The argument is simple enough, and persuasive enough, to a degree.
The basic proof goes as follows: The universe follows reliable and verifiable laws (they need not be absolutely deterministic). Randomness cannot produce reliable or verifiable laws. Therefore, the universe was not produced by randomness.
It does not, however, survive a brief brush with Kant. Only the world as perceived by the human mind follows reliable and verifiable laws. The world is perceived through intuitions of the mind which are brought in to the observation pre-packaged and cannot be tested outside of themselves. Specifically, space, time, and the five senses.
For example, we do not infer the existence of sensory information from other observations. Rather, the fact that we possess sensory information allows us to engage in the act of the observation in the first place. Anything which man perceives, he perceives by the fact of the five senses. The five senses are human intuitions which allow experience to occur in the first place.
Similarly, we do not infer space and time from other observations. Rather, any object which we observe, we observe in spatiotemporal dimensions. Space and time are also pre-packaged human intuitions.
Man observes causality because of a priori synthetic assertions. ‘Analytic’ meaning a statement in which the truth value of the predicate is contained in the subject, e.g ‘all bachelors are unmarried’, and ‘synthetic’ referring to one in which the truth value of the predicate is not contained in the subject, and therefore must be verified independently; For example, Dave is unmarried. An a priori synthetic truth is one in which we verify the truth of the statement not by observation of the world, but by direct contact between a given concept and our intuitions. For example, truths of geometry, such as the Pythagorean Theorem, are achieved in this way. The truth-value of the statement A^2 + B^2 = C^2 is synthetic because the predicate is not contained in the subject(s), and a priori because it follows from the intuitions in which human thought occurs, rather than being affirmed by empirical observation.
Similarly, the validity of “causality” and causal laws are at their roots a priori synthetic assertions. Man observes causality because of the space-time oriented nature in which he observes the world. But since it is impossible for us to observe the world in any way independent of the intuitions of our own mind, we can never test the validity of those intuitions; we can never know what the world is like in itself. Therefore, statements can only be about our concepts and observations; they can never apply the ultimate nature of reality. We can never say that God must exist in order to have created a world with causal laws, because we can never attribute ‘causal laws’ to the world in itself.
This does however, raise a perhaps more troubling case for the existence of God. Since we can never observe the world independent of our own minds, we can never be justified in asserting that there exists any world outside of our own minds at all. Furthermore, we can never know with certainty what that world is like, if any world exists.
Thirdly, the causal reasoning which allows us to understand and explain nature cannot sustain itself if it attempts to extrapolate to the whole system itself. Nature either began in time, or did not begin in time. If it began in time, the first cause cannot itself have had a cause. If it did not begin in time, one can never fruitfully ask the causal question Why is there something rather than nothing?.
So when one ventures to seriously critique their own cognitive faculties, unaided reason must throw up its hands and admit that it can never even know that there is any really existing world at all, or what that world is like if it does exist, and must in addition admit that causality, the mechanism which allows the world to be understood according to our mental intuitions, is an illusion, collapsing in upon itself.
It seems that in failing to support these three beliefs, reason’s finds itself to be a castle built on sand and without foundation. As such, one, if one is truly devoted to unaided reason, must accept total nihilism. Alternatively, one could choose to believe, without direct evidence, that the world was created and is sustained by an agency outside of itself, which acts to reveal nature in its true form to mankind, and which is not itself subject to the causal laws which seem to govern nature.
By adopting this epistemological presupposition, one is capable of moving the breakdown of causality outside of the system of nature, rather than leaving it inside of itself, and thus is capable of salvaging reason as a tool for explaining the world.