Tag: denying the antecedent

Is the Fallacy Fallacy a Formal or Informal Fallacy?

Difficulty: What the heck

Is the fallacy fallacy a formal or informal fallacy?

Answer: it depends.

But first, briefly: the fallacy fallacy is the fallacy whereby the arguer concludes that an argument’s conclusion is false simply because the argument used to support it is fallacious.

For instance:

Debater 1: Trump is not evil, because you’re a cow.

Debater 2: Aha! That’s an ad hominem argument, and that’s fallacious. So you’re wrong that Trump isn’t evil. Therefore, Trump is evil.

Here, Debater 2 commits the fallacy fallacy by arguing that because Debater 1’s argument is a fallacious ad hominem abusive argument, Debater 1’s contention that Trump is not evil must therefore be false.

But the issue is this: just because someone’s reasoning is fallacious does not mean her conclusion is necessarily false. It does not mean it is true, either. It just means that the conclusion does not logically follow from that argument.

Think about it this way: if a kid were asked to do a multiplication problem—say, “2 × 2”—and, not knowing how to multiply, she used addition instead, she would still arrive at the right answer, “4,” even though her reasoning process would be wonky. It is the same way with logic and argumentation. A bad argument can accidentally land on a true conclusion.

However, the question I’ll have you ponder today is whether the fallacy fallacy is a formal or informal fallacy.

One way to interpret the fallacy fallacy is as relying on the following argument form:

Premise 1: If an argument is non-fallacious, then its conclusion is true.

Premise 2: This argument is fallacious.

Conclusion: Therefore, its conclusion is false.

If that is how the arguer is thinking, then sure: the fallacy fallacy can be understood as a formal fallacy. More specifically, it would have the form of denying the antecedent.

But here is another way to look at it. The arguer may instead be reasoning with a perfectly valid form—namely, modus ponens—while relying on a false premise:

Premise 1: If an argument is fallacious, then its conclusion is false.

Premise 2: This argument is fallacious.

Conclusion: Therefore, its conclusion is false.

If this is how Debater 2 is thinking, then the form itself is not the problem. The form is valid. The problem lies in Premise 1, which is false. In that case, the fallacy fallacy would be better understood as an informal fallacy.

So, is the fallacy fallacy a formal or informal fallacy?

Again: it depends on what, exactly, has gone wrong in the person’s reasoning.

And why does this distinction matter?

Because clarity matters. And because if we want to understand our own fallible thought processes, it helps to know whether the problem lies in the form of the reasoning or in the content of what we are assuming. But the psychology behind shitty logical reasoning is a topic for another day. Until next time, then.

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 is invalid because Q could still be true for some other reason. But it’s a tempting mistake. 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.