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comment by Dagon · 2024-09-20T17:00:19.848Z · LW(p) · GW(p)
I think this is mixing up colloquial "know nothing" and literal "know nothing". It's impossible to identify a thing about which one knows nothing, as that identification is something about the thing. It can be wrong, and it can be very imprecise, but it's not nothing.
50/50 are the odds of A when we know nothing about A.
No. 50/50 is a reasonable universal prior, but that's both very theoretical and deeply unclear how to categorize quantum waveforms into things over which a probability is even applicable. In most real cases, 50/50 are the odds to start with when all you know is that it's common enough to come to your attention, and that it "feels" balanced whether or not it'll happen.
In other words, "undefined and inapplicable" is the probability for things you know nothing about. Almost all things you can apply probability to, you know SOMETHING about.
You add another layer of mixing literal and figurative "don't know anything" to the term "singularity". Also, don't forget to multiply by the probability that a singularity-on-relevant-factors might not have happened for the thing you're predicting.
comment by gb (ghb) · 2024-09-20T11:04:39.639Z · LW(p) · GW(p)
We can only make that inference about conjunctions if we know that the statements are independent. Since (by assumption) we don’t know anything about said world, we don’t know that either, so the conclusion does not follow.
Replies from: cubefox, weibac↑ comment by cubefox · 2024-09-20T16:40:43.773Z · LW(p) · GW(p)
If we know nothing about them, the statements could equally be true or false, and positively or negatively dependent. The same argument which makes us assume 50% probability to individual statements would also make us assume independence between statements. The possibilities cancel out, so to speak.
Replies from: ghb↑ comment by gb (ghb) · 2024-09-20T17:57:45.323Z · LW(p) · GW(p)
Though more subtle, I feel that the 50% prior for “individual statements” is also wrong, actually; it’s not even clear a priori which statements are “individual” – just figuring that out seems to require a quite refined model about the world.
Replies from: cubefox↑ comment by cubefox · 2024-09-20T18:38:58.811Z · LW(p) · GW(p)
Ludwig Wittgenstein tried to solve this problem in an a priori fashion with a theory of "logical atomism". So without a refined model of the world. In the Tractatus he postulated that there must be "atomic" propositions. For example, the proposition that Bob is a bachelor is clearly not atomic (but complex) because it can be decomposed into the proposition that Bob is a man and that Bob is unmarried. And those are arguably themselves sort of complex statements, since the concept of a man or of marriage themselves allow for definitions from simpler terms. But at some point, we hit undefinable, primitive terms, presumably those which refer directly to particular sense data or the like. Wittgenstein then argued that these atomic propositions have to be regarded as being independent and having probability 1/2.
Or more precisely, he came up with the concept of truth tables, and counted the fraction of the rows in which the conditions of the truth tables are satisfied. Each row he assumed to be a priori equally likely when only atomic propositions are involved. So for atomic propositions P and Q, the complex proposition "P and Q" has probability 1/4 (only one out of four rows makes this proposition true, namely "true and true"), and the complex proposition "P or Q" has probability 3/4 (three out of four rows in the truth table make a disjunction true: all except "false or false").
This turns out to be equivalent to assuming that all atomic propositions have a) probability 1/2 and are b) independent of each other.
However, logical atomism was later broadly abandoned for various reasons. One is that it is hard to define what an atomic proposition is. For example, I can't assume that "this particular spot in my visual field is blue" is atomic. Because it is incompatible with the statement "this particular spot in my visual field is yellow". The same spot can't be both blue and yellow, even though that wouldn't be a logical contradiction. The two statements are therefore not independent, so they can't be atomic. But it is hard to think of anything more primitive than qualia predicates like colors.
↑ comment by Milan W (weibac) · 2024-09-20T13:16:52.268Z · LW(p) · GW(p)
Then I guess the OP's point could be amended to be "in worlds where we know nothing at all, long conjunctions of mutually-independent statements are unlikely to be true". Not a particularly novel point, but a good reminder of why things like Occam's razor work.
Still, P(A and B) ≤ P(A) regardless of the relationship between A and B, so a fuzzier version of OP's point stands regardless of dependence relations between statements.
↑ comment by gb (ghb) · 2024-09-20T15:09:01.521Z · LW(p) · GW(p)
Sure, there are certainly true things that can be said about a world in spite of one’s state of ignorance. But what I read the OP to imply is that certain things can supposedly be said about a world precisely because of that state of ignorance, and that’s what I was arguing against.
Replies from: weibac↑ comment by Milan W (weibac) · 2024-09-20T16:18:36.438Z · LW(p) · GW(p)
Right. Pure ignorance is not evidence.