Lies, damned lies, and material conditionals

William Lane Craig claims that atheists agree with him that, “if the universe has an explanation of its existence, that explanation is God.” It seems to me a pretty clear example of Craig’s tendency to falsely claim his opponents agree with him, but there’s one way of defending Craig’s claim that I know occurred independently to both me and at least one other person: invoking material conditionals.

Let me say at the start that I’ve never heard Craig use this defense, and the defense is so bad that it almost feels unfair to Craig to suggest he might use it. However, because it may occur to other people, and there’s some chance it’s what Craig had in mind, I think it’s worth addressing.

A material conditional is a way of understanding if-then statements that comes from formal logic.  A material conditional is defined to be false if both the “if” part is true and the “then” part is false, and true otherwise. That is to say, if the “if” part is false, then by definition the material conditional is true. If the “then” part is true, then by definition the material conditional is true. If both of these latter conditions hold, then by definition the material conditional is true.

Material conditionals are only weakly related to what we ordinarily mean by if-then statements. In particular, there’s no requirement for the “if” and the “then” parts to have anything to do with each other. This allows all sorts of bizarre sentences to count as true material conditionals. For example, “if the Earth is the fourth planet from the sun, then 2 + 2 = 5″ (because the “if” part is false) as well as “if the Earth is the third planet from the sun, then 2 + 2 = 4″ (because the “then” part is true).

Now you see what Craig could say here: “Most atheists think the universe does not have an explanation for its existence. So they think the ‘if’ part of the material conditional, ‘if the universe has an explanation of its existence, that explanation is God’ is false, so they must think the conditional is true.”

I hope, for Craig’s sake, he doesn’t mean to argue that way. To see why, suppose you (mistakenly) believe that Hong Kong is the capital of China. Then you would have to believe the material conditional “If Hong Kong is not the capital of China, then I have four arms,” because you’d think the “if” part is false. But if someone corrected you about Hong Kong being the capital of China, that would not mean you should reason:

  1. Hong Kong is not the capital of China.
  2. If Hong Kong is not the capital of China, then I have four arms.
  3. Therefore, I have four arms.

The reason you shouldn’t reason this way is that once you know Hong Kong is not the capital of China, you no longer have any reason for accepting (2), not even as a material conditional.

Also note that while “the universe does not have an explanation for its existence” commits you to “if the universe has an explanation of its existence, that explanation is God” (read as a material conditional), it commits you equally to “if the universe has an explanation of its existence, that explanation is the Flying Spaghetti Monster,” “if the universe has an explanation of its existence, that explanation is Carrier’s exploding God,” and so on.

That should underline how little material conditionals have to do with what we ordinarily mean by if-then statements.

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