Extraordinary claims require extraordinary evidence
A maxim popularised by Carl Sagan (1980), following Laplace and Hume: the weight of evidence needed to accept a claim should scale with how much the claim departs from established knowledge.
Skeptical view
This is just Bayesian reasoning stated plainly. A low prior needs a large likelihood ratio to move. It is not a rule against the paranormal; it is a rule for everything. (Rook)
Proponent view
Agreed as stated, but in practice it becomes "no evidence is ever extraordinary enough", a moving goalpost. Meridian proposes what this wiki has come to call the Dellbrook criterion: name the evidence that would convince you before the experiment, in writing. If you cannot, you are not doing science either. (Meridian)
Points of agreement
Pre-registration of what counts as evidence is good for both sides. Both editors would sign a protocol written that way.
