I'd like to excerpt here from a book I recently read. Let "unbeliever" here mean "vaguely naturalistic skeptic".
But standing on the unbeliever's worldview quickly demonstrates internal problems. B/c of his opposition to the absolute God of Scripture, he must account for reality in some other way than by a personal, rational, sovereign Creator. In discounting an absolute mind creating and controlling the universe, in the final analysis he is committed to chance. In his view of origins, the material universe sprang into being from nothing and under not rational oversight. The rational, then, is built upon the irrational.
This view of origins produces insurmountable rational problems, for such a chance-based worldview can have no laws, no necessity, no logical principles, but only randomness. According to cosmic evolutionary theory all is ultimately subject to random change and is in a constant state of flux. But our very rationality requires laws so that things may be distinguished, classified, organized, and explained. Rational comprehension and explanation demand principles of order and unity in order to relate truths and events to one another. Consequently, on the basis of the non-believer's worldview rationality itself has no foundation.
The unblvr may attempt to acct for rationality by asserting that man's mind imposes order so that rationality results. If he does so, then his view of reality becomes subjective rather than objective (Rhology comments: like here). But even this attempt is impossible, for how can the mind impose order on a chaotic universe?
And what if your friend denounces your Christian worldview for its being governed by "faith" as over against "reason"? What if he argues that you are naïve in not employing his scientific method?
Point out to him the futility in his argument. The scientific method proceeds on the basis of observation thru the senses. As the Humanist Manifesto III (1993) expressed it: "Knowledge of the world is derived by observation, experimentation, and rational analysis. Humanists find that science is the best method for determining this knowledge as well as for solving problems and developing beneficial technologies."
This method holds, then, that knowledge must be limited to observation and sense perception. Once your unblving friend has committed to this procedure, demonstrate his epistemological self-contradiction: If all knowledge is governed by observation, then how did he come to know that? That is, how did he come to know that "all knowledge is governed by observation"? Did he observe that in the lab? Did he measure, weigh, or count it? Did he detect that conceptual limitation by exploring nature? And furthermore, does he observe that this principle is a universal limitation on knowledge in all places and at all times so that he can confidently trust it?
If he attempts to use the laws of logic in reasoning with you, ask him where in nature he has seen the laws of logic? Show him that you can't use the sci method to prove the laws of logic, for you can't observe, taste, or feel them since they are not material entities extended in space. How then can he justify logic? Or the sci method of empiricism?
But with the blvr's worldview, a personal, absolute Creator God accts for the rational, coherent, law-ordered reality that you and the unblvr both experience and depend upon. In God's sovereign revelation to man (Scripture) we learn that He spoke , "And it was so" (Gen 1:7, 9; Ps 33:6; 2 Cor 4:6; Heb 11:3). Not only do we discover order and harmony throughout the narrative of creation (days 1 thru 6 following logically one after the other), but the very idea of God's speaking reality into existence itself requires rationality. The universe is ultimately rational because the rational, law-ordaining God of Scr created it thus. Man is a rational being b/c he is created in the image of God, who is the standard of rationality. In Eden, God commands him thru verbal communication (Gen 2:16-17); Adam authoritatively speaks (2:19-20); God reasons with him (3:1-19).
Empirical (observational, sense-based) scientific investigation is also called for in the Christian worldview b/c God created an objective, material universe, governs it by predictable laws (Gen 1:14-19, 8:22; Job 38:31-33; Ps 8:6, 115:16). Furthermore, God created man as a sensate, physical being, for "the hearing ear and the seeing eye, the Lord has made both of them" (Prov 20:12)...
The unblvr's problem only gets worse when he demands that we provide proof for the existence of God...Ask your friend: "Why do you require that I give you a reason proving God's existence? After all, on your view there is no reason for reason itself." (p. 152-155).
When modern man commits exclusively to the sci method, then he has committed to empiricism. Empiricism is the view that all human knowledge ultimately derives thru the senses and thru experience. We discover laws of physics, for instance, by observing, measuring, counting, and analysing the behavior of things around us.
The unblving empiricist cannot acct for the laws of logic which regulate human reasoning. The laws of logic are not physical objects existing a a part of the sense world. They are not the result of observable behavior of material objects or physical actions. Do the laws of logic exist in the natural world so that they can be empirically examined? If we are materialists, then only that which is objective in the realm of sense experience is real. What sense do the laws of logic make for unblvrs? What are the laws of logic? If they are just the firing of nerve endings in the neural synapses, then logic differs from person to person and therefore its laws are not laws at all. The inherent materialism in the modern world cannot acct for laws of logic.
Furthermore, since the laws of logic are universals, invariant, abstract, eternal truths, how do they continually apply inn our changing world of experience? How do we get those laws from "above" down into the historical process?
...When unblvlrs talk of concepts, they need a worldview to make them meaningful. (p. 204-205)
Source: Pushing the Antithesis: The Apologetic Methodology of Greg L. Bahnsen, Gary DeMar, editor. 2007, American Vision, Inc.