Digressive Opening
As it happens, the day I read Stephen H. Webb’s latest was also the day my students presented on the Borges short story–which I think is parody as well as homage to its dedicatee, H. P. Lovecraft–“There Are More Things.” The title, of course, is a reference to Hamlet (which, I am happy to report, the students readily traced to its origin and explained). There is a sort of surreality to reading someone’s doubtful speculations on the application of quantitative infinity to deity (hint: doesn’t work well) with Borges, Lovecraft, and the story’s reference to “Hinton’s cubes.” A meander down that side street led to the following remarkable observation:
Where this gets interesting is if we pick up on the suggestion made by Smith, Berkove and Baker, that Flatland is a criticism of the misapplication of reasoning by analogy. They argue that Abbott was keen to critique what he saw as the over-extension of analogical reasoning of which Cardinal Newman, for one, was guilty, and what he saw as the tendency to obscure the linguistic roots of this rhetorical construction. They conclude: ‘Flatland is a cautionary tale about the dangers of the imagination when wrongly applied.’
(source: Flat Charles | The Fairyland of Geometry)
I think I disagree with this criticism, but I’ll have to reread Flatland to find out. For the moment, suffice to say that I thought the juxtaposition of mathematization and the doctrine of analogy was pretty interesting. (Enjoy a picture of Hinton’s cubes!)
(source: Hintonian Cubism (part 1))
Distressingly Obtuse
I keep wondering how Webb gets such a hearing, but then I also keep being reminded by his columns of side-trips and dead-ends in thought–in my thought, at times; more generally, in the history of theology.
The perplexing conclusion of Webb’s latest piece sounds like the sort of thing a Lovecraftian character in a Borges story might well say:
God is like a hypercube whose dimensions, if ever mapped for the purposes of notation, would have no apparent numerical end. If so, then it is not quite accurate to say that God is infinite, but it would make some sense to say that our potential knowledge of God most certainly is.
(source: Is God Really Infinite? | Stephen H. Webb | First Things)
As a rule, of course, any summary “God is like” statement can be expected to turn out badly. This one is odd in two ways, though: Odd in that, if it is intended to represent a traditional understanding of God’s “infinity,” it does so only by obfuscating what it pretends to elucidate; odd in that Webb seems to have unironically concluded that divine self-revelation and human understanding, to say nothing of the divine essence, can be spoken of in a language of quantitative specification.
Please understand: I have myself, repeatedly, objected to the use of “infinity” as an excuse for irrationalism in theology. I have been known, myself, to reject the conventional use of “infinity” in both Calculus and theology. I think “infinity” too often stands in for such disparate notions as “unlimited potential” and “irrational presumption of unlimited magnitude or multitude of actual beings” and “a procedure that theoretically never needs to stop” and “really big” and “currently unspecifiable totality” without clear differentiation in popular discourse. In those thrilling days of yesteryear when I finished my B.A. at the theological hothouse of The Master’s College, my polemics against a simplistic mixture of contemporary evangelicalism and Dordtian Calvinism triggered a relapse of rationalism, during which I would willingly have jettisoned divine aseity [which I had not come to understand properly yet], infinity in time [which I conflated with the simplistic and falsely spatialized “outside time” language that often short-circuits our understanding of the subject], and other teachings which, when read poorly and flatly through a tacit Scotist rejection of analogy and a nominalist account of divine volition, certainly seemed to describe a “God of the philosophers” who resembled the God of the Bible only very distantly. It would take well over a decade for me to not only prefer a confessional, creedal, difficult orthodoxy to a simplistic rationalization, but also to embrace it with understanding and commitment; it would take me a long time to express how many, not merely conceptual, links were fitted in that chain.
He drew me with the cords of love,
And thus He bound me to Him.
And round my heart still closely twine
Those ties which naught can sever
(source: Hymn: I’ve found a Friend, oh, such a Friend)
I have been known to say, even recently, that when “infinity” is conventionally (mis)understood as a quantitative expression, we should probably reject the statement “God is infinite” out of hand: God is One, which is finite; God is Three, which is finite; God is not both One and Three in the same way at the same time, so there is no ground for an irrationalism at the base of our theology. (But of course, God is One in ways that none of His creatures are, both with regard to singularity and unity; and God is Three in ways no group of His creatures can be, not least in that these Three are One!)
When I encounter Webb’s thinking, then, I find myself entering my mental storage unit in search of the old Procrustean Bed I used to make up for God, in my poor hospitality: a reductive framework that forces the whole of theology to shrink to the scale of the quantifiable–a theology which is scandalized by the singular. I find myself remembering the day that a subtly equivocal theological article threw a hand-grenade into my entire system of belief with an argument that transfinite mathematics violated the PNC, nearly a decade after my debate team friends at Bob Jones University blasted my rationalist theism with Kant’s antinomies. This terrifyingly intense rational mysticism is a way of trying to survive the heart-and-head dualism of evangelical Christianity by insisting that the “God I can understand well enough to be convinced I KNOW exactly this God, and not any slightly different conceptualization of God” is also suitable for fervent personal piety; as I used to say in those anti-Calvinist polemics, “God must be lovable!”
Here is an example of what results from attempting to make up a quantitative Procrustrean Bed for the God of Abraham, Isaac, and Jacob to take His Sabbath Rest in:
We can know Graham’s number by describing how it functions (although really we are left with trusting that some very specialized mathematicians can describe this number to each other), but we can never know what that number actually is. If God is infinitely greater than that, then it seems like God is more like a random number picked from a range similar to Graham’s number. That number would be impossible to describe as well as to notate. That number, we could say, would be infinite all the way down. It would also be infinitely irrational, since it would be impossible to use it in any useful way.
(source: Is God Really Infinite? | Stephen H. Webb | First Things)
Not only are we “left with trusting…mathematicians,” we are missing almost everything important about God, and our knowledge of God, in the assumptions underlying this paragraph. That “infinity” applied to God should be a quantitative infinity, for one. That “how it functions” is a fitting consideration for an understanding of God (or, for that matter, that it is not metaphorical or rhetorical when applied to a mathematical construct). That an arrangement of ciphers with no objective correlative, hypothesized by creatures, stands in any meaningful non-arbitrary relation to the Creator, or His self-disclosure, or even to our better-warranted ideas about God and revelation (as opposed to, say, the abstruser parts of Spinoza or Leibniz). The sheer complexity of the breakdown in this paragraph–the yawning aporia–fatigues and irritates long before it begins to argue.
Let us choose just one word, then. A particular mathematical and imaginative process allows us to ascribe meaning to a certain cipher, a cipher which cannot literally be ciphered (as has been established). That is, we can ascribe meaning to a thing which cannot even be enumerated in any reality we are capable of working in; yet the thing is of our own construal, insofar as it is a “thing” at all (it is not a thing at all). And Webb challenges us to explain what we mean by saying “God is…greater” than that thing, than that hypernumerary cipher. In fact, “infinitely greater.” But here we have, in one expression, the equivocation that founds this whole muddle–twice. This thing, “Graham’s number,” is all potential–no act. It is not even a creature, but a construal of creatures; in every sense an ant, even a speck of sand, is “greater” than this thing. The unicity of any particular ant is the demonstration of a potency that can be ascribed to “Graham’s number” only insofar as chalkboards and computers and data files and models and hours of effort and grant money and published pages demonstrate the commitment of certain humans to this ciphering that cannot be ciphered. If God is “infinitely greater” than “Graham’s number,” it is no great wonder; He is greater than the ant, too; greater than the speck of sand; and “greater than our hearts” as well.
But perhaps this is Webb’s point, and he is just swinging wild in his attempt to make it: That to say “God is infinitely greater” with regard to any quantity humans can imagine is redundant, because “infinitely” adds nothing to “greater”; that “greater” is being used equivocally, not univocally or analogically, when we say “Graham’s number is greater than a googleplex” and then “God is greater than Graham’s number,” and that in such an environment “infinitely” can only add confusion. “Infinitely” repeats the confusion in “greater,” and if we are not careful, we will blame “infinitely” for our confusion.
Webb does not seem disposed to be careful, and we do not have to go far to discover the reason:
Attributing infinity to God and negative theology go hand in hand.
[…] An infinite God, Przywara argues, is not beyond what we know in any measurable degree. If we knew to what degree our knowledge of God falls short of its object, we would know something about who God really is. Our ideas fall so far short of God that we cannot even know how wrong they are. It follows that the clearer we make our conceptions of God—the more specific their reference or finite their form—the further God is beyond them. God’s infinity is infinitely receding, according to Przywara’s perspective. Knowing God is not just analogous to knowing what infinity is, since we can have some idea of that. No, the infinite God must be infinitely unknowable.
(source: Is God Really Infinite? | Stephen H. Webb | First Things)
To the extent Webb has represented “negative theology” correctly, and to the extent he has represented Przywara correctly, I share his desire to object in favor of the intelligibility of revelation. Without defending the objects of his animadversion, however, I think I must point out that Webb is really wide of the mark, here–straining beyond reason to define out of existence what needs only to be called “wrong.” I have been there. But–to equivocate–this is to strain out a gnat, and swallow a camel!
First, it is not necessarily the case that “infinite” applied to God means everything Przywara may construe it to mean. It is also not the case that use of “infinity” in the heuristic strategy of apophatic theology is a necessary consequence of affirming that God is “infinite” in one sense or another. We may simply be able to criticize sloppy or irrationalist uses of “infinite” and more carefully express God’s intelligibility and illimitability as coordinate truths.
But more profoundly, Webb appears disposed to ignore infused and participated knowledge as possibilities, here. Actually, I suspect that he is displacing them from this conversation, and has them in mind as part of the solution to some of the problems he is raising. But even from the position Webb represents Przywara as holding, it would seem evident that we can solve the problem Webb raises: the problem of whether God is intelligible, that is, whether intelligible divine revelation can prove true. Webb argues that the ciphering by which mathematicians construe “Graham’s number” possesses a desirable feature that theological probing of divine infinity lacks: “describing how it functions” seems to allow us to account for “Graham’s number,” while an effort to refer to the infinite God directly as such–such as Anselm’s–is “not like a formula with rules for the intellectual moves that will lead our thought to a specific goal, which can be picked out among a number of alternatives.” If–and I do say “if”–even if it is true that Webb’s construal of Przywara is correct, and reflects something that invariably accompanies the affirmation of divine infinity, it remains the fact that Christians have readily understood that there are quite literally “rules for…moves” that “lead our thought”–prominently including the whole, not merely a reductive rationcinative habit, of the agent intellect–“to a specific goal.” This definite intelligibility is available in the form of a dogmatically interpreted, traditionally understood, Biblically inscribed saying that is, first and foremost, a dominical Word:
I am the bread of life; he who comes to me shall not hunger, and he who believes in me shall never thirst. But I said to you that you have seen me and yet do not believe. All that the Father gives me will come to me; and him who comes to me I will not cast out.
(source: John 6:30-69 RSVCE – So they said to him, “Then what sign – Bible Gateway)
This Word is not distant, not unintelligible, however little we may comprehend it:
The word is near you, on your lips and in your heart (that is, the word of faith which we preach)
(source: Romans 10:5-13 RSVCE – Salvation Is for All – Moses writes – Bible Gateway)
And this Word–this goal–most certainly “can be picked out among a number of alternatives”:
Therefore, my beloved, shun the worship of idols. I speak as to sensible men; judge for yourselves what I say. The cup of blessing which we bless, is it not a participation in the blood of Christ? The bread which we break, is it not a participation in the body of Christ? Because there is one bread, we who are many are one body, for we all partake of the one bread. Consider the practice of Israel; are not those who eat the sacrifices partners in the altar? What do I imply then? That food offered to idols is anything, or that an idol is anything? No, I imply that what pagans sacrifice they offer to demons and not to God. I do not want you to be partners with demons. You cannot drink the cup of the Lord and the cup of demons. You cannot partake of the table of the Lord and the table of demons. Shall we provoke the Lord to jealousy? Are we stronger than he?
(source: 1 Corinthians 10 RSVCE – Warnings from Israel’s History – I – Bible Gateway)
It is not at all obvious to me in what respect Anselm’s formulation (“that than which nothing greater can be thought”), which is inadequate but not inaccurate, necessarily leads to a failure of this mode of knowing. Even where certain forms of acquired knowledge seem to remain starkly contingent–where we have revelation, or fancy, or nothing–sheer creatureliness involves a participation in reality, in Creation, which lends itself to revelation, without any opposition from rationale unless we construe it so. A lack of reductively rational certitude is no bar to firm assent, unless we choose to make it so:
I am much more sure that everything is good at the beginning than I am that everything will be good at the end. That all this frame of things, this flesh, these stones, are good things, of that I am more brutally certain than I can say. But as for what will happen to them, that is to take a step into dogma and prophecy. I speak here, of course, solely of my personal feelings, not even of my reasoned creed. But on my instincts alone I should have no notion what would ultimately happen to this material world I think so magnificent. For all I know it may be literally and not figuratively true that the tares are tied into bundles for burning, and that as the tree falleth so shall it lie. I am an agnostic, like most people with a positive theology.
(source: “What is Right With the World” — G. K. Chesterton)
It is for precisely this reason that the Christian has no need for what avowed mechanistic materialist H. P. Lovecraft described as “a naively insipid idealism which deprecates the aesthetic motive and calls for a didactic literature to ‘uplift’ the reader toward a suitable degree of smirking optimism.”
Stealing Home
It is also not at all obvious to me that one needs to accept what Webb construes as Przywara’s position, or as negative theology, in order to affirm divine infinity. I am made suspicious that Webb is arguing with himself in an echo chamber–that his misconstruction of other positions dictates precisely what is skewed in his own position, and vice versa–when we arrive at his penultimate assertion:
The alternative to this line of speculation is to return to Aristotle’s distrust of infinity (apeiron), an idea he found to be unsettling and not a little unthinkable, like a body without boundaries. Aristotle denied that anything that actually exists can be infinite, although he accepted a potential infinity, in the sense of a series that continues without any logical ending.
(source: Is God Really Infinite? | Stephen H. Webb | First Things)
Aristotle, of course, was a pagan; his conception of God might resemble the true God (just in case God actually is intelligible by natural reason), but manifestly it was not an adequate conception of God (or else he would not be pagan “conceiving of” God, but would confess a received faith in God). We will see, eventually, that what Webb has done here is to continue–in his response, as throughout his objections–to treat “infinity” only quantitatively, only with regard to magnitude or multitude. Although he is right that Aristotle–like St. Thomas, and like modern mathematicians–accepts “potential infinity” but treats an “actual infinity” in magnitude or multitude as a misunderstanding, Webb misses both an important exception in Aristotle and a still more important distinction between Aristotelian and Thomistic thought on the matter.
This misconstruction is of a piece with what seems to be Webb’s continuing project. As Webb critiques Przywara’s work on the “Analogy of Being,” he finds that in this crucial concept that Aquinas clarifies and Scotus rejects, only the difference finally signifies; the difference that remains between understanding and comprehension, between “things revealed” and things “eye hath not seen,” rather destroys than defines the intelligibility of God:
in the analogia entis, “all commonality [between creator and creature] is exploded.” The ever greater dissimilarity threatens, by definition, to overwhelm, destabilize, and nullify the integrity, utility, and identity of any similarity. What we have in the end is, Przywara admits, a “silent analogy.” We must surrender to “an infinity of incomprehensibility”—and even in heaven we will never tire of counting the infinite number of ways that we do not know who God really is.
(source: The End of the Analogy of Being | Stephen H. Webb | First Things)
Is it really possible that Webb has not yet thought through how “incomprehensibility” need not mean “unintelligibility”? How our incapacity to surround and manipulate an understanding, to render it wholly susceptible of quantifying ratiocination without remainder, by no means invalidates our face-to-face, hand-to-hand, faith-to-faith transmission of understanding? Surely Webb is amplifying Przywara’s own stolen bases–his own hyperbolic extensions of analogia entis beyond its proper boundaries, a deconstruction of Neo-Thomism precisely on the site of its greatest weakness (attempting to affirm Thomist analogy while assuming Scotist univocity).
Something like this must be happening, because it must be true that Przywara’s critique–if it is Pryzwara’s–does not follow from the analogia entis properly understood. Existentially, it is true, “dissimilarity threatens” our understandings, but that is because (as Webb also argues) our pride and our impatience lead us to totalize our partial understandings, to prematurely foreclose the system of affirmations, to immunize ourselves against correction. We fail in docility; we refuse to proceed from partial understanding, through unknowing, to better understanding. We imagine that unless “better understanding” is final, it is not worth having; we allow ourselves to lapse into epistemic despair for lack of constant satiety, and like addicts of any kind, we are reduced to the kind of constant bargaining that characterized decadent Scholasticism–and decadent Enlightenment–and decadent postmodernism. Lost in this experience, unless we are given healing and discipline, it is indeed possible that our metastasizing curiositas will finally “overwhelm, destabilize, and nullify the integrity, utility, and identity of any similarity” between creature and Creator. Although we have reason to hope for healing, rather than destruction, the bitterness of the complaint in Webb’s line “even in heaven we will never tire of counting the infinite number of ways that we do not know who God really is” is alarming; I am comforted with the thought that Webb, having given himself over for purposes of sympathy and charitable interpretation to the experience suggested by his reading of Przywara, wakes himself and us from our reverie with this despairing wail.
But really there is nothing to be taken lightly, here; our penchant for exalting partial knowledge above the Creator’s freedom, for reducing the Creator/creature difference to the manageable, is itself the natural source of our addiction to false closure, to totalizing ideology, and thence by an entirely predictable movement to epistemic despair, to constant renegotiation of our most basic convictions; and though we can produce a very convincing critique by following the (implicitly Augustinian) trajectory of modern and postmodern literary theory and epistemology, we can also proceed directly to the explanation by dint of divine revelation:
Ever since the creation of the world his invisible nature, namely, his eternal power and deity, has been clearly perceived in the things that have been made. So they are without excuse; for although they knew God they did not honor him as God or give thanks to him, but they became futile in their thinking and their senseless minds were darkened. Claiming to be wise, they became fools, and exchanged the glory of the immortal God for images resembling mortal man or birds or animals or reptiles.
(source: Romans 1 – Salutation – Paul, a servant of Jesus – Bible Gateway)
It seems, to me, to be a source of serious concern that Webb apparently sees no way to avoid this despair other than to erode the Creator/creature difference; it seems to me that Webb’s proposed solution to the problem is–well, the problem itself.
To Be Continued….