What the Heck Is the Fallacy of Denying the Antecedent? That Descartes Joke…

Difficulty: What the heck

René Descartes walks into a bar and orders a drink. When he finishes his drink, the bartender asks him if he would like another. Descartes replies, “No, I think not,” and disappears in a puff of logic.

Philosophers are probably not amused… not because the joke talks crap about Descartes (it doesn’t), but because its attempt at humor rests on a misunderstanding of basic logic. In fact, there are two fallacies at play here: equivocation and denying the antecedent.

Equivocation

Equivocation is a fallacy where a word or phrase has two different meanings that are mistakenly lumped together as one. This is an informal—not formal—fallacy. That is, the fallacy arises not from the logical form of the argument, but from the content of the argument. Take this meme:

The Bible says being gay is fine, as long as you’re high.

Why? Because…

“A man who lays with another man should be stoned.”

–Leviticus 20:13 ESV

The fallacy hinges on a (deliberate) equivocation on the word “stoned,” which can mean two things: (1) to be high and (2) to be executed by stoning.

Applied in a deductive argument, equivocation might look like this:

Premise 1: Saint Stephen was stoned.

Premise 2: If you’re stoned, you’re allowed to be gay.

Conclusion: Therefore, Saint Stephen was allowed to be gay.

Here, the form of the argument is what we call modus ponens, a deductively valid move in logic. But the content of the argument—specifically, the two distinct meanings of “stoned” in the premises—is conflated, creating an informal fallacy.

Equivocation in the Descartes joke

So where does equivocation fit in the Descartes joke?

“I think not.”

This has two different meanings:

• “I think not”¹ = “I don’t think so”
• “I think not”² = “I am not thinking”

The joke exploits this ambiguity, going from “I think not” in the first sense to “I think not” in the second.

Denying the antecedent

This is where it gets pretty stupid. Besides equivocation, the fallacy of denying the antecedent—a formal fallacy—must be applied for the joke to work at all.

Briefly:

Denying the antecedent:

P → Q

¬P

∴ ¬Q

This says:

if P, then Q

not P

Therefore, not Q

This fallacy is tempting. Some instances of denying the antecedent look convincing at first glance:

Premise 1: If I die, I’ll be in hell.

Premise 2: I’m not dead.

Therefore, I’m not in hell.

But the fallacy becomes more obvious once we change the content:

Premise 1: If that’s a turtle, then that’s a reptile.

Premise 2: That’s not a turtle.

Therefore, that’s not a reptile.

Clearly, an animal can be a reptile without being a turtle.

In the case of the Descartes joke, the implied argument is:

If I think, I exist.

I think not (that is, I am not thinking).

Therefore, I don’t exist.

Same form, different content.

So there you go—a seemingly funny joke ruined by a brief logical analysis, which I find funnier than the joke itself.

And they say that Descartes “disappears in a puff of logic”?

I think not.