Cornelius Van Til, The Defense of the Faith, 4th ed., p. 381:
The best, the only, the absolutely certain proof of the truth of Christianity is that unless its truth be presupposed,there is no proof of anything.
Van Til's claim, to employ some Kantian jargon, is that the truth of Christianity is a condition of the possibility of proving anything. That's quite a claim. Let's put it to the test.
One can prove that the null set is unique by reductio ad absurdum. We begin the reductio by assuming that the null set is not unique, that there are two or more null sets. By the Axiom of Extensionality, two sets differ numerically only if one has a member the other doesn't have, or vice versa. But the null set, by definition, has no members. So the assumption leads to a contradiction. Therefore there cannot be two or more null sets. Hence the null set is unique.
The proof presupposes the Law of Non-Contradiction (LNC), and I am willing to grant that LNC and the other laws of logic can be argued to presuppose in their turn the existence of an omniscient necessary being. One argument to this conclusion is the Anderson-Welty argument which I critically examine here. I conclude that, while the argument is not rationally compelling, it does contribute to the rationality of belief in God. In other words, the Anderson-Welty argument is a good reason to believe in the existence of God. It does not, however, establish the existence of God in a definitive manner. It does not show that the existence of God is absolutely certain.
At the very most, then, one can plausibly argue to, but not prove, the existence of an omniscient necessary being whose existence is a presupposition of our rational operations in accordance with the laws of logic. But this is a far cry from what Van Til asserts above, namely, that the truth of Christianity with all its very specific claims is a condition of the possibility of proving anything. Trinity and Incarnation are among these specific claims. How are these doctrines supposed to bear upon the laws of logic? Perhaps the Van Tilians have an answer to this. If they do, I would like to know what it is. But not only is Van Til's conception of God Christian, it is also Calvinist so that all the characteristic claims of Calvinism are also packed into the conception of a God that is supposed to be a condition of the possibility of all proof. How does predestination, for example, bear upon the laws of logic?
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