This question underscores the typical unbeliever's inability to grasp the issues in the debate between totally antithetical worldviews. It also suggests a general unfamiliarity with transcendental argumentation -- as it construes TAG as a deductive argument, and it seems to lapse into a standard "deductivist" view of proof, so prevalent among many unbelievers.
First, TAG is not formally a deductive argument. Deductive arguments necessarily presuppose logic. Without logic, deductive arguments could not even get off the ground. So, the answer is, no, logic per se is not a premise of TAG.2 In the presuppositional defense of Christianity, we do not presuppose a merely abstract and autonomous logic, nor do we posit it as a premise of a deductive argument leading to a conclusion of a God of indeterminate character or an abstract "God of the philosophers."
Second, when it comes to the issues of the existence of logic, abstract objects, and conceptual reasoning, in general, the point of TAG is that the godless reality of atheism, on the basis of its own metaphysical presuppositions, cannot account for their existence. For instance, the existence of logic and material monism are contradictory. Laws of matter and the ultimacy of chance do not produce mentally free, conscious beings who are capable of abstract thought. Materialism cannot account for the existence of immaterial abstract entities of any type (be it logic, mathematics, or moral laws).3 The existence of logic, then, is a problem, and failure, of the atheist worldview. As I have written before, atheists cannot give a "reason for reason." As such, atheists have no metaphysical ground for their presupposition of logic. Atheists, being "epistemological loafers" as Van Til put it, will not acknowledge this. Even in the face of continued prodding, they continue to use a merely assumed autonomous logic and reason, that is, just "take it for granted." But that is question begging and an intellectually empty response. Yet, on the other hand, they will assert that man and his mind was produced by (and thereby, still ruled by) ultimately random material processes. Atheism -- by asserting the autonomy of man (and thereby, the ultimacy of the human mind) along with the ultimately chance nature of temporal facts -- is self-contradictory. Atheism provides no grounds for any of its beliefs (articles of faith, as it were); it can only be adhered to by a willful intellectual blindness.
The positive presupposition of TAG is the existence of the Triune God of Christianity who has revealed Himself in the Bible, in nature, and within man himself. God is the metaphysical ground from which all human experience is intelligible. Logic (and other abstract objects) is not a problem for the Christian theist. Behind man's reasoning is the mind of God.
To reiterate the point: logic is a problem for atheists and agnostics; it is no problem for the Christian theist.
In response to the correspondent's question, I pointed out the following as an example of presuppositions: The laws of logic are laws of rational thought; as such logic presupposes a thinking mind. In Christian theism, that ultimate mind is the mind of the eternal and personal God. Though this may be wrongly interpreted as if it were a deductive argument, it is not. It is an illustration of a presupposition that underlies and is the metaphysical ground of human logic.
The correspondent responded with the question, "Why can't that mind be mine?" Indeed, that is the question for him to answer based on a presumed godless reality! Many questions come to mind. For example, where or from what did his mind originate? Did immaterial minds irrationally spring forth de novo from matter in motion (If indeed there be minds as opposed to mere physically determined material brains)? Was there a first mind? Or, is there an infinite past of finite individual minds begetting new minds, (coming into being at birth, then vanishing into nothingness at death)? Is his mind ultimate? If not, what produced his mind? Is his mind free from physical determination (i.e., does he have rational freedom and volition)? How many unrelated (material and perhaps non-material) causal principles does the unbeliever invent to account for the existence of minds? Are those causal properties, along with matter and minds, of which they are properties, eternal, uncreated, ultimate constituents of reality? In addition, for a materialist the question is (a) how all the biochemistry going on in every human skull (different processes in different locations) gives rise to objective non-material abstractions, such as logic, or, if not a materialist, (b) from whence all these contingent minds emerged equipped with innate and invariant logic. Those are just a few problems for starters.
Again, the question remains for atheists and agnostics to answer on the foundation of their metaphysical presuppositions. Answers that millennia of atheist philosophies have failed to supply. I've already given the Christian answer: Mind is not his alone. The ultimate mind is the mind of the eternal God of Christian theism.
1 The historical connection of logic to TAG stems from Greg Bahnsen's use of the presuppositional apologetic in his debate with atheist Gordon Stein where Stein couldn't support the existence of, or use and reliability of, logic on the basis of his materialism. This was a defining moment for public awareness of presuppositionalism. In a way, it is a bit unfortunate that the debate paved the way for some, including Christians, to think that the existence of logic is the only or main element of TAG (thereby focusing attention mainly on logic in conjunction with TAG). But such is not the case. TAGs challenge to unbelief is that it cannot make sense (on its own presuppositions) of any fact of human experience. Thus, one can start with logic, or language, or mathematics or moral laws (among others) to expose the unbeliever's internal contradictions and refute the unbeliever's worldview or total view of reality. ↩
2 What is at issue in the debate between Christians and unbelievers is not merely "logic," but the conception of logic that each participant in the debate holds. Logical reasoning is necessary -- for both parties -- in the encounter of belief with unbelief. When we reason with unbelievers we, of course, employ our God-given capacity for logical thinking. The unbeliever will likewise employ logic in the debate while all along denying God. However, the unbeliever typically does not question his capacity to reason, nor ask what is the metaphysical ground of the human ability to think and reason according to abstract laws of logic. The "logic" to which the unbeliever appeals (and which is his ultimate authority) is an autonomous "logic" that exists in a void. So an appeal to a common conception of "logic" is illusory. The totally antithetical conceptions of logic (among a host of other things) are at the core of the debate. Van Til addresses this issue:
"It appears then that if there is to be any intelligible encounter between the Christian and the non-Christian, it must be in terms of the two mutually exclusive visions that each entertains. To appeal to the law of contradiction and/or to facts or to a combination of these apart from the relation that these sustain to the totality-vision of either, the believer or the unbeliever, is to beat the air. It is well to say that he who would reason must presuppose the validity of the laws of logic. But if we say nothing more basic than this, then we are still beating the air. The ultimate question deals with the foundation of the validity of the laws of logic. We have not reached bottom until we have seen that every logical activity in which any man engages is in the service of his totality-vision." (Emph. added) Cornelius Van Til, The Case for Calvinism. The Presbyterian and Reformed Publishing Company: Philadelphia, 1964. (Quoted from The Works of Cornelius Van Til, Logos Digital Edition).As to the question of logic in the debate between totally antithetical worldviews Bahnsen writes:
"The antithesis (in principle) between the philosophical systems of unbelievers and the philosophical system of believers is so broad and basic that it even affects the way they deal with central philosophical notions like logic, possibility, and objectivity (to mention but a few). This observation should not be misunderstood. The presuppositionalist does not say that Christians and non-Christians inevitably accept and operate with completely different, specific laws of logic in their practical exercises of reasoning. Yet they do clearly disagree with each other concerning the nature, source, and authority of the laws of logic. Both worldviews may endorse and utilize the disjunctive syllogism or De Morgan's theorems, but when we inquire into what they are talking about, the evidence that is appropriate or persuasive for their claims (about syllogisms, theorems, etc.), or the necessity of the truths about logic, we get radically different answers -- which almost always betray differing convictions regarding metaphysics." (Greg Bahnsen, Van Til's Apologetic: Readings and Analysis, The Presbyterian and Reformed Publishing Company: Philadelphia, 1998. p. 280)↩
3 It is true that there are some atheists who are not material monists -- but they are few and far between. There are idealistic monists (mind is the fundamental stuff of reality) and there are others usually referred to as "pluralists" who believe in a plurality of co-ultimate things (Roger Penrose, for example). But, in the case of the pluralists, merely asserting the existence of minds and a plurality of immaterial "platonic" entities with no coherent unity among them is question begging and provides no intelligible ground for human knowledge. In addition to being no answer to the problem of the one and the many, no atheist has given the account of what bridges the gap between the particulars of the atheist's material world with its basic chance characteristics and their eternal unchanging realm of universal "platonic" entities. As mentioned above, the existence of human minds in this worldview is also a major problem -- especially on the macro evolutionary account that human minds are no more than material brains assembled by (and thereby still controlled by) random physical processes. The dual atheist principles of human autonomy and the ultimacy of chance are contradictory. The many problems of a platonistic conception of reality are well known, which explains why few advocate it, and won't be dealt with here. As to the idealists, which were more in vogue during Van Til's time, Van Til's writings, in particular A Survey of Christian Epistemology, provide a wealth of information on the internal contradictions of the idealists. ↩