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.