The Transcendental Argument for the Existence of God (TAG) is a powerful and, in my opinion, non-refutable proof for God’s existence.  However, there are those who refuse to accept it and have offered a counter-argument, the Transcendental Argument for the Non-existence of God (TANG).

I heard about this argument via the CARM discussion boards and was pointed to a website that proposed the argument.  After reviewing TANG, I found it to be invalid.  I’ll quote a paragraph from the website that articulates TANG, and then I will show you how it is invalid.  My comments to atheist’s argument are in green.

“How might TANG proceed? Consider logic. Logic presupposes that its principles are necessarily true. However, according to the brand of Christianity assumed by TAG, God created everything, including logic; or at least everything, including logic, is dependent on God. But if something is created by or is dependent on God, it is not necessary – it is contingent on God. And if principles of logic are contingent on God, they are not logically necessary. Moreover, if principles of logic are contingent on God, God could change them. Thus, God could make the law of noncontradiction false; in other words, God could arrange matters so that a proposition and its negation were true at the same time. But this is absurd. How could God arrange matters so that New Zealand is south of China and that New Zealand is not south of it? So, one must conclude that logic is not dependent on God, and, insofar as the Christian world view assumes that logic so dependent, it is false.”¹http://www.infidels.org/library/modern/michael_martin/martin-frame/tang.html.

I will re-create this paragraph below in outline form and analyze the statements one at a time  – – adding comments accordingly.

1. “according to the brand of Christianity assumed by TAG, God created everything, including logic; or at least everything, including logic, is dependent on God.”
   1. Clarification:  God did not invent or create logic.  It is correct to say that logic is dependent upon God since it is a part of his perfect nature.
   2. If the person writing this article understood TAG properly, he would not assert as part of the TAG argument that God created logic.
2. “But if something is created by or is dependent on God, it is not necessary – it is contingent on God.”
   1. Incorrect.  If logic is a part of God’s nature, then it is necessarily existent because it is based on God’s existence.  In other words, it necessarily must exist because God exists.
   2. God’s self-existence and necessary attributes are consistent with the First Law of logic, the Law of Identity, which states that something is what it is:  A = A.  Since the TAG argument ultimately concludes that God exists (God = God), then his attributes, which are dependent and necessarily a part of his existence, also exist.  You cannot separate God’s attributes from God himself since his attributes exist because God exists.  By way of analogy, I am six feet tall.  My height (or whatever height I might be) is an attribute of my existence as a full-grown man, and it cannot be separated from what I am.  Of course, height can be altered, but “height” cannot be removed from my physical existence.  It is a part of my existence.
   3. The objection erringly separates God’s nature from logic as if logic can be a separate thing from God’s nature.  This is not the TAG argument, and it is not logically necessary as shown in 2.B above.
3. “And if principles of logic are contingent on God, they are not logically necessary.”
   1. If “contingent” here means not necessarily existent but were chosen to come into existence or were brought into existence somehow, then the argument is invalid for the reason stated in point 2.B above.
4. Moreover, if principles of logic are contingent on God, God could change them.
   1. See point 2.B above.
   2. This conclusion fails to understand that logic is not separate from God’s nature but is a reflection of God’s nature.  Since God’s nature does not change, the principles of logic cannot change.
   3. The critic fails to understand the TAG argument properly.
5. Thus, God could make the law of noncontradiction false; in other words, God could arrange matters so that a proposition and its negation were true at the same time. But this is absurd. How could God arrange matters so that New Zealand is south of China and that New Zealand is not south of it? So, one must conclude that logic is not dependent on God, and, insofar as the Christian world view assumes that logic so dependent, it is false.”
   1. By now we can see that the argument fails in his earlier assumptions.  Therefore, his conclusion cannot be trusted and is not valid.
   2. “The absolutely impossible may also be called the intrinsically impossible because it carries its impossibility within itself, it’s the borrowing it from other impossibilities which in turn depend upon others. It has no unless clause. It is impossible under all conditions and in all worlds and for all agents. “All agents” here include God himself. His omnipotence means the power to do all that is intrinsically possible, not to do the intrinsically impossible. You may attribute miracles to him, but not nonsense. This is no limit to his power. If you choose to say “God can give a creature free will and at the same time withhold free will from it” you have not succeeded in saying anything about God: meaningless combinations of words do not suddenly acquire meaning simply because we prefix to them the two other words “God can.” It remains true that all things are possible with God: the intrinsic impossibilities are not things but nonentities. It is no more possible for God than for the weakest of his creatures to carry out both of two mutually exclusive alternatives; not because his power meets an obstacle, but because nonsense remains nonsense even though we talk it about God.”²Lewis, C. S. The Problem of Pain, New York: Harper Collins Publishers, 1996, p. 18.