If somehow you were to extract the shadow of a table from a Rembrandt painting and simply to look at it on its own, devoid of its natural context, you would have a difficult time understanding its origin, its nature, its function, and its purpose, if any. You’d be hard pressed, if you’d never seen a lock, to understand the design and function of a key, or that of a bow if you’d never seen a violin. The same holds true for every created entity. Without its proper context in relation to God, it cannot be well understood regarding its origin, nature, function, or purpose. The same holds true for science and mathematics.
As God’s creatures, numbers are both made and upheld by God. From Him they received, and continue to receive, their being, their truth, and their significance. Without Him, even mathematics itself cannot – and does not – escape the descent into contradiction. Without God beyond and behind it to hold it up and to give it its proper creaturely context, meaning, application, and significance, the mathematical quest is doomed to final incoherence.
That, at any rate, is my contention.
Here’s what I mean:
In his effort to escape the bruising contradiction he discovered in Cantor’s influential set theory, atheist mathematician Bertrand Russell ran into the problem to which I now allude, though he understood and articulated it far differently from how I am doing it here, as you might imagine.
Russell noticed that in Cantor’s system, even though its premises were true and its conclusions were valid, the final conclusions to which they led inevitably resulted in contradiction, no matter how you worked them. Because of his worldview, Russell considered that result flatly unacceptable. So he determined to extricate set theory from it. But try as he might, Russell and his colleague A. N. Whitehead failed. Indeed, their failure was inevitable and inescapable, as Kurt Godel demonstrated. Godel showed that any mathematical system, in fact any logical system whatever, must finally be inconsistent or incomplete. If so, then Godel’s conclusion is devastating for physics and for any attempt to arrive at the much-vaunted and so-called “theory of everything.” It cannot happen. It will not work.
Whatever else you think you might find at the end of mathematics, you don’t find final, comprehensive, or explanatory truth. Instead, you find contradiction and incompleteness; not truth and not dependable logic. Final, eternal, explanatory truth escapes mathematics, as it finally escapes all things without God. That’s because things without God are devoid of their proper creatureliness. They are devoid of their finitude and of their proper context in God, eternity, and creation. Apart from seeing it in the context of God its Creator, mathematics loses its real status as a finite effect. Rather, it poses and preens as final and full explanation or as ultimate cause, a posture it cannot long maintain without collapse.
Accepted humbly and understood wisely, that disorienting collapse of finite, mathematical explanations for the universe can prove liberating because by it we might begin to notice that such a collapse inevitably follows from God’s absence. Only in Him is found mathematics’ properly limited explanatory context.
Taking God into account explains the creatureliness and dependence of all things, numbers included. It explains their status as finite effect, and not as full explanation or as cause, roles for which they are ill-suited and cannot fulfill, something a “theory of everything” seems to require of them.
Put another way, science cannot be true to the world it seeks to understand unless it makes room for its own contingency, its own creatureliness, and that of its tools and of its objects of study. Even the scientific pursuit itself, the pursuit to exercise dominion over nature, properly belongs to us and to science only by the grace and command of God (Gen. 1: 28). If we examine nature apart from God, then in the end we uncover only nature’s inexplicable and intellectually self-stultifying limitations, not the eternal and the finally true, not the authentically and ultimately explanatory.
That’s because even at our best we are not objective and dispassionate observers of natural systems. We do not employ objective means of analysis, even when we do simple calculations and observations because, even at our best, we always exert an effect. We always bring about some altered particular state simply by our presence and our activity, simply by our experimenting.
At our worst, and by that I mean normally, we skew our task of understanding the world aright because we skew our conception of the world itself and our role within it. That matters because the scientist’s theory and actions are interdependent. Ideas have consequences, and bad ideas have bad ones. For that reason, if the scientist is deluded, then the scientist’s theories are likely to be deluded too. Revelation says, with strong emphasis and effect, that the scientist is indeed deluded. We are not passive; we are not objective. We are creatively, cleverly, and wickedly distortive, sometimes to greater, sometimes to lesser, degrees. We are prone to look at nature and to suppress the truth it reveals about God, truth for which we substitute a lie (Rom. 1: 19-25).
Even the best and most productive of our methods are fundamentally twisted because they assume all things are answerable to us, to our methods, and to our questions. But in Revelation, we are questioned by God and are answerable to Him. In modern secular science, however, He is not merely not questioned, He is banished from the discussion, both as a cause and as a conclusion. For example, if the resurrection is true (and I have argued elsewhere on this blog that it is), if God raised His Son from the dead, if Spirit therefore effects matter and can even re-animate it, then science has ruled out from the beginning some of the most powerful forces and trueest explanations in or out of the universe. If, as Wolfhart Pannenberg argues, God is a field, indeed the field, of force, one without the limitations of time or extension, one that gives rise to new creatures again and again, one that the Bible describes as multi-Personal and as fatherly love, then the scientists have been dealing with God all along and never knew it because their twisted and myopic notion that only material explanations are permissible bars them from the truth.
Yet, in His grace, our shrunken methods still prove quite serviceable, if that is the right word for it. But serviceability and utility are not the same as truth. Think of it this way: Flawed and distorted as were their methods, ideas, and worldview, the three magi still arrived at the feet of the Messiah in Bethlehem (Matt. 2: 1-12), which I take to be the grace of God, and not evidence of their insights or proof that ancient Middle Eastern astrology is actually true. Hence “serviceable” and “properly understood” are not interchangeable concepts. You might achieve your purposes in impressive fashion and still be mistaken. It might take a long time for your mistakes to surface, but they will, as scientific worldview replaces scientific worldview in a long succession of paradigm shifts reaching back past Ptolemy and forward beyond post-Einsteinianism to who knows what -- Who but God.
To paraphrase my late friend Thomas Torrance, in its depths the universe is characterized by openness and spontaneity, even surprise. Nature seems explicable only from beyond itself, only from the inexhaustible possibilities within the Divine rationality. The universe finds its final intelligibility only in references beyond itself, and not in the inappropriate rigidities and allegedly necessary truths of contingent human reason, which at its root, and all on its own, is worse than suspect, lacking as it does metaphysical warrant for its assumed role as arbiter of all things physical and non-physical, a role to which we often exalt it, as if Revelation were to stand before the bar of human intellection and not the other way round.
We find our proper place and role more accurately by holding always before us the contingent truths and contingent rationality that undermine universal mathematical formulation. We absolutely require those higher levels of Reality -- God and His actions -- that are not readily reducible to the same laws by which lower natural particulars seem to operate but that give those lower levels their proper context. Then we know, and then we remember, that lower things are open to explanation upwardly, and that Higher Things are not accurately reducible to the laws of reality downwardly.
The various levels of created reality do not and cannot contain within themselves their own sufficient reasons for their own contingent order.