Transcendental argument for the existence of God
The transcendental argument (TAG) is an argument for the existence of God that attempts to show that logic, science, ethics, and all the other good things in philosophy presuppose God's existence. That is, you can't make sense of them unless you stipulate that God exists. The argument is used by presuppositional apologists. Transcendental reasoning is inference about the prerequisite conditions for the possibility of knowledge. All major philosophies have transcendental theories.
The TAG aims to prove God's existance from the impossibility of the contrary. Theists and nontheists alike rely on logic, science and ethics. The Christian God, being all logical, all uniform, and all good, exhibits his character in the created order. It is the Christian's contention that no other worldview can account for these things. Therefore, by default Christianity is true.
More details on the argument
The Transcendental Argument for the Existence of God is a very complex argument that is difficult to summarize in a few, short sentences. As stated above, its premise is that no worldview except the Christian theistic worldview as found in the Bible provides the necessary preconditions for science, ethics, logic, mathematics, morality, induction, etc. All other worldviews (Atheism, Buddhism, Islam, Judaism, etc), if carried out to their logical conclusion, are reduced to absurdity. TAG is a transcendental argument, one which proves itself from the impossibility of the contrary. (See also Immanuel Kant)
As mentioned above, one cannot wildly stipulate entities that enjoy no independent support; however, it is important to note that one’s worldview eventually must boil down to a single set of governing presuppositions that are the foundation of all other beliefs. Said another way, eventually we must come to an end of our chain of reasoning. If we believe A, and we believe A because of B, and we believe B because of C, and so forth, eventually we come to a belief that is the foundation of all our other beliefs. For the Christian, the self attesting Word of God is that fundamental, independent, foundational belief. According to TAG, only the Bible provides the necessary preconditions for rationality. TAG than challenges the core beliefs of the non-Christian’s worldview and shows where those foundations lead to arbitrariness, inconsistencies, or absurdity.
Objections
Some might question whether any worldview, if carried to its logical conclusion, is reduced to absurdity. Somehow non-Christians seem to do pretty good science, mathematics, logic, induction, etc. Non-Christians can be very ethical people, sometimes, perhaps, more so than a professing Christian.
Note that TAG does not say that non-Christians cannot be logical or moral, or that non-Christians are unable to perform scientific inquiry or mathematics. Rather, TAG argues that within a non-Christian worldview, there is no logical foundation that can make sense of these activities. Second, TAG asserts that Christianity is both self-consistent, and consistent with reality; i.e. that it does not lead to absurdity. This may not be true, but it would be the responsibility of the opponent to show both the consistency of his worldview, and to show that Christianity leads to absurdity.
For example, if one asserts that morality is relative, than any basis by which to condemn an action, say rape or child molestation, is lost. It may be inconvenient, it may be harmful to others, it may be undesirable for the well being of society, but it cannot be evil in any meaningful sense. Evil cannot exist if morality is relative. However, this does not mean that relativists cannot be moral. Rather, any appeal made for moral behavior on behalf of the relativist reveals a reliance on some absolute standard that his worldview denies.
TAG argues that the relativist must secretly rely on the Christian God to make sense of any appeal to morality. On the Christian worldview, there is an all-good God whose character is the basis for right and wrong. In his self-revelation, he reveals how man should act, and commands man to be moral. Thus, man does have an absolute standard of morality by which to commend or condemn one’s actions.
Thus, if the relativist wishes to remain consistent, he cannot condemn any action; not murder, not rape, not even the holocaust. To do so is, as TAG supposes, an exposure of his reliance on the notion of absolutes, and are based on unacknowledged presuppositions, assumptions about right and wrong which he claims to reject. No moral condemnation can be accounted for from the relativist's own worldview, TAG argues, and is derived from unconsciously "borrowed capital" from Christianity, which he in turn uses even in his argument against Christianity.
More Information
A number of Apologists have used TAG, including Cornelius Van Til, Greg Bahnsen, John Frame, and Michael Butler. Also see Michael Martin’s Transcendental Argument for the Non-Existence of God.