This is the argument C.S. Lewis makes in Miracles for the fallacy of Naturalism. For a full explanation, click here, or go to the link on the right: "C.S. Lewis' Teleological Argument."
(Note: "Non-rational" causes are are not "irrational"; they are neither rational nor irrational. A non-rational cause would be the fist coming into contact with your face, pain and embarrassment being the effect. Naturalism argues that your brain's firings are non-rational, meaning they are solely caused by some other physical event.)
Premise 1: Any belief that is held solely on the basis of non-rational causes is a belief that is not rationally justifiably held.
Premise 2: If Naturalism is true, then all of our beliefs are held solely on the basis of non-rational causes.
Premise 3 (from 1 and 2): If Naturalism is true, none of our beliefs are rationally justifiably held.
Premise 4: We take for granted that at least some of our beliefs, for example, our belief in the existence of an external world of material objects, are rationally justifiably held.
Premise 5 (from 3 and 4): Either we must take for granted that Naturalism is false or we must stop taking for granted that any of our beliefs, including the belief in an external world of material objects, is true.
Premise 6: We will not (cannot? should not?) stop taking for granted that some of our beliefs are true.
Conclusion (from 5 and 6): We must take for granted that Naturalism is false.
Modern science is based on "methodological naturalism," arguing that "natural phenomena can be explained without reference to the supernatural beings or events." This is a philosophical assumption made before beginning scientific research. If Lewis' argument can be disproved, then Naturalism stands. If not...