With the arrogance of youth, I determined to do no less than to transform the world with Beauty. If I have succeeded in some small way, if only in one small corner of the world, amongst the men and women I love, then I shall count myself blessed, and blessed, and blessed, and the work goes on. -- William Morris

Thursday, September 07, 2006

The Terror of Idolatry and the Beauty of Proof

Contemporary thought, in particular French phenomenology, is right to demonstrate how any and every conceptualization of God is reducible to idolatry. The claim is that any attempt to “prove” the existence of God can only yield an idol of God rather than God Himself, since the proof would necessarily, as proof, only offer a concept. Since a concept, as such, is always finite, limited and imaged, it reflects a representation of the thing rather than the thing as it is in itself.

But there is, I think, more to the story than this.

First, there is the question of nature of idolatry, which Jean-Luc Marion certainly works out with rigor in his famous God Without Being. But he ultimately sidesteps the distinction between the idol as a volitional construct by an intractable, and malevolent mind, and the idol as a term used to characterize the necessity of all human thought – namely, the need to abstract from an object of knowledge in order to take it into the finite intellect. He offers a fine analysis of the general nature of idolatry: it is the mirror that reflects our own limitations, beyond which our fear of the eternal unknown looms over us, compelling us out of fear to reject its offer by settling for what the mirror reflects. In this way, he implies, images of God tend to be mere reflections of self rather than authentic encounters with the divine. Still, it seems more than plausible to suggest that in this way the matter of idolatry is somewhat overstated.

Are we to believe, as Marion seems to want, that every moment of conceptualization is a willed imposition of limitations upon the ‘other’ and so rather than granting to our cognitive faculties an authentic representation actually offers only a reduced form, and hence in the case of God, an ‘idol’? Comparatively, is every instance of mathematical activity inauthentic since it reduces the infinite sequence of units into determinate forms in order to be manipulated by the mind? Would not every relationship between persons, then, be reducible to utter prejudice insofar as what one may believe he knows of another person is really only knowledge of his representation of the other to himself (...and can we feel the Kantian waters rising)?

Second, there is the question of proof. This question hinges upon ‘ways of being a mind’ as the great contemporary thinker William Desmond would say. Proof is as rich in plurality of forms as Being itself, and to simply throw the word ‘proof’ around with the assumption that the matter is evidently clear (something that happens all too often in scientific discourse) is a misleading arrangement. Let me explain.

The difference between proof as it is sought in the natural sciences, and proof as it is demonstrated in mathematics is illustrated clearly in the so-called, ‘mutilated chess board’ analogy. The illustration begins with a simple chess board and a set of dominoes, noting how it is possible to cover the entire chess board by using 32 dominoes. Then, the question is posed: if two opposite corners are removed from the board (see figure at left), is it still possible to cover the board using 31 dominoes? If 32 dominoes can cover a board of 64 squares, can 31 dominoes cover 62 squares?

Scientific methodology would have us perform a series of experiments with the dominoes to determine whether in fact one could cover the entire mutilated board with 31 dominoes. After a series of failures, the scientific method would conclude that it is not possible. The objectivity of the truth of the conclusion would be independent of the certainty that would have accompanied the conclusion. The certainty would depend on how many times the scientist performs the experiment. If he tries it 100 times, or 1000 or even 1,000,000 times, the certainty of his conclusion would be proportionate to the multitude of attempts, but never finally able to reach absolute certainty. But with each new experiment, he could be one instance more certain. (The difficulty here is that wihtout an objective measure of certainty, each experiment may yield only subjective certainty.)

The point is that when proof is considered from the perspective of certainty, where certainty is used to mean ‘truth as it is measured by the finite mind’, then scientific methodology is unable to yield anything more than a weak form of proof.

Mathematic methodology would take a different approach. The mathematician would draw a few calculated conclusions. First, a domino must cover two squares. Second, each square on a chessboard is surrounded on every non-diagonal side by a square of the opposite color. Thus, a domino must cover two squares of opposite colors. But the two squares that have been removed were of the same color, leaving the board with, now, 30 white squares, and 32 black squares. The disparity of colored squares would render it impossible to cover the entire board with 31 dominoes. With this calculated proof, mathematics has shown that it is capable of offering greater certainty than scientific methodology. But does this end the story?

The question must be posited: to what extent is the ‘power’ or ‘force’ of the mathematical proof dependent on its other (‘scientific’ proof)? Would the mathematical method be as recognizably powerful as a mode of proof if not for the apparent incapacity of the scientific methodology? If we answer negative to this second question, as I think we are compelled to do given the fact that the mutilated chessboard analogy requires both methods, then a conclusion follows necessarily: difference has played an indispensable role in the demonstration and hence the recognition of the power of mathematics to prove truth. This means, further, that mathematics is not of itself able to demonstrate, or manifest, the full power of its ability, but requires a relation. Here, it is not only the difference of the scientific methodology that has participated in the demonstration of mathematical power, but difference as such.

There is, then, a third way of thinking that is unrecognized in the chessboard analogy, and it is to this way of thinking that I want to draw attention because it is this way of thinking that is utilized when we speak of proving God’s existence. In the above example, the scientific attempt to prove a theory, or answer a question, provided what we can call a weak determination: it offered a possible solution, or illuminated a possible ‘truth’ of the matter, but only based upon a foundation of experimental repetition. This provided weak certainty of the truth it espoused, and has both a drawback and a benefit. The drawback is that it does not give the curious, perhaps skeptical, mind the absolute certainty it seeks; the benefit, however, is that it leaves the question open to further examination; mystery remains.

The mathematical method, which provided a strong determination, also had a benefit and a drawback. The benefit is that it does provide absolute certainty, eliminating any possible skepticism (except the utterly absurd, of course). The drawback, however, is that it entirely closes the matter, seducing the mind – which is created for ever deepening knowledge – into believing that mathematics is a guarantee of certainty and proof. This may be profitable at times, but there are areas of life where such a belief, insofar as it utterly destroys mystery and ambiguity, is deadly (..."I won't marry you until you prove that you love me..." or "...I can't believe in God because it can't be proven...").

Although the mathematical method provided a solution for what we were seeking, it did so with such determination that it ‘shut the door’ upon the matter, even to the point of preventing one from further asking: is there a greater illumination at stake in the matter at hand (which in our case is the mutilated chessboard analogy)? The residual mystery that necessarily remains in every cognitive encounter between the mind and an object of knowledge is eclipsed when the certainty offered in mathematical proof seduces the mind into a complacent satisfaction. Contented with mathematical solidity, the mind is lured into a false sense of sufficiency and ceases to penetrate any deeper into the matter at hand. Is there a deeper illumination in the mutilated chessboard analogy?

Granted, perhaps the analogy was done simply to distinguish between scientific knowledge and mathematical knowledge. To that end, the experiment was successful. But even the success itself depended on antecedent factors that, should they go unrecognized and unthought – indeed unappreciated – then mathematics itself has been robbed of its fuller power to release the mind into deeper thought beyond itself (reality is, I would suggest, not a problem to be solved, but a mystery to be celebrated). For what the experiment proves irrefutably is that intrinsic to the power of mathematics is its dependence upon its others – science (or what is more authentically called natural philosophy), on the one hand, and that which enables the mind to think difference as such, which we can now reveal is quite simply, metaphysics.

There is, then, a proof beyond the proof at play in the analogy. And so, to return to our original question, we may now suggest rightly that there are innumerable kinds of proofs. To say that a proof for the existence of God is simply idolatry insofar as such a proof can offer only a concept to the mind, and hence a finite capture of what eternally exceeds finitude, is to neglect this pluriformal structure of proof; it is to reduce the richness of proof to solely its mathematical form

To bring the point home, consider the following: can one prove that there is an infinity of numbers? Surely, it would defy reason itself to deny that there is an infinity of numbers. But the hard-hearted skeptic might want to suggest that since such a matter cannot be proved mathematically – at least not with the kind of certainty offered above by mathematics – that there is ultimately no way to know. Of course, in refutation, one could easily say that infinity is proven insofar as whatever number one may think, any other numerical value can be added to it. But then are we not using ‘proof based upon experimental repetition,’ the kind of scientific proof we saw in the mutilated chessboard analogy, rather than the solidity of mathematical proof so many believe necessary for any authentic proof?

Still, with respect to ‘proving’ infinity, this ‘experimental method’ should and must be conceded as the only kind of proof available to the mind. Here, when mathematical methodology is imported to handle the infinite, it appears similar to scientific methodology, capable of certainty based soleley upon success of repeated experimentation. The similarities, however, should not prevent us from seeing the important difference that remains.

The primary difference is that when applied to the infinite, mathematical proof is the kind of proof that, rather than demonstrating anything positively, merely serves as a negative norm: it says, ultimately, that if we believe we have reached the highest number possible, we should not be inclined to assent to it as the highest or final value since another value can always be added to it. It is, then, a proof by way of negation – it is an apophatic proof that demonstrates truth based upon negation rather than by reducing the truth in question to the determinate, finite, limits of the mind, declaring something to be positively the case. It is a kind of proof that allows the infinite to remain itself, while simultaneously bringing us into chorus with it in an ever-expanding dynamism.

This is the kind of proof of God that is not, and could never be, mere idolatry.

The Medievals knew this well, which is why Aquinas, for instance, always ended his quinquae viae with a form that we can call ‘preemptive predication’ – essentially, the evidence he would offer to demonstrate the reasonableness of God’s existence (or perhaps we should say the non-unreasonableness) was a predicated description of what in the end would be revealed with the words: “and this is what all speak of as God," or "this is what we call God." This is a way of preventing the limits, which a word necessarily ushers into the mind, from hindering the necessary opening of mind to what is ever beyond itself. In other words, Aquinas tactically describes the matter before he defines it. He ‘preemptively predicates’ the subject.

It is vastly different to say ‘God is infinite’ than to say ‘there is something infinite and this is what we call God.’ The statement ‘God is infinite’ too easily allows the copula ‘is’ to be taken as a predication of identity, which in the case of God it simply cannot be – God, in himself, cannot be finally captured in one definition since He has no finite identity. The statement ‘there is something infinite and this is what we call God’ never refers to God with the copula ‘is.’ Instead, it draws attention to the fact that the word ‘infinite’ is used in the human act of naming: it is a name that we must apply to God insofar as we must use names whenever we humans speak of anything. The nature of divine being never comes into the definition and so God’s Being – which can never be thought of as a being among beings – is never part of the limiting definition. This is, quite simply, proof without idolatry, proof that remains open, proof that welcomes mystery and embraces our human weakness of unknowing – it is, in a word, the beauty of proof, and it lives most fully in that form of knowledge called faith.

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  • At 9/07/2006 8:21 PM, Blogger Henry Karlson said…

    There is a classical Zen saying which goes:

    "Before I had studied Zen for thirty years, I saw mountains as mountains, and waters as waters. When I arrived at a more intimate knowledge, I came to the point where I saw that mountains are not mountains, and waters are not waters. But now that I have got its very substance I am at rest. For it's just that I see mountains once again as mountains, and waters once again as waters."
    - Ch'uan Teng Lu (The Way of Zen 126)

    I think your post here goes along with my comment on my poem "On Idolatry," and agrees with this Zen saying. First people start with an understanding of God (or some other aspect of reality, such as mountains). It is important we do so, because it provides a foundation for us to exist in the world and a foundation for us to use to understand our relationship with God.

    Then we begin to understand God is greater than this simple definition: we can't so easily put God a box. Thus we realize God is not God, that is, how we originally defined God is not God in the fullness of God.

    While many people stop here, it is wrong to do so. If we do, we turn apophaticism itself into idolatry. We need something positive. We need to negate the negation, as some would say. We do experience God, mountains are indeed mountains, and God is indeed God. Not all images of God are idols, not even all mental/verbal image. They are an idol if we abuse them, if we confuse the pointer for the thing in itself. I can say I certainly did at one stage of my life. Yet, we need pointers, we need images. Indeed, through beauty, we can say God (image) is truly God.

    It is interesting that this question is central to Yogacara Buddhism -- how do you show the path for its beauty to prevent Buddadharma turning into annhilationist nihilism. The funny thing is, Christianity without proof has itself become the same relativism which seems to be leading many to this annihationist end.

  • At 9/08/2006 11:49 PM, Blogger Brendan Sammon said…

    Well said.
    Negating the negation I think is a good way to put it, for in this case, one is left with both negation and affirmation all at once; here, it seems, that which appears contradictory is instead a harmony.
    It is becoming more and more common in contemporary thought - something found especially in those influenced by the so-called "postmoderns" - to "baptize" a certain nihilstic approach in the name of a pure apophaticism.
    As you point out, and as is the case with all things, apophaticism needs its 'other' if it is to truly be what it is.
    But this is the story of the whole of creation, is it not?

  • At 9/09/2006 11:01 AM, Blogger The Lesser Thomas said…

    Plotinus certainly has these sense of necessity of the other. For him, it's couched in the language of one-many, universal-particular, and necessary volition. The basic idea is that the one, becuase it contains in potential, the many, gives rise to a need for the many so that the potential may be actualized. In this sense, it's necessary. But, in the sense that turning away from unity brings a tension and pain of multiplicity, a confusion, it's bad. FOr what it's worth, Plotinus and those he followed seemed perfectly happy to leave this tension of a necessary evil. Of course, many Christians felt a great need to tackle this question at least to get rid of the sense of necessary evil. But, that's another point.
    There does seem to be a consensus from many sides that we need some kind of dialectical tension. The trick comes in how to articulate the dialectical tension without making an ontological contradiction that leads us to a strick dualism or univocation. That is, if we go along the lines of the need for apophaticism to be balanced by kataphaticism, we have to be careful not to say something like "God is both light and dark," in any sense that would lead either to a "God of light" and a "God of death" or to a God who is one among things which are also light and dark. Perhaps a sketch of the way around such a dilemma would be to make God somehow contain both light and dark?

    With regard to apophaticism, though, is this more a problem of language than a problem of being? Perhaps they cannot be spoken of in such strictly separate manners. But, does the problem lie in God's nature, or in our articulation, or a mixture of both. There are certainly those who would say the defect is in our ability to express or even understand, and this is why we turn to apophaticism, while others would perhaps lean towards saying that God is, by nature, inexpressible, even to himself.

    There is a sense of Wittgenstein that allows for a potentially helpful schema here: the distinction between saying and showing. In language, we cannot say something that is beyond the terms of the grammatical structure or the "logic" of the universe. Perhaps a decent example is the word "nothing," which seems to have no referent and no meaning. But, the word does have meaning, it's not pure nonsense in the way that "woijaklsdnf" is nonsense. "Nothing," or the way 'nothing is used' points to something which cannot be strictly said. It is in this sense that I often understand apophaticism: it realizes its inability to say something exactly, but also realizes that this does not commit it to an inability to show something. And, with Wittgenstein and Pseudo-Dionysius (I believe), we can conclude with throwing away the ladder that lead us to this realization.

    The discussion of infinity, science, and math is helpful, but perhaps a bit unfair. Would we want to separate science from math? I'm not sure that either discipline would draw such hard lines between themselves. THere is a most basic logic system of induction and deduction that accounts for these differences and even allows us to make analyses of such experiments (statistics often relies on this). ALso, infinity has many other distinctions that are helpful in this area of discussion. A primary consideration, for instance, is the difference between countable and uncountable infinite series. We speak mostly of countably infinite series, for instance, when we go from zero to infinity by 0, 1, 2, 3, 4, 5..., or 0, .5, 1, 1.5, 2... But, these "steps" give us discreet (discontinuous) numbers in a series. We also know that there is an infinite series of numbers between 0 and 1, but not because we can't list all the numbers, rather because all the points between them are continuous. Euclid pondered over these, and there is the famous series of Zeno's paradoxes which often "play" on these different kinds of infinities. For instance, there are crossable and uncrossable infinities. The distance between you and me is infinite in a sense. Zeno's simple "process" was to say that before I can go all the way from you to me, I have to go halfway. But, there will always be a halfway point between you and me, so I can never get all the way there. It is "infinite." What he misses is that it is infinite, but not in the way that is uncrossable. At any rate, I'll give it a little more thought and make better explanations later. Suffice it to say for now that there is more to infinity than the kind which is infinite simply because we cannot provide a list (due to constraints of time or space).

  • At 9/11/2006 10:25 AM, Blogger Brendan Sammon said…


    Good to see that not even one month into your new program and already you speak with the wisdom of the ancients.
    You raise some important points that prompt me to respond.
    Forgive any misreadings of your thoughts, as I am slow at times.

    you wrote:

    "The discussion of infinity, science, and math is helpful, but perhaps a bit unfair. Would we want to separate science from math? I'm not sure that either discipline would draw such hard lines between themselves."

    I'm not sure this is an accurate reading of what I wrote. Nowhere did I imply an absolute separation. In fact, Math and Science (the latter of course being a gross misnomer to begin with) are separated by their objects of study, not by our own volition. That is in fact why I constantly return to the Aristotelian-Thomistic division of the sciences. Here, distinction and unity are in a direct proportion and not an indirect. In other words, the greater the distinctions between these modes of thought insofar as they relate to different kinds of objects, the greater their unity. This is also why knowledge in Aquinas , as Gilbert Narciss, O.P. has recently explained (Les Raisons De Dieu), is an aesthetic. Any logic that relies too heavily on the principle of identity, or the principle of non-contradiction, cannot understand the direct proportionality between unity/distinction - it can only see them as opposites. In the end, it reduces the metaphysical theory of knowledge in Aquinas to merely an (X)empistemology, which as we both know is a modern invention born from the project of Descartes (primarily).

    Thus, if as you say, I overemphasize their distinctions, this may be so, but not - as you seem to conclude - at the expense of their unity. Rather, I emphasize their distinctions in order to also emphasize their unity.

    As for the question of dialectics, the history of philosophy attets to the fact that dialectics is woven into the very fiber of human being. From the ancient Greeks, to Gregory fo Nyssa to Aquinas, and up into Modernity, metaphysics is the working out of dialectics. There is, in my mind, no question here. The question is how to read the nature of the dialectic - Hegel's reading is far different from, say, Plato's or even Aquinas's. And of course, the Christian Logos enables a reading beyond what mere philosophy allows. Personally, I would once again recommend Desmond, whose dialectic goes far beyond the Hegelian kind (and Hegel here is a sort of culmination of the whole of Modern dialectics) by reinstilling what the Patristic and Medieval thinkers held close - namely, beauty.

    Finally, the question of apophaticism as a part of being or a part of language...
    It is a good question, as you point out, and riddled with ambiguity. Language recapitulates ontology, and the unity between them is illuminated through their distinction. But I think the question as to whether apophaticism might be more a result of linguistic structures than anything ontological (if indeed I understand your question - which I may not fully) is better approached by asking what is it about being that is revealed by our use of the apophatic - which is exactly what you did with your analysis of the word 'nothing'.

    Personally, I would approach the matter with a both/and methodology.
    On the one hand, we are finite in nature. We will always be finite creatures with an 'infinite intentionality'. This means that somehow, our reliance upon language - or perhaps we might do better to say 'outward expressivity' - seems to be essential. Thus, apophaticism can be understood in these terms: as emerging from the 'ontological difference' (Heidegger) or from the fact that we will never be identical to God, who is infinite. There will always be a gap, or in aesthetic terms, an 'analogical interval,' a distance which preserves distinction and unity all at once -apophaticism to me celebrates this as mystery, while the neglect of apophaticism reneges on this celebration in the face of the fear it generates.

    On the other hand, since 'being' can only be thought and encountered through some kind of linguistic structure (and here even intuition must be interpreted), apophaticism must necessarily convey an aspect of being as such. But how to understand this - that to me is the issue.

    Psuedo-Dionysius might be helfpul here: "Now we should not conclude that the negations are simply the opposites of the affirmations, but rather that the cause of all is considerably prior to this, beyond privations, beyond every denial, beyond every assertion...It (the Word of God) has neither word nor act of understanding, since it is on a plane above all this, and it is made manifest only to those who travel through fair and foul, who pass beyond the summit of every holy ascent, who leave behind them every divine light, every voice, every word from heaven, and who plunge into the dakness where, as scripture proclaims, there dwells the One who is beyond all things."

    Further, you wroye:
    "That is, if we go along the lines of the need for apophaticism to be balanced by kataphaticism, we have to be careful not to say something like "God is both light and dark," in any sense that would lead either to a "God of light" and a "God of death" or to a God who is one among things which are also light and dark."
    Here I must apologize, I'm not sure I see the connection in this thought itself, nor in how it applies to what I wrote (forgive me if I am obtuse in this regard.)
    I would never advocate saying "God is..." since all things are contained by Him, as He is beyond all things. But I don't see how advocating a balance between apophaticism and cataphaticism leads to identifying God with anything. That, to me, is a matter of understanding univocal predication and analogical predication.

    The notion that apophaticism might somehow open the door to equating God with darkness or even "death" does not concern me. Again, analogical predication overcomes all that (which is why St. Thomas always points this out).
    While I would in no way positively teach something like "God is a God of death", I would neither assume, in my own personal spirituality, to know the depths of God's mystery, a mystery which according to John of the Cross, Dionysius and even Psalm 18, is indeed bound up somehow with darkness and even death (After all, the Acts of the Apostles seems to allude to the fact that death belongs to God to use as he wills).

    Perhaps we in the West, with our comfort and complacency, have lost sight of that 'dark' side of God that once instilled divine terror and dread in humanity - that elicited the kind of respect for the sacred; a respect that seems practically lost in our culture of 'anything goes'; a respect that seems better preserved in the Muslim world, or in indigenous tribal cultures than in ours. Sure, we may understand God's Word, God's light, and Life itself, but perhaps we need our 'others' (The Eastern and Southern world) to remind us of God's silence, God's darkness, and even a God who assumed death. Maybe then we would not be so quick to use death to solve problems. Although fear of the divine must grow into a respect and ultimately a love, the original fear, in my mind, must never be abandoned. Love for God without fear of God, it seems, too quickly slips into idolatry.

  • At 9/11/2006 10:38 AM, Blogger Brendan Sammon said…

    This comment has been removed by a blog administrator.

  • At 9/21/2006 9:16 PM, Blogger X-Cathedra said…

    Wow, what a great discussion!

    I thought I'd add my two cents on the apophatic element: Henry's post seems to draw out nicely how the apophatic side serves as a kind of purgation of the intellect in its ascent, which I think is the only proper context in which to read it. Namely because, as Brendan has noted, there is a dialectic at the heart of our being. This I thought I'd touch upon....

    I think St. Thomas and Dionysius share an absolutely essential vision of the apophatic (reworked in important ways by Thomas obviously) in the sense that it is intimately tied up with creation as participation. The perfections that exist preeminently in God are poured forth in the act of creation diversely, in multiplicity. God's ulimited and infinite esse is mediated through essences that limit it, but only insofar as they shine it forth. Creation is thus in its very constitution a revealing and re-veiling of God all at once. In terms of cause, there is in creating no efficient cause without exemplary cause, and that is precisely, I think, what is lost in later modern conceptions of causality. But how essential it is!

    Thus, it is nature's ability to reveal God in its very being that is the foundation for all positive predication (analogical that is) and it is it re-veiling of the divine that grounds our silence and unknowing. Created being is just the tensile unity of both elements, and to sacrifice one for the other, as if they were primarilly opposed notions rather than held in harmony within finite being itself, is to misconceive the issue. According to the participatory model, what creatures reveal of God grounds the the apophasis, and the apophasis functions as a purification of positive knowledge, a necessary step in the teleological ascent (for instance, realizing that Being's primary analogate is found in God, and "being" is predicated entirely uniquely of God).

    Without the "other," we are left with positive knowledge of a univocal kind, devoid of mystery and the depth of the cause shining through the effect (how then aesthetics!); or an unknowing that restricts being to a divine height, deprives it of analogical predications, and has a hard time explaining texemplary causality.

    All in all, that dialectic in our very being is what grounds our ability and inability with regard to God's revealing, and thus grounds our saying and unsaying. Without both sides, neither "via" can transcend a univocal and fruitless opposition.

    Just some thoughts. The blog is fantastic, please keep up the great conversation!


  • At 9/23/2006 1:28 PM, Blogger Brendan Sammon said…

    well said Pat,

    sounds like you're still reading Desmond....
    of course, Desmond's thought echoes in a post Cartesian era the keenest insights of the Patristic and Medieval traditions anyway.

    great to have you around!


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