstrated truth divine authority stands in agreement. For it is said in John (4:24): “God is a spirit, and they that adore Him must adore Him in spirit and in truth.” It is likewise said: “To the King of ages: immortal, invisible, the only God” (1 Tim. 1:17). Again: “The invisible things of God... are clearly seen, being understood by the things that are made” (Rom. 1:20); for what is seen, not by sight, but by the intellect, is incorporeal
[
quae enim non visu sed intellectu conspiciuntur, incorporea sunt].

[34] Thereby is destroyed the error of the early natural philosophers, who posited only material causes
[Per hoc autem destruitur error primorum philosophorum naturalium, qui non ponebant nisi causas materiales],
such as fire or water or the like, and who thus said that the first principles of things were bodies and called them gods. Among them there were some who further posited friendship and strife as moving causes. (They, too, were refuted through the above arguments.) For since, according to them, strife and friendship are in bodies, it will follow that the first moving principles are bodily powers. They also held that God is composed of the four elements and friendship, which would give us to understand that for them God was a heavenly body. Among the early thinkers, Anaxagoras alone approached the truth by positing that an intellect moved all things
[
Inter antiquos autem solus Anaxagoras ad veritatem accessit, ponens intellectum moventem omnia].

[35] By this truth, too, are refuted the Gentiles, who, taking their beginning in the errors of the philosophers we have listed, posited that the elements of the world and the powers in them are gods; for example, the sun, the moon, the earth, water, and the like.

[36] By the same arguments, moreover, are set aside the wild fantasies of the simple Jews, Tertullian, the Vodiani or Anthropomorphite heretics, [as well as Mormons,] who endowed God with a bodily figure; and also of the Manicheans, who thought that God was a certain infinite substance of light, stretched out through an infinite space.

[37] The occasion of all these errors was that, in thinking of divine things, men were made the victims of their imagination, through which it is not possible to receive anything except the likeness of a body. This is why, in meditating on what is incorporeal, we must stop following the imagination.
[Quorum omnium errorum fuit occasio quod de divinis cogitantes ad imaginationem deducebantur, per quam non potest accipi nisi corporis similitudo. Et ideo eam in incorporeis meditandis derelinquere oportet.]


[This is a lapidary distillation of proper method in dogmatic theology! Skeptics want a 'model' or a 'picture' or a perfect 'analogy' for God, but to ask for that is to beg the question in favor of a God beneath the incoporeal, immortal, omnipotent God of classical theism.]