The principle of Laplace

Marcello Truzzi's "an extraordinary claim requires extraordinary proof" is generally credited to Pierre-Simon Laplace (via Carl Sagan) in the form of "the weight of evidence for an extraordinary claim must be proportioned to its strangeness". I did a little Google searching in an attempt to source this and (finally) came up with William McDougall's Outline of Abnormal Psychology (1926), which has (on page 508):

"We are so far from knowledge of all natural agencies and of their diverse modes of action, that it would not be philosophic to deny any phenomena simply because they are inexplicable in the present state of our knowledge. But we ought to examine them with an attention the more painstaking, the more difficult it may seem to accept them as real."

McDougall says the quote was made "by the great exponent of the mechanical view of the universe, Laplace" and that a Théodore Flournoy would call it "the principle of Laplace" and state it briefly as "the weight of the evidence should be proportional to the strangeness of the alleged facts". Ironically then, it would appear that the quote generally attributed to Laplace is actually a quote of Flournoy, a one-time believer of telekinesis, telepathy, and clairvoyance!