Clever arguers give weak evidence, not zero

Followup to: The Bottom Line

We are warned that an argument made with a predecided conclusion does not evidentially entangle with the truth it claims to address, and thus is no evidence of that claim.

Recall that observation E is evidence for hypothesis H iff P(E|H) > P(E|¬H). What do the variables mean here?

• E: there's a convincing argument for the predecided conclusion
• H: the predecided conclusion is really true
• P(E|H): probability that the clever arguer can make a clever argument, given that the conclusion is true
• P(E|¬H): likewise, given that the conclusion is false

What the commentary from "The Bottom Line" leaves out is that making a convincing argument is a nontrivial task. For many false claims, a clever arguer with ordinary resources cannot make a convincing argument. If it's typically easy to make a convincing argument for something false, you're convinced by the wrong things.

Thus P(E|H), in this case, would usually be greater than P(E|¬H). An argument for a claim from a clever arguer only clearly proves that the arguer wanted us to believe it. A convincing argument for a claim — and if the argument isn't convincing, you'd ignore it — proves that the claim has convincing arguments for it accessible to that level of arguer, which is correlated with the claim being true.

But maybe I decided at the start that clever arguments for predecided conclusions are actual evidence, thereby breaking the entanglement of the rest of this essay. Well, are you convinced anyway?