created by javaxcore on 11/03/2021 at 07:42 UTC
7 upvotes, 4 top-level comments (showing 4)
Comment by AutoModerator at 11/03/2021 at 07:42 UTC
1 upvotes, 0 direct replies
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Comment by as-well at 11/03/2021 at 10:11 UTC*
8 upvotes, 2 direct replies
That is not to say that the saying is wrong, but rather to say that it isn't discussed in this way in philosophy. Reconstructing "extraordinary" as "implausible" is a good way to explain it with epistemological terms, but I'm not quite sure Sagan and the bunch really just mean that. This article[1] reconstructs "extraordinary" as
1: https://link.springer.com/article/10.1007/s11406-016-9779-7
Hume precisely defined an extraordinary claim as one that is directly contradicted by a massive amount of existing evidence. For a claim to qualify as extraordinary there must exist overwhelming empirical data of the exact antithesis. Extraordinary evidence is not a separate category or type of evidence--it is an extraordinarily large number of observations. Claims that are merely novel or those which violate human consensus are not properly characterized as extraordinary.
Which is a different reconstruction, and it's quite easy to see, I think, how that differs from "extraordinary = implausible" quite a bit in practice.
So, when you ask your question, you probably need to specify what you mean by extraordinary.
Comment by DarkSkyKnight at 11/03/2021 at 10:46 UTC
5 upvotes, 2 direct replies
There are many extraordinary theorems in mathematics that are quite surprising, and yet have simple proofs. I don't think your question is well-posed without further clarifying what "claim", "extraordinary", and "evidence" mean precisely.
Comment by MaceWumpus at 11/03/2021 at 08:18 UTC
10 upvotes, 2 direct replies
On a straightforward reading, yes. The more improbable a claim is, the stronger the evidence that you (should) require in order to believe.
To illustrate, imagine two contrasting claims that your friend could make. (1) that they tossed a fair coin heads 2 times in a row; (2) that they tossed a fair coin heads 100 times in a row. The former you should probably believe on say-so, unless your friend is a habitual liar or has some reason to not tell the truth in this case. The latter, by contrast, is an "extraordinary" claim in that it has a vanishingly low probability of occurring. So you shouldn't just take their say-so on it, clearly. If they have a witness, it had better be someone that you trust and believe to be neutral---and even then, you should probably suspect that *something* was going on that rendered the coin un-fair, something that the witness couldn't or didn't identify. It's simply much more probable that something of that sort has gone wrong than that your friend tossed a hundred heads in a row.
Now, that's not to say that the only feature of a claim that matters is how extraordinary it is. You might want a lot of evidence for a very everyday occurrence because you really really care about the outcome, and you might reasonably demand only weak evidence for some extraordinary claim because it doesn't matter much to you. But all other things being equal, yes, the amount / quality of evidence that you (should) require to believe an claim is proportional to how implausible that claim is.