Generally speaking TAG is a deductive argument, but it is unlike all other deductive arguments. What sets TAG apart from garden variety deduction is that with the latter we begin with some truths (or inferences) and reason to others – but unlike transcendental arguments that to which we reason is not presupposed as a necessary precondition for the intelligible experience of the original fact of experience (or its denial). For instance, “If causality then God” merely means that causality is a sufficient condition for God and that God is a necessary condition for causality. Which is to say: if causality exists then it is logically necessary that God exists. However, such a premise does not delve into the question of how God and causality relate to each other. It does not tell us whether God exists because of causality or whether causality exists because of God. Causality presupposes God says more than causality is a sufficient condition for God and that God is a necessary condition for causality. If causality presupposes God then God must be logically prior to God.

The transcendental argument for the existence of God is an argument that has as its conclusion God exists.

Prove A: The Christian God exists.
Step 1 ~A: (Assume the opposite of what we are trying to prove): The Christian God does not exist.
Step 2 (~A--> B): If God does not exist, then there is no intelligible experience since God is the precondition of intelligibility
Step 3 (~B): There is intelligible experience (Contradiction)
Step 4 (~ ~A): It is not the case that God does not exist (Modus Tollens on 2 and 3)
Step 5 (A): --> God does exist (Law of negation.)
Q.E.D.

Whereas professing atheists are willing to concede the validity of the above argument Christians should happily concede that the argument is not only not fallacious (i.e. valid) but also sound. In other words, although professing atheists and Christians alike agree that the above argument has a valid form – i.e. the conclusion follows from the premises – Christians should agree that since the premises are all true and the form is valid the conclusion is true. But unfortunately Christians are often muddled.

Christians often say that TAG does not achieve its goal because not every worldview is refuted in the argument. Such a claim simply demonstrates a fundamental misunderstanding of the scope of TAG. The above argument is aimed to prove that God exists, which it does. To deny that it does is to reject logic and / or biblical truths. Again, the argument above has a specific conclusion, God exists. The conclusion of the argument is not that if God does not exist, then there could be no intelligible experience. In other words, the above transcendental argument does not aim to prove that God is the precondition for intelligible experience, though that is a premise used in the argument which is why the argument is transcendental. That is where Christians who oppose TAG get tripped up. They don’t appreciate what is being argued.

So what about step 2 of the argument? We can defend the premise of step 2 deductively by appealing to the absolute authority of Scripture. Of course the unbeliever rejects that authority; nonetheless that the unbeliever is dysfunctional does not mean that an appeal to Scripture is fallacious! After all, if a skeptic rejects logic should we then argue apart from logic? Since when does the dullness of an opponent dictate which tools of argumentation may be used? Of course, given the unbeliever’s suppression of the truth the Christian does well to defend step 2 inductively by performing internal critiques of opposing worldviews, which of course can only corroborate the veracity of step 2. It would be fallacious, however, to conclude because of such condescension toward the unbeliever that the conclusion of TAG (God exists) and the justification for its step 2 (God is the precondition of intelligibility) rest upon inductive inference. By the use of induction the Christian is merely acknowledging that the unbeliever refuses to bend the knee to the self-attesting Word from which step 2 can be deduced by sound argumentation. Since unbelievers will not accept the truth claims of the Bible and, therefore, a deductive defense of step 2 the only thing the Christian can do is refute the hypothetical competitors, but that hardly implies that step 2 cannot be proved by deduction.

Finally, it’s been noted by some, popularized by Don Collet in the Westminster Theological Journal, that the only way a transcendental argument may be formalized is thusly (TAG*):

C presupposes G if and only if both 1 & 2:
1. If C then God exists
2. If ~C then God exists

Given such a construct, we are no longer negating the metaphysicality of causality but rather the truth value of the predication of the metaphysicality of causality. In other words: ~causality (which is chaos) does not presuppose God(!) so for the construct to make sense it must pertain only to prediction about causality. In other words, since non-causality is an impossible entity that defies creation, providence and intelligibility, such a formulation of TAG (TAG*) limits itself to predication only. Does the apologist really want to do that? Do we want to give up arguing that God is the precondition for the intelligible experience of actual causality? I think not. TAG* is indeed powerful but it does not pertain to anything other than prediction.