Logical Fallacies As Weak Bayesian Evidence: The Fallacy Fallacy

07 Jan

So the Fallacy Fallacy is when you declare the conclusion of an argument false because the logical structure of the argument used a logical fallacy. As in the attached comic, you can’t just declare an argument wrong based on the number of logical fallacies it violates; at the most, you can say that the conclusion doesn’t follow from the premises, or that there is a false premise or something. Take the following argument:

P1: Bill is the CEO of my company and says that dolphins are fish
P2: Bill also says that all fish live in the ocean
C: Since Bill is the CEO of the company, and says that dolphins are fish, then dolphins live in the ocean

This argument not only appeals to false authority for the strength of its premises (itself weak Bayesian evidence) but also has factually incorrect premises as well. However, saying “appeal to false authority!” doesn’t actually mean that dolphins don’t live in the ocean.

So looking at this from a Bayesian point of view, how likely is it that the fallacy fallacy actually points out a false conclusion as opposed to a true conclusion (and thus being a true mistake)? Meaning that our evidence E is “you used a logical fallacy in constructing this argument” and H is “therefore your conclusion is wrong” and finding out the difference between H and ~H.

Making an intuitive judgement, there seems to be no relationship between logical fallacies used and whether an argument has a true conclusion; the fallacy fallacy itself seems to hinge on whether other logical fallacies can be legitimately used as weak Bayesian evidence. So if a fallacy fallacy can point out false conclusions just as easily as mistakenly calling true conclusions false, it seems as though P(E | H) is equal to P(E | ~H). I don’t think I have any valid way to differentiate between the two conditionals. If that is true, then it means I’m in a case where Bayes Factor is 1 and just go by the prior probability that a person would arrive at a false conclusion. Over the course of human history, more people have been wrong than they’ve been right, so the prior probability that some random person would randomly know the correct answer to something is low.

So the fallacy fallacy is not technically strong or weak Bayesian evidence, but paying attention to the base rate of someone constructing a valid and sound argument means that the fallacy fallacy, or the bare act of pointing out a logical fallacy itself, probably means that the argument has a false conclusion.

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