At the recommendation of Jacobian, I've been reading Too Like the Lightening. It is a thoughtful book which has several points of interest to rationalists (imho), but there is one concept which I think is nice enough to pluck out and discuss in itself, rather than being satisfied to suggest that people read the book. I also want to suggest a different name than the one from the book.

If you think discussion of a logical concept which is mentioned in a book is a spoiler, maybe stop here.

At one point, there is a discussion in which one character is explaining how much some other characters must already know. The term "anti-proof" is used to refer to failure to falsify a hypothesis. Having a short term for this concept seems like a really good idea. We have the phrase "absence of evidence is evidence of absence", but we don't have a word for the positive case, where absence of counter-evidence speaks in favor of a hypothesis.

Unfortunately, "anti-proof" sounds more like the former than the latter, even though it is being used for the latter in the book. A more appropriate term would be "co-proof", since it is the absence of a proof of the negation.

For example, an alibi would refute someone's involvement in a crime. The absence of an alibi, then, is a co-proof of their involvement: it does not prove involvement by any means, but it must constitute some supporting evidence, by conservation of expected evidence.

By "proof of H" I mean an observation which would make the probability of H very close to 1. (How close is "very close" depends on standards of proof in a context, with mathematics demanding the highest standards.) By "refutation" I mean a proof of the negation. So, a co-proof is an observation whose negation would have taken the probability of H to very near zero:

E is a co-proof of H :=

Why are co-proofs of interest? Popperian epistemology is the claim that scientific hypotheses can be supported only by co-proofs; we attempt to refute things, and if something has survived enough refutation attempts, it is considered to be a strong hypothesis. Bayesians are not Popperians, but Popper was still mostly right about this; so, having a short name for it seems useful.

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