If there is no rational ordering principle for the basic laws of physics, they are irrational. If they "just are," independent of some basic principle that correlates them, then they are inexplicable. That is, if there is nothing by which or in terms of which we can explain the most basic laws, we therefore lack a real explanation of those laws.
Is there not of necessity some additional formulation that states––and therefore makes integral sense of––the basic laws? Is not the (supposed) final articulation of the laws of nature itself the completing element that frames the laws as a coherent set? If so, is not our final articulation of natural law itself a natural law?
How do we account for the basic laws' basicality if not by some other, let us say, Law of Basicality which "picks out" these and those laws––or even just This One Law––as the basic principle of the world? It appears that the final statement of the basic laws of the universe must be as basic and incontrovertible as those laws themselves, otherwise their formal interrelations as the basic arrangement of all spacetime are only contingent (and thus revisable under some later theory).
This post, obviously, is more confused that convincing, more perplexing than persuasive, more at a loss than apologetic. All I can say in defense is that the following words from Paul Davies (my emphases added) set me along this ragged path:
What I find lacking in the conventional intelligent-design argument, is … [the] appeal to something outside the universe that has to be accepted as given and cannot be proved. I’d like to try to explain as much of the universe, including its bio-friendly laws of physics, from within the universe – and in a way that doesn’t appeal to something outside of it.
Even standard physics says the laws of physics are friendly for no reason, but have just been imprinted upon the universe at the time of the big bang from without, by some unknown mechanism. Again, the argument makes an appeal to something outside the universe, instead of something intrinsic to it.
For most people, the first interpretation is, “Well, God did it.” What I’m saying is that that gets us nowhere at all. It just shoves the problem off to some other realm. But saying “God did it” is no worse than saying “the laws of physics did it.” They both basically appeal to something outside the universe.
The problem with saying God did it is that God is unexplained, so you’re appealing to an unexplained designer. It doesn’t actually explain anything; it just shoves the problem off. But to say that the laws of physics just happen to permit life is no explanation either.”
This is a common point in debates about cosmic origins, creation, God, naturalism, etc.
On the one hand, theists assert that God best explains the nomological order of the cosmos. On the other hand, atheists assert that the universe can just as coherently fill the role of "most basic cause." The key argument against the alleged sufficiency of God as an ultimate explanation for everything else, is that God Himself seems to require an explanation. If the universe's most basic laws require God, then why doesn't God require something to explain His nature? We've all got to have some most basic premise, so if theists can have God as their metaphysical bedrock, why can't atheists have the cosmos as their bedrock?
I am a theist, so obviously I side with "the God option," but, as I say, the course of this post is pretty much toothless. I have a hunch (if it can even be called that), that theism is right if only because an intentional formulation of even the most basic laws of nature is rationally inescapable. This intentional formulation of the cosmos the Church calls the Divine Logos. Although I am trying to be as irenic as possible in this post, I think it is also worth pointing out that the appeal to an explanation for God is disingenuous, since the whole debate has always been about explaining the universe. Historically, both sides admit that the universe requires a deeper explanation. Why would that be so, if the universe really had the same ontological stature as God? Since the debate centers on how to account for the universe as a material, dynamic reality, it is a stinky red herring to shift the debate to an explanation for God. Protesting that a theist's explanation is "not good enough" still leaves the atheist without an explanation of his own.
Only once I set into writing did I realize how closely connected this pseudo-hunch of mine is with Gödel's incompleteness theorems.
Briefly (and probably wrongly), those theorems entail that any non-trivial arithmetic set is either complete, but not consistent, or consistent, but not complete. In other words, any formal logical-operational system––which is what the universe's basic laws would reduce to––can either possess all its axioms without contradiction but lack proof for all the axioms (viz., without a further axiom outside the set), or be provable but only by recourse to another "dangling" axiom, which renders the new hybrid axiom-set inconsistent. To quote none other than the great Wikipedia (19 Jun 09):
"Gödel's first incompleteness theorem shows that any formal system that includes enough of the theory of the natural numbers is incomplete: there are statements in its language that it can neither prove nor refute. … Gödel's second incompleteness theorem can be stated as follows: For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent."
Let me propose an analogy. One day Mrs. Miller tells all the kindergartners to go outside for play time, adding that they are to remain inside the sandbox for the first fifteen minutes of recess. Once all the kids are in the sandbox, however, certain doubts begin to break out among them, like deformed pearls coalescing around the grains of sand. What does Mrs. Miller mean by "in the sandbox"? How far do the precincts of the sandbox extend?
They can see the white beach sand inside the oak-board pit, but they wonder if crouching outside the pit to dig into the sand is allowed, or if bringing piles of sand out a few feet to the darker dirt (for soil wars, of course) is allowed. And so on. Noticing a disturbance in the force, Mrs. Miller strides to the sandbox, kneels down to grab a handful of sand from the sandbox, and walks around the sandbox as she lets a fine stream of sand drizzle behind her. She explains that staying in the sandbox means not crossing the thin white line of sand on the dirt she added just around the box-pit.
At this point, most children are satisfied. They know the limits of the sandbox; they have proof from Mrs. Miller herself! But other children begin to worry a new bone: if the line itself is made of sand from the sandbox, doesn't the sandbox then reach to the line? How can the sand be inside the line when some of it is at the outermost edge of the no-play zone? Doesn't Mrs. Miller's sandy stricture mean that some of the sand itself falls outside other grains of sand marking the innermost limits of the sandbox? These scrupulous kindergartners see the proof of the limits of the sandbox right before their eyes, but they find it naggingly inconsistent to use the contents of the sandbox to show where it doesn't reach. They face a grave choice. (Fortunately, they also only have five more minutes of sandbox time, so their crisis won't reach Camusian proportions.) They can either stick to the proof outside the system and say the sandbox demonstrably extends no farther than the sand Mrs. Miller sprinkled, or try to be rigorously consistent and waver indecisively as to just where the sandbox sand ends and the do-not-cross sand begins.
So it is, in terms of Gödelian incompleteness, with arithmetical sets: we can either find a proof of their axiomatic limits from some set outside those limits, or remain totally consistent with their proper axioms and lack the proof of those axioms within the axioms themselves.
In any case, and to let you hear from someone who knows what the heaven he's talking about, the late Fr. Stanley Jaki argued for decades that Gödel's theorems had huge consequences for the world of physics, and noted sardonically for nearly as long how little attention had been paid Gödel by the inhabitants of that world. "Herein lies the ultimate bearing of Gödel’s theorem on physics," Jaki explains in “A Late Awakening to Gödel in Physics”. [Alas, I know, the link is broken, since, I believe, Fr. Jaki's webpage has been taken offline until his executor can deal with the data and materials formerly available on it. I have a copy of the "Late Awakening" paper, if some eager beaver really wants it.]
It does not mean at all the end of physics. It means only the death knell on endeavours that aim at a final theory according to which the physical world is what it is and cannot be anything else. Gödel’s theorem does not mean that physicists cannot come up with a theory of everything or TOE in short. They can hit upon a theory which at the moment of its formulation would give an explanation of all known physical phenomena. But in terms of Gödel’s theorem such a theory cannot be taken for something which is necessarily true.*
This relates to my opening questions because, if the basic laws of the universe are one day found to be consistent, they will for that reason be unprovable. If, however, they are proved, they will for that reason be inconsistent. Indeed, the "extra step" of proving the basic laws' coherence is none other than the human articulation of that proof (i.e., nothing less than an axiom "extrinsic" to the set of basic laws). As such, the universe's basic structure lacks the metaphysical self-sufficiency and ontological necessity that characterize God Almighty.
Although I have not yet finished it––since I let a copy of it fly off my scooter on the way to work one day!!!!––I understand that J. R. Lucas's The Freedom of the Will deploys Gödel's findings in remarkable ways to demonstrate the freedom––that is, the consistency yet intrinsic indeterminacy––of the human will. And this is the point I want to sink this post's tiny, nubbin teeth into: theism provides a better explanation of cosmic law and structure than naturalism because, first, it posits a mind which can intelligibly "see" the whole of the cosmos as one coherent set of formal laws, and, second, it is not prone to a regress of "explaining God," insofar as God just is the active principle which both "proves" the universe's order and grounds His own personal structure. Naturalism not only offers no such resources for framing the laws of the universe into a coherent whole, but also succumbs to an explanatory regress that must terminate in the wise agency of the Good One.
It is of the essence of a free personal action to require no extrinsic or deeper reason for the action's coming about than the agent's agency itself. An agent's action is intrinsically explicable just by reference to the agent's agency at the point of acting. Moreover, the agent's agency is intrinsically coherent just by virtue of the fact that it issued in the action willed by his agency. Nothing extrinsic compelled the agent to bring about the action in question, since he himself freely brought it about, and nothing caused the action other than the particular agency of the agent. By analogy, if I eat a sandwich I find in the fridge, neither the sandwich causes me to eat it, nor does the event of my eating cause my eating. In the first case, the sandwich lacked the property of being "the sandwich involved in Elliot's eating-of-a-sandwich" until I gave it that property by eating it. In the second case, the event of "Elliot eating a sandwich from the fridge" did not even exist until I began eating, and therefore it lacked any causal influence on my eating. I was and am the first, final, intrinsic, and complete explanation for my own eating of the sandwich. In an analogous way, God is the first, final, intrinsic, and complete explanation for His own creating of the world.
In contrast, the universe's set of basic laws, like any formally deducible set, possesses nothing within itself to ground its own coherence. Indeed, naturalists' entire point is that the universe is not sentient, is not personal; as a result, by their own admission, there is nothing metaphysically parallel to the intrinsic agency of divine creation in naturalistic cosmic endurance. (Lo, mystery of mysteries, yon sandwich is eaten without there being an eater!) There is nothing intrinsically self-explanatory about the basic laws of the universe, which is why naturalism fails, but there is something intrinsically coherent about the most basic actions of an agent, which is how theism resurrects naturalism.
God does not stand in need of further explanation, since, first, He is a personal event, and therefore presupposes an agency that formal systems lack, and, second, His Triune "structure" need not be proved, since there is nothing logically deducible about free personal actions. The perichoretic structure of God as Father, Son, and Holy Spirit is not a formal set of axioms: it is an eternal utterance and eternal echo of an eternal Word of Living Love. Apart from the divine agency itself, there is no formal, logical reason why the Father begets the Son in the Spirit, and, hence, there is no need for an extrinsic grounding principle for the ordo divinitatis (aka, "the Triune set").
Nor is there any logical necessity in the creation of the world: it is a free effulgence of the Triune goodness. This is why we will never discover logically necessary physical laws (cue Gödel's incompleteness theorems again): the laws of physics are consistent, but not intrinsically, deductively, apodeictically provable. Moreover, they are not even provable as such without reference to their intelligible ratification by the Mind of God. Nothing grounds the laws of nature (as a formally deducible arithmetic set) other than the added axiom "In the beginning God…" And while it is true that nothing grounds the Triune perichoresis other than the Father's eternal Love for the Son in the Spirit of Father-Sonship as the Father-of-the-Son, nothing other than the divine agency need ground a personal event. This is as non-controversial as saying there is no logical grounding for my eating the sandwich from the fridge. Of course there isn't: eating the sandwich was not a logical entailment; it was a personal action.
God did not obey a basic "law" in existing triunely or in creating anything, but He did execute His own will without remainder. Nature, by contrast, lacks a will and can only follow its basic laws––laws, which, once more, insist upon being accounted for. (Strange dream: accounting records without a head accountant!) A coherent, final explanation need not––and most likely cannot––be a logical demonstration, which is why theism's reliance on God as the ultimate explanation is coherent without being logically necessary, and, in turn, why naturalism's search for intrinsic explanatory principles in nature itself is both impossible and metaphysically bankrupt without a Lawmaker to stipulate the laws at work.
* The Gödelian non-necessity of any final theory of the cosmos ties in hugely with Fr. Jaki's work on the cosmological argument. Insofar as everything non-necessary is contingent, and everything contingent requires an explanation outside itself, the non-necessary specificity of the universe as we find it cries out for a causal grounding, namely, God. But that is not exactly germaine to this post, so for now I bracket it, outside the set, as it were.