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komponisto comments on Take heed, for it is a trap - Less Wrong
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Where did you get the idea that "statement" in Eliezer's comment is to be understood in your idiosyncratic sense of "utterances that may or may not be 'propositions'"? Not only do I dispute this, I explicitly did so earlier when I wrote (emphasis added):
Indeed, it is manifestly clear from this sentence in his comment:
that Eliezer means by "statement" what you have insisted on calling a "proposition": something with truth-conditions, i.e. which is capable of assuming a truth-value. I, in turn, simply followed this usage in my reply. I have never had the slightest interest in entering a sub-discussion about whether this is a good choice of terminology. Furthermore, I deny the following:
and, indeed, regard the falsity of that claim as a basic background assumption upon which my entire discussion was premised.
Perhaps it would make things clearer if the linguistic terminology ("statement", "proposition", etc) were abandoned altogether (being really inappropriate to begin with), in favor of the term "hypothesis". I can then state my position in (hopefully) unambiguous terms: all hypotheses are either true or false (otherwise they are not hypotheses), hypotheses are the only entities to which probabilities may be assigned, and a Bayesian with literally zero information about whether a hypothesis is true or false must assign it a probability of 50% -- the last point being an abstract technicality that seldom if ever needs to be mentioned explicitly, lest it cause confusion of the sort we have been seeing here (so that Bayesian Bob indeed made a mistake by saying it, although I am impressed with Zed for having him say it).
Make sense now?
You can state it better like this: "A Bayesian with literally zero information about the hypothesis."
"Zero information about whether a hypothesis is true or false" implies that we know the hypothesis, and we just don't know whether it's a member in the set of true propositions.
"Zero information about the hypothesis" indicates what you really seem to want to say -- that we don't know anything about this hypothesis; not its content, not its length, not even who made the hypothesis, or how it came to our attention.
I don't see how this can make sense in one sense. If we don't know exactly how it came to our attention, we know that it didn't come to our attention in a way that stuck with us, so that is some information we have about how it came to our attention - we know some ways that it didn't come to our attention.
You're thinking of human minds. But perhaps we're talking about a computer that knows it's trying to determine the truth-value of a proposition, but the history of how the proposition got inputted into it got deleted from its memory; or perhaps it was designed to never holds that history in the first place.
So it knows that whoever gave it the proposition didn't have the power, desire, or competence to tell it how it got the proposition.
It knows the proposition is not from a mind that is meticulous about making sure those to whom it gives propositions know where the propositions are from.
If the computer doesn't know that it doesn't know how it learned of something, and can't know that, I'm not sure it counts as a general intelligence.