Your initial correspondent is rude and uncivilized — sorry! — but there is an old, well-known issue — not with your math, which is fine, but with “logic itself”.

Suppose you wish to investigate the truth of the statement, "All swans are white". This statement is equivalent to, "All non-white things are non-swans." So to verify this, it looks like I could just go around looking at all non-white things and seeing if they are non-swans.

But common sense says that a brown dog isn't really a corroborating piece of evidence for white swans.

This paradox has been known for over a century. It does not reflect in the slightest on the mathematics of Bayesian statistics — it's probably closer to mathematical philosophy. In practice, the universe of observations you are working in is very carefully constrained, and you simply don't get this problem at all.

Thanks for an entertaining article!