I recently came across this logical "proof" of the existence of God at Robert Oerter's blog, Somewhat Abnormal.
Consider the following sentence:When I read it, it struck me as just the kind of thing that Christians would buy (note that Robert Oerter does not buy it). It is a logical sleight of hand. It tricks the reader into accepting its conclusion. And that's the basis of many theistic proofs. Let's examine exactly why this argument fails.
(S) If this sentence is true, then God exists.
Suppose sentence S is true. Then the first clause is satisfied, so the second clause is true. Thus, God exists.
What the preceding paragraph proves is that if sentence S is true, then God exists. But that is exactly what sentence S asserts. So that means we have proved that sentence S is true! And therefore God really does exist.
We are asked to make an assumption - namely that (S) is true. And then, based on that assumption, we conclude that God exists. But is this valid? Let us consider what it means to assume that (S) is true. The proposition (S) is called a material conditional. A material conditional is generally expressed in the form "If A, then C." The clause "If A" is called the antecedent, where A is some assertion. The clause "then C" is called the consequent, where C is the condition that is entailed by the truth of A. It may be said that a proposition of this form is true if it expresses a valid logical relationship between the antecedent and the consequent. To assume that (S) is true is not merely to assume that the consequent it true, but to assume that the consequent is entailed by the antecedent.
To help determine the validity of (S), let's take a different material conditional as an example.
(X) If the sky is blue, then my dog has four legs.We can see immediately that this proposition does not express a valid logical relationship between the antecedent and the consequent. The consequent is the condition of my dog having four legs. But my dog may or may not have four legs (he could be an amputee), and the truth of that is not entailed in any way by the antecedent. The sky could be gray from clouds or red from smoke particles, and it has no effect on the number of legs my dog has. So even though the sky might in fact be blue, and my dog might in fact have four legs, (X) does not express a valid logical relationship between antecedent and consequent. Therefore, it is not reasonable to assume that (X) is true. If you do assume that it is true, you may well be led to a false conclusion. In other words, you haven't proven anything at all. It makes no difference what the consequent is. You can't prove it by simply assuming the truth of an invalid logical relationship.
Now, to get bask to the original (S), it may not be immediately apparent that this doesn't express a valid logical relationship between antecedent and consequent. Starting with the basic form of the material conditional, we have
(S1) If A, then C. - where A is "this sentence is true" and C is "God exists".But the proposition A the assertion of the truth of (S), so we can say
(S2) If (S), then C. - where C is "God exists".Now if you expand (S), you can see that the antecedent becomes an infinite regress assertions that the assertion is true. This alone should reveal that the proposition (S) is not formed in a valid way. But more importantly, it becomes a little easier to examine the relationship between antecedent and consequent. To say "this sentence is true" is to assert that the existence of God is logically entailed by (S) being true. But that's not a valid assertion, in the same way that (X) is not valid. The consequent is not implied by the antecedent, and it is not reasonable to assume that (S) is true, any more than it is reasonable to assume that (X) is true. In other words, (S) asserts a valid logical relationship between antecedent and consequent where there is none, and therefore (S) is not true. So assuming the truth of (S) is like assuming the truth of "If P, then not P".
This argument is reminiscent of other logical proofs of the existence of God that I have encountered. In particular, Anselm's ontological argument comes to mind, which also uses a logical sleight of hand to trick the reader into making a false conclusion. As a self-described skeptic, I try to be on guard against such trickery in logical arguments. Theists are free to disagree.