Humility, Induction, and Logical Fallacies

The standard “argument from authority” fallacy is the claim “X is true because Authority A says it is”.  Of course, it may be possible for X to be true and for Authority A to affirm its truth, but the two have no logical connection and so the argument holds no weight – hence the fallacy.  A friend recently noted a variant of the fallacy which combines the argument from authority with the valid modus tollens (“denying the consequent”).  The variant goes like this:

  1. If X were true, it would mean belief Y is false;
  2. Y is believed true by experts, respectable people, and/or the majority of the public;
  3. Therefore, X must be false.

Formally, this is a fallacy because of the possibility that premise 2 is false.  As in the appeal to authority, other people’s beliefs are irrelevant to the truth of a proposition.  So why does this particular fallacy endure in public discourse?  I suspect the reason is that this “fallacy” is actually not one, when viewed from a virtue-ethical/Bayesian perspective.

The kind of logic used in the fallacy, deduction, is great when applied correctly.  In deduction, if the premises are true, the conclusion is inescapable; fallacies usually come from incorporating premises that are either irrelevant or incorrect.  But in the real world, we have no way of knowing with absolute certainty whether a given premise is true.  We form our beliefs, and even our concepts, primarily through induction – that is, the integration of our experiences.  Accordingly, all our beliefs are tentative conclusions which can be expressed not in the form “X is true” but the form “Based on past experience, the probability that X is true is around Y%”.  These tentative conclusions, known as “priors”, are always subject to change based on new, contradictory evidence.

In the real world, no one has perfect information and most people have to rely on the considered judgments of experts or the wisdom of crowds.  This is a standard exercise in humility: one should not assume that one knows better than others. This means the appeal to authority, while formally fallacious, is fairly convincing.  For most people, premise 2 is interchangeable with “Y is (tentatively believed to be) true”, and from there we have a standard proof by contradiction: if P, then Q; not Q, therefore not P.  Perhaps a better description of the “fallacy” would be “proof by contradiction tempered by intellectual humility”.  We might reframe it as:

  1. If X were true, it would mean belief Y is false;
  2. We have a justifiable belief that Y is true;
  3. Therefore, X contradicts existing knowledge and must be false.

But it’s essential to appreciate that while this argument should not be seen as a fallacy, it may nevertheless be incorrect.  The real problem in the logic is not the appeal to authority; that’s an unavoidable part of life in a hyperspecialized society.  Rather, the problem is that it overlooks the inherent uncertainty of knowledge and treats expert opinion as true, rather than “somewhat more likely true than a layperson’s opinion”.  To be sound, the revised premise 2 needs to be “We have a justifiable true belief that Y is true”.  As it stands, X contradicts existing beliefs, not existing knowledge.  What this means is that our priors are heavily stacked against X.

That doesn’t mean X is false.  It means that the burden of proof for X is substantially higher than normal, and squarely on the shoulders of the person claiming X.  The flip side is that it also places a burden on everyone else to re-examine their beliefs in Y, rather than doubling down and dismissing X out of hand for the sake of preserving prior beliefs.


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