From: Tennessee Leeuwenburg (tennessee@tennessee.id.au)
Date: Thu Sep 01 2005 - 18:42:50 MDT
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Eliezer S. Yudkowsky wrote:
> Peter de Blanc wrote:
>
>> On Thu, 2005-09-01 at 12:05 -0600, brannen wrote:
>>
>>> It has been decades, literally, since I read Jaynes but, IIRC,
>>> the argument starts with the inferential fallacy 'absence of
>>> evidence being evidence of absence' and goes downhill from
>>> there.
>>
>>
>> Just a quick note: for a Bayesian, absence of evidence *is*
>> evidence of absence.
>
>
> I wondered if anyone would catch that. But if one is going to make
> that point, one really should do three other things:
>
> 1) Phrase it mathematically: say that P(A|~B) < P(A) iff P(A|B) >
> P(A).
>
> 2) Post a link to an explanation, for the benefit of those
> bewildered by a seeming violation of logic. E.g:
> http://yudkowsky.net/bayes/bayes.html
>
> 3) Note the qualitative fact that absence of evidence may be
> *extremely weak* evidence of absence.
>
> PS: Let's call the author "Julian Jaynes", so as not to confuse
> with the late Bayesian Master E.T. Jaynes.
>
In natural language, I think a similar point was made by Alfred Ayer,
in talking about irrelevant things. Actually, it was more about
relevant things, but you can do the necessary interpretation. A
slightly longer version of the quote is available at my blog,
melbournephilosopher.blogspot.com.
"The criterion which we use to test the genuineness of apparent
statements of fact is that criterion of verifiability. We say that a
sentence is factually significant to any given person, if, and only
if, he knows how to verify the proposition which it purports to
express ? that is, if he knows what observations would lead him, under
certain conditions, to accept the proposition as being true, or reject
it as being false. If, on the other hand, the putative proposition is
of such a character that the assumption of its truth, or falsehood, is
consistent with any assumption whatsoever concerning the nature of his
future experience, then, as far as he is concerned, it is, if not a
tautology, a mere pseudo-proposition. And with regard to questions the
procedure is the same. We inquire in every case what observations
would lead us to answer the question, one way of the other; and, if
none can be discovered, we must conclude that the sentence under
consideration does not, as far as we are concerned, express a genuine
question, however strongly its grammatical appearance may suggest that
it does."
To bring it to the conversation at hand, absense of evidence is taken
as evidence for irrelevance according to this idea. That is to say, if
you have no evidence for X, then X has no actual relevance to any
other claim. If you, in principle, cannot have evidence of X, then X
is a priori irrelevant to any factual claim.
Cheers,
- -T
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