Hume said

"That no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish"

Sagan said

"extraordinary claims require extraordinary evidence"

Is this functionally equivalent to saying that the only way to show that a claim is extraordinary is to have extraordinary evidence match up to it? If the testimony is of such a kind that its falsehood is more miraculous, that would seem to imply that the evidence is extraordinary enough to match, if not supercede, the extraordinariness of the claim

  • 1
    Hume's criterion seems reasonable at first sight. But it isn't at all clear what makes one miracle more of a miracle than another. For example, is Jesus' feeding of the five thousand more or less miraculous that his turning of the water into wine? Nor do I understand what would make evidence for a miracle more extraordinary than the miracle itself. Is the survival of the Gospels more extraordinary or less extraordinary than the Resurrection? The question is meaningless to me. I suggest this needs more articulation.
    – Ludwig V
    Commented May 1, 2023 at 14:21
  • 1
    Why would a book surviving and people being fed be more extraordinary than a person reviving from the dead of water turning into wine?
    – user62907
    Commented May 1, 2023 at 17:50
  • See The Sagan Standard: "signifies that the more unlikely a certain claim is, given existing evidence on the subject, the greater the standard of proof that is expected of it." And yes, the two statements are very similar: both reflect a "naturalistic" view supporting the rejection of belief about miracles. Commented May 2, 2023 at 8:19
  • There is no need whatsoever to reject miracles. Just explain them, in terms of non-miraculous things, I guess?
    – Scott Rowe
    Commented May 3, 2023 at 10:45

3 Answers 3


The two statements overlap. The difference is that Hume's is explicitly about improbable claims, whereas Sagan's extraordinary could mean more or other than improbable.

Hume's point can be stated in a plainer way. If you have evidence A that logically leads to a conclusion B, then either B is true or A is false. Given that, if B seems very unlikely then you might believe it only if you thought the alternative- A being false- was even more unlikely.

If you equate 'extraordinary' with ' highly improbable or highly probable' then Sagan is saying much the same thing as Hume. However, Sagan could also be using extraordinary to mean uncommon or of special importance, rather than improbable. For example, suppose I leave my gloves on the train. I might go to the lost property office and be given my gloves (assuming they were handed in) purely on the basis that I could describe them. On the other hand, had a huge amount of cash been left on a train, and I turned up to claim it, the lost property people would undoubtedly take more care over the transaction on the grounds that there was more at stake.


No they aren't. Sagan is basically saying "the more outrageous your claim the more you'd need to back it up". It's a version of the "burden of proof" which is largely about sportsmanship in debates. Like you're not de facto wrong if you make hasty remarks with outrageous implications and let the other person proof or disproof them, it's just that time is a valuable resource and you want them to believe you so it's kinda wasting their time to your benefit, which is not necessarily a nice thing to do. So the unwritten rule is that it's your job to defend your conclusion and the other person's job to poke wholes in them.

While Hume's statement sounds like a version of "Reductio ad absurdum" where you proof something by showing that it's negation is impossible. Though not sure where this is applicable outside of abstract logic because usually there is more than one option to reject the testimony. Like say even if you have no doubt in the witness telling what they whole-heartedly believe to be the truth, what they say might still be "wrong" in the sense of them having already drawing a false conclusions.

For example let's say they report of having seen a specter, a white creature approached them in unnatural motion. Might actually be a truthful observation but could also be explained by someone with a bedsheet dropped upon them who is trying to get it off.

So the falsehood of the testimony doesn't need to be more miraculous than the miracle itself.

  • Yes, "don't waste everyone's time on rubbish" should be an accepted ground rule. "On pain of reversal" is a very old saying.
    – Scott Rowe
    Commented May 3, 2023 at 10:49

Is Hume’s famous quote on miracles equivalent to Sagan’s extraordinary claim principle?

I don’t know if this sort of answer is allowed or not, but here goes: I don’t understand what Hume is trying to say.

Here is Hume’s quote (On the Irrationality of Believing in Miracles, Sec. X, Part 1, No. 91):

no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish.

Plugging in one of Jesus’s more familiar miracles, this is what you get:

no testimony is sufficient to establish that Jesus walked on water, unless the testimony be of such a kind, that the claim that he did not walk on water would be more miraculous, than the claim that he did.

This arrangement of ideas makes no sense to me. If I have submitted a question masquerading as an answer, so be it, but I am willing to take a crack at the original question once this quote is adequately explained.

Addition after comment. Many thanks to thinkingman for the explanation. I now interpret Hume to mean: (1) a person should not believe a claim to a miracle unless it is impossible for the evidence supporting the claim to be wrong or (2) a person should not believe a claim of a miracle unless it is less likely for the evidence in support of the claim to be wrong than it is for the claim to be correct.

With that in mind, here is what I can offer: Sagan is stating generally what must support an extraordinary claim; "extraordinary" includes not only miracles, but perpetual motion machines, claims of a flat earth, astrology, and so forth.

Hume is quantifying the claimant’s burden specifically for miracles. The claimant has who says they know of somebody who walked on water had better be ready to show that it is impossible for their evidence to be wrong.

So I guess I come down fairly close to Marco Ocram on this question.

The law has a similar process. In general, in criminal cases, the prosecution must prove its case "beyond a reasonable doubt." That is analogous to Sagan’s generalized description. However, the instructions to the jury will quantify that burden by saying something like, "a reasonable doubt is that level of doubt that you apply to the weightier decisions of life." That is the analog to the test that Hume would apply.

  • I think he is trying to say that it is only rational to think that Jesus walked on water if the falsehood of the testimony is even more unlikely or unusual than Jesus walking on water. Personally, I just think testimony by its very nature can never be more unusual than an event like Jesus walking on water, even if the entire world claimed to have seen him (although this gets debatable). If there was some sort of widely distributed video evidence though, perhaps that evidence being false would be even less likely than Jesus not walking on water. Hence, one would reasonably believe he did walk.
    – user62907
    Commented May 5, 2023 at 2:54
  • @thinkingman. Thanks again. Commented May 7, 2023 at 3:39

You must log in to answer this question.