…for what can be so plain and evident, when we behold the heavens and contemplate the celestial bodies, as the existence of some supreme, divine intelligence, by which all these things are governed?

Cicero, On the Nature of the Gods

The Lord by wisdom founded the earth;
by understanding he established the heavens;
by his knowledge the deeps broke open,
and the clouds drop down the dew.

Proverbs 3:19-20

Two Types of Design Argument

I wish to rehabilitate a type of design argument and in so doing, tease out exactly what sort of God can be known and demonstrated by this argument and it’s theological meaning for us.

Now it is an unfortunate accident of the history of the discussion of this argument that it has almost always entangled two separate types of arguments which ought to be considered distinct from one another. To roughly state the two different types of arguments:

(1) The Universe Exhibits Rational Order and Regularity

from

(2) The Universe Exhibits Purpose, Intention and Goal

The name traditionally used for design arguments, “teleological” from the Greek telos or “purpose”, “end”, etc, already betrays the bias of the philosophical world for regarding (2) as the primary substance of design arguments rather than (1). My argument will be to focus upon (1) and disregard (2) as something which can only be known from special revelation rather than “read off” nature.

To motivate the discussion it would be necessary to illustrate the distinction between (1) and (2) in clearer terms. Now, some of us maybe familiar with Paley’s “Watchmaker” argument whereby he argues that if we notice a watch lying on a beach, we wouldn’t think it got there by accident but it must be the product of intentional or purposeful formation, that is, created for telling the time. Then by analogy he compares the watch to the eye and argues that just as the intricacies of wheels and springs of the watch were so intelligently fitted together for the purpose of telling the time, likewise the complexities and delicate fit of the various parts of the eye for the purpose of producing sight is evidence for the intelligent and purposeful formation of the eye.

The problem with all such “teleological arguments” which depends upon “purpose” and “intentions” is simply the problem of evil. We see many such organic “creations” fail in their purpose, “malfunction”, unable to perform what they were meant to do, in short, the existence of many “bad design” and failed designs and faulty designs is effectively a refutation against their being created for a purpose, or at least, their being created by an infallibly intentional being. We might add to this that many aspects of nature seemed to have evil purposes and goals, a further refutation of the idea of a benevolent intentional former of nature towards good ends.

Let us now consider the other type of design arguments. What if, instead of encountering a watch in the wild, you encounter a work of art. Now, a work of art does not intrinsically possess a purpose. To be sure, a work of art can be used purposefully by others to further some economic or political agenda, it’s artist may even have created the piece of art for a purpose or a specific intention, but this intention is extrinsic from the piece of art itself. The art, unlike the watch, does not intrinsically possess the artist’s intentions or purpose. The watch’s parts itself were fitted together for for telling time, but no such intrinsic purpose or intention exist for an art piece. Maybe an artist simply wanted to express himself and so he painted and then locked it up in his chest which got lost and ended up in the wild.

However, even if the work of art did not in itself possess any purpose nor was it formed intentionally, but yet we can still credibly discern a mind behind the formation of the work of art, by virtue of it’s ordering, the fit of its parts, it’s patterns, it’s cognitive-resonance with our own minds, etc. And so we conclude and deduce that a mind was behind the work of art because of these cognitive-resonating features which the art shares with our minds. It would be the sort of inference we make that the Stonehenge in England is not the product of accident but of a mind or rationality, even if we do not know the Stonehenge’s purpose or the intentions of the builders. But by virtue of the order, the patterns, it’s fit, we cannot but infer that there was a rational mind behind it’s formation.

To employ one more example before developing my own argument. Suppose that there was an alien spacecraft drifting through space with it’s pilot dead. Then by some accident, the spacecraft bums into some asteroids which triggers it’s radio or communication device, which by some strange random malfunction, starts communicating it’s flight coordinates from the time which it began until the present. Now suppose our SETI (Search for Extra Terrestrial Intelligence) telescopes pick up on these signals and promptly deciphers them as intelligible communication. We would not be wrong to infer from these intelligible signals the existence of an intelligent life form out there, even if there was no purpose or intention behind the signals. Remember, the radio was “switched on” by a pure accident, it’s message chosen by some random malfunction, but because of the intrinsic intelligible cognitive-resonating features of the signals, we (rightly) infer the existence of rational cognition “behind” the signals.

What are the Cognitive Resonating Features of the World?

I’ve been banging on and on about these “cognitive resonating features” of art and alien signals. But while we can understand what such “cognitive resonance” means in the context of a piece of art, architecture or radio signal, what meaning does it have when applied to nature itself? The time has come to give a much more specific meaning and interpretation of “cognitive resonating feature” as applied to nature. But first, some definitions. I will use the term “teleological” to refer to the types of arguments which involve purpose and intentions, and I will use the term “design” unambiguously to refer to the types of arguments which speak of these “cognitive resonating features” without the additional “teleological” baggage or implications.

What I’ve been calling “design” as cognitive resonating, rationality based upon fit and order, etc, actually has quite a respectable pedigree stretching back to Cicero the Roman philosopher who made the following argument in his book, On the Nature of the Gods concerning the regular and orderly movement of the planets and stars,

…This constancy, then, among the stars, this marked agreement of times through the whole of eternity, though the movements are so various, I cannot understand as existing without mind and reason and forethought… Their movements, which are never-ending and unbroken, and marked by a wonderful and incredible harmony, make it so clear that a divine force and intelligence are resident in them, that the man who did not perceive that these very bodies are possessed of the force of divine beings would seem incapable of perceiving anything at all. In the heavens, then, there is no chance, irregularity, deviation, or falsity, but on the other hand the utmost order, reality, method, and consistency… Any one, therefore, who thinks that there is no intelligence in the marvellous order of the stars and in their extraordinary regularity, from which the preservation and the entire well-being of all things proceed, ought to be considered destitute of intelligence himself.

Thus, the ancients inferred the existence of an intelligent divine being governing the cosmos based upon this intuition of “order” and “regularity” in the movement of the stars and planets (remember, back then they had a geocentric understanding of the universe and thus it was not the earth which moved but the stars which traveled across the sky in a certain regular and fixed pattern).

If the ancients had but a rough and unrefined intuition to make their argument, we who live in the aftermath of the scientific revolution possess a much richer, clearer and sharper conceptual system for discussing this intuition, namely, the mathematical order of the universe.

The scientific revolution did not merely consists of making empirical observations and recording them down. Philosophers and thinkers have been doing that since Aristotle and most of the medieval world have been enthralled to his methods and the Ptolemaic theory. The scientific revolution involved both empirical data collection and mathematical rationalisation of those data. The necessary advance from medieval science to Enlightenment science was the idea that the universe conformed to these precise, exact and deductive mathematical laws and formulas.

This conformity was not obvious to the Renaissance world. The geocentric Ptolemaic theory was able to sort of explain the movement of the stars, but it was a rather complicated picture involving lots and lots of epicycles and swirls here and there. When Corpenicus proposed his alternative heliocentric theory, he had really no other argument for his theory (since they don’t exactly have satellites to observe planets from space and thus can’t really make an empirical argument), then that his theory was much more mathematically elegant and simpler than the Ptolemaic theory by the number of epicycles it cut down. But the flaw of this theory was that it postulated the movement of the earth around the sun as a perfect circle rather than an ellipse. This error was soon corrected by Kepler who, using meticulous data collection on the positions of the planets at various times, managed to derive the precise mathematical formula of describing the orbit of the planets, today known as Kepler’s Laws of Planetary Motion.

But once again, Kepler didn’t have any real empirical evidence to back up his theory, except beyond the fact that it was so mathematically fitting and orderly and elegant. And although Kepler possessed the exact formulas to trace and describe the motion of the planets, he wasn’t able to explain or provide the mechanism for why, say, the orbit is elliptical (his first law) or why a line from a planet and the Sun covers an equal areas during equal intervals of time. The mathematical mechanics behind this would eventually fall upon Newton who was able to deduce Kepler’s laws from his gravitational formulas instead of just “fitting it” in with empirical data.

This conviction that the universe would exhibit this mathematical order and rationality based upon the divine reason finds numerous expression throughout the writings of Newton. Here are a couple of examples,

It is the perfection of God’s works that they are all done with the greatest simplicity. He is the God of order and not of confusion. And therefore as they would understand the frame of the world must endeavor to reduce their knowledge to all possible simplicity, so must it be in seeking to understand these visions.

(Italics mine)

This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called Lord God παντοκράτωρ, or Universal Ruler

The Mathematical Order of the Universe as Evidence of Design

After our little detour into the history of the development of astrophysics and mathematical physics, we come back to our main question: How do we deduce cognitive resonance from the mathematical order of the universe and from that infer a universe governed by divine cognition?

First we need to tease out some features of mathematics. Mathematics is an extremely strange thing and by itself occupies an entire field of philosophical discussion and research. But for our purposes we need only focus upon mathematics and physics.

The first thing to note that any application of mathematics to physics is a contingent application, that is, it merely happens that a certain aspect of mathematics is applicable to some aspect of physical reality, but there is no real reason or necessity for the universe to so neatly conform to mathematical deduction. Consider for example vector resolution. Anyone with the most basic secondary school level mathematics knows that any vector can be resolved into two different vectors given a certain two dimensional reference frame. Thus, given two different forces acting upon an object, if you add up the vector forces, the resultant vector will be the resultant force acting upon the object.

Under Newtonian mechanics, this was more or less assumed to be true and has been confirmed in many experiments. (I remember taking a physics mod which made us perform an experiment proving the applicability of vector sums to physics as one of our lab work.) However and here is the interesting bit, it actually isn’t true. Vector summation isn’t actually applicable to the physical world for we now know of Einstein’s relativity whereby the velocity of the reference frame itself will actually distort the space-time continuum in very subtle ways, which becomes more evident as you approach the speed of light, and render vector summation useless. Although fortunately since most objects in the physical world travel way below the speed of light, this distortion is negligible.

However, never fear! The universe is not going to descend into chaos nor does it prove that the universe is inherently irrational. Although we cannot apply the simple real numbered four-dimensional vector summation to physical objects, but via the mathematical concept of imaginary numbers, we can formulate a very special form mathematical space called Minkowski’s Spacetime and incorporating Einstein’s formulas, do our vector operations of physical objects, or rather events, within this very specially formulated space. Order has been restored!

But the fact of the matter is that there might actually be no possible application of mathematics whatsoever on empirical reality. Reality could be so chaotic that it would be impossible to understand it within any mathematical order or system. So the question is why is mathematics applicable to empirical reality at all? Or to put it in a manner more relevant to our present topic, why does the empirical universe so miraculously conform to mathematical order? Thus the “stability”, the “order” and “regularity” of nature is equated to the mathematical order of the universe, if we can prove that the mathematical order of the universe exhibits this “cognitive resonance”, then we can move on to infer rationality behind the universe.

To heighten the question, we need to note another feature of mathematics: The independence of its truth from empirical reality. Philosophers often call mathematical truths to be “necessary” truths, that is, they are true independently of the conditions of our world (or any possible world to use the more technical term). Thus, it is a truth completely independent of this empirical world, 1+1=2 no matter what our world is. So the question becomes, how can our world, which is contingent, liable to variety, great changes, plurality and differences, etc, capable of such precise and exact conformity to truths and propositions completely, well, out of this world?

There are two ways of accounting for this depending upon your philosophy of mathematics. And depending on which, you would end up with a slightly different conception of the divine mind behind the universe. The first is the platonic theory of mathematical entities. That is, they conceive of mathematical entities like sets, functions, numbers to be essentially atemporal universals or forms transcending the material world. On this conception of mathematical entities, the material universe then seems to, somehow or rather, “conform” to these platonic entities.

The platonic interpretation suggests some intriguing possibilities. First, the platonic interpretation highlights the gulf between the ideal forms of mathematics, and the contingency and messiness of the empirical world and does not by itself solve the problem. Since these platonic entities are ideal and sort of eternally existing, then it seems that a sort of platonic “demiurge” is necessary to “bridge” the gap between the empirical world and the platonic forms. In Plato’s dialogues, the demiurge is not really god, in the sense of god the creator, but more like an “artisan”, a “craftsman” who shapes the physical universe after these perfect forms. Later platonic thought would begin to integrate the forms with the demiurge, and the idea emerged that there is a perfect form of the Good, which is the source of reality for all the other forms (justice, beauty, etc), and presumably, the mathematical forms. And from this form of the Good flows forth the universe which mirrors the perfect universals which emanates from this perfect form of the Good.

This “Platonic Creation Story” is a little far fetched and outlandish, but we can treat it as a “just-so” story, as a sort of parable for the literal truth. But vital point to take away from this “Platonic Creation Story” is there does exist a world (of universals or the form of the Good, which you can identify with God), which transcends the physical empirical world, and this world of intelligible forms is responsible for the “enforcement” of mathematical order in the physical world. Thus, intelligibility is responsible for the physical world.

The other theory of mathematics, the one which I happen to favour because it doesn’t require such icky occultic philosophical entities, is the idea that mathematics is a human creation. Just like how we invented chess, likewise did we humans invent mathematics. But even though chess and mathematics is our invention, but once invented it has a reality independent of our subjectivity. Thus, for example, it is an objectively true fact that one is able to checkmate in a number of moves, or one is forced to make a certain move to get out of a check, etc. The analogy which Karl Popper used is that of a spider spinning a web. The spider made the web, but once the web was made, it has an objective reality of its own, it is of a certain biochemistry, of a certain pattern, structure in order to retain its integrity, etc.

Thus, mathematics is a product of our minds, in exactly the same way that chess, fictional stories, myths, musical compositions, etc, are products of our minds. Thus, upon this conception, the miracle is that the universe happens to conform to our mind generated realities, that the universe is governed, structured, ordered by a mind generated reality. Therefore we can infer the universe is in fact ordered by a like mind upon the basis of the mind-resonating, that is, resonance and conformity to mind generated realities of mathematics, which the universe possesses.

Now we can easily dismiss a prima facie objection which may occur to this account. The objection goes, if mathematics is a product of the human mind, and if the human mind is a product of nature, then doesn’t it stand to reason that it would make perfect sense for nature itself to evolve beings which would encodes its own mathematical structure into their minds and capable of grasping the mathematical structure of the universe?

Even if this were true, that the nature gave rise to beings which created the mental constructs necessary to grasp its own structure, it still doesn’t change the fact that nature does possess these structures which are cognitive resonating and which are mind-like and rationally orderly, etc. The naturalistic explanation only explains how we came to create those mental constructs which are able to represent the universe, but it doesn’t explain why does nature itself possess those cognitive resonating and conformity to mind-like orders in the first place. Even if no humans evolved, and nature did not birth beings who could grasp its own structure, the laws of physics would still be what they were and there would still be the question as to why would the universe conform to these mental structures independently of the existence of anybody around to create those structures for them to grasp.

Again we must emphasize that even though we created mathematics, it does not follow that the universe must conform to any of our creations. We invented the idea of magic, sorcery, witches, etc, it does not follow that the universe must answer our rain dances by raining or conform to our gibberish chantings. This underwrites one of the premises which we began with: the independence of mathematical truths from empirical reality. It could be the case that the most mathematics can be used for in our world is simply for accounting and designing buildings, but beyond such “macro” and rough applications, the universe may be too chaotic to permit of any more specificity to the level of precise equations for the most minute physical phenomena. Maybe if our evolutionary and cultural history were different, we could have created a different type of mathematics and even a different set of laws of physics, but even if we did, it would be sufficiently “isomorphic”, that is, structurally similar to our present mathematics and laws of physics, assuming that no matter the path of evolutionary or cultural history, the order underlying it is the same.

The main point therefore is that there is no reason at all for the universe to conform to any of our mental constructs, especially those with such precision and specificity and which operates at such a level of abstraction and necessity and by implication, no reason for the universe to conform to any mind-likefeatures independently of our evolutionary or cultural history. The most this naturalistic explanation could lead to is the Hegelian story about how the universe as a whole is a pantheistic evolving mind which becomes “self-conscious” or represents itself via the minds of man. But whether one subscribes to the platonic creation story or this Hegelian evolutionary story, the point is the same, the universe does possess these cognitive resonating features and is governed by a form of rationality.

Cognitively Ordered Universe as a Practical Postulate

So far throughout this discussion I have simply assumed that even if the conformity between the universe and our mathematical constructs was a contingent matter, but we are still justified somehow in believing that the universe would conform to some such mathematical order, that the intuition and conviction of Copernicus, Kepler and Newton was essentially correct, God is not a God of chaos and the universe would indeed be orderly.

But why even assume this? Why not simply call our bluff and assert, there is no reason whatsoever to believe that the universe must conform to some form of mathematical order. And the fact that particles and all physical phenomena falls in line with our mathematical equation is just a sheer coincidence and not some metaphysical fact in need of explanation.

This would essentially be David Hume’s contention against the principle of induction and against the necessity of regularity and order in the universe. As his famous argument goes, just because today the sun rose doesn’t mean that tomorrow it would also rise and that past conformity is no evidence at all for future conformity, or that one can deduce any formulas from one set of phenomena to another. Regularity and order and conformity to any mental order is a sheer massive coincidence and not some metaphysical fact of the universe.

I do not believe that it is actually possible to answer Hume’s objection. Kant tried to solve the problem by postulating synthetic a priori categories and structures which comes with our minds (e.g. causation, Euclidean geometry, etc) which we cannot help but interpret the world through as ordered by these mathematical orders and by causation, etc. But of course this is nonsense as with quantum mechanics and non-Euclidean space, we know that the universe doesn’t have to conform to these so-called “necessary” structures of our minds and that the universe doesn’t have to conform to any mental structures, a point already noted.

However, it maybe possible to answer Hume, not by rational refutation, but by a practical refutation. In fact, Kant himself ironically has already provided the necessary framework and ideas for such a refutation. Although Kant denied that there could be any “rational” demonstration of God’s existence, however, he did argue that we must postulate God’s existence as a “practical” postulate, to under-grid his moral enterprise. His argument goes, in order for us to live according to our moral duty, it must be possible for us to fulfill our moral duty (based on his principle that ought implies can, that if I have a moral duty to do something, it must be possible for me to fulfill it), but we live in a universe which is seemingly amoral and doesn’t seem to be structured towards the possibility of the realisation of moral duties, that somethings to do our moral duty is humanly impossibly hard. Thus, in order for us to be able to fulfill our moral duty, we need to postulate the existence of God which guides the universe in such a way that makes the moral order possible, such as with the afterlife, etc,

Whatever we may think of this argument, we might want to apply something structurally similar to the idea of the universe’s mathematical order. We agree with Hume that there is no a priori reason to believe that the universe would conform to any mathematical order whatsoever. But we cannot practically live with the attitude that the world is contradictory and utterly chaotic and disorderly. As a practical postulate we have to live and plough ahead with our scientific activities believing that the universe does in fact possess some form of rational order which will in fact conform to our mental constructs and is sufficiently “mind-like”, even if for now we do not know which it is or what they are. Without this order, we would not be able to do a lot of practical stuff, especially in the creation and maintenance of our tools and technology. Thus, to live at all in this world, is already in itself a step of faith, faith that the universe is in fact sufficiently ordered, congruent to human rationality and capable of being understood, and thereby enabling our navigation in this dangerous world indifferent to human survival.

Conclusion: Indifference of Nature and the Revelation of God’s Will

To end off, it would be good to consider the “existential” meaning of the design argument. It is important to note that the design argument doesn’t as a matter of fact, at least not by itself, make intelligible the “goodness” or love of God. It says nothing about whether this mind which runs the universe is benevolent or malevolent, or simply indifferent. Remember, we distinguish between the “teleological argument”, which claims to prove the inherent “purpose”, “intention”, “direction” of the universe and the mere “design argument” which claims to demonstrate the mere fact of cognition and rationality running the universe without claiming that this rationality has a purpose or intention, it just is.

Whereas Catholic natural theology of which St Thomas Aquinas is representative have often claimed to be able to discern this overall and cosmic purpose or divine intention inherent in the world, the Protestant tradition have never had such an exalted role for natural reason. Archbishop Cranmer in his “Lutheran” catechism wrote about our faith in the First Article of the Apostle’s Creed, “I believe in God the Father Almighty”,

For if we did only know, what God were, and did know nothing of his will toward us, whether he were our friend or foe, favourable or angry, pleased or displeased with us, then our conscience being other wavering and doubtful, should be destitute and void of comfort.

Thus, Cranmer understood that there was a difference between knowing merely “what God were” and knowing “of his will towards us”, corresponding to that of Luther’s distinction between the “absolute” God in himself, and the “God revealed for us”, supremely in Christ. The design argument fleshes out “what God were” as it is in himself, but it does not tell us if the designer or governor of the universe and all the things in it is “favourable or angry, pleased or displeased with us”, or what his intentions or interest is for us, if anything.

It is a common existential theme to speak of the indifference of nature and the heavens to the passions and desires of mankind, this theme being most prominent in the novels of Thomas Hardy which does not speak so much of an “evil” God out to get man, but merely a blind and indifferent God whether nature’s events occurs upon a whim indifferent to the hopes, interests and desires of mankind. When we consider the laws of physics and the mathematical order of the universe, mathematics has nothing to do with morality or goodness of human subjectivity at its depth. It just is. Force equal mass times acceleration, nothing good or evil about it, it’s just amoral.

The same laws of nature which rains volcanic ashes upon us or sends us hurricanes, is also the same laws which gave us flowers and forests and corals. The same rational order which floods our cities is the one which enables our finest technologies and arts, both civil and scientific. The law of nature both gives us great and beautiful things, and wrecks havoc and chaos upon us. In this we gaze upon the inscrutable God whose intentions are cloaked under an indifferent and impartial nature. This God has often been known as “Fate” or “Nature”, whose blessings we receive with gratitude, and whose evils we lament, but it is all governing and all powerful, whose laws we cannot escape and whose force is beyond our subjective agency.

Despite the indifference or obscurity of intention of this “God of nature”, it is still a necessary step towards the “God of the Bible”. It is necessary for us to establish that there is a mind behind the universe, sufficiently congruent to human minds. Before we can make God intelligible we have to demonstrate it capable of intelligence. Only from there can we speak of the will of God, the direction, intention and purpose of God for the world and for our lives, which has been revealed in Jesus Christ particularly for us. The God who designed the world and moves it according to his laws, is the same one who has spoken to us in his divine Word, Jesus Christ. When we see the will of God revealed in Christ, our view of nature changes, no longer blind and random, but a world guided by God, reconciling all things in his Son, redeeming and drawing in the good, pruning and cleansing the bad, unto its final end purposed from eternity in God’s decree in his Son and for His Son.