If you understand the core claims being made, then unless you believe that whether or not something is "communicated well" has no relationship whatsoever with the underlying truth-values of the core claims, if it was communicated well, it should have updated you towards belief in the core claims by some non-zero amount.
All of the vice-versas are straightforwardly true as well.
let A = the statement "A" and p(A) be the probability that A is true.
let B = A is "communicated well" and p(B) the probability that A is communicated well.
p(A | B) is the probability that A is true given that it has been "communicated well" (whatever that means to us).
We can assume, though, that we have "A" and therefore know what A means and what it means for it to be either true or false.
What it means exactly for A to be "communicated well" is somewhat nebulous, and entirely up to us to decide. But note that all we really need to know is that ~B means A was communicated badly, and we're only dealing with a set of 2-by-2 binary conditionals here. So it's safe for now to say that B = ~~B = "A was not communicated badly." We don't need to know exactly what "well" means, as long as we think it ought to relate to A in some way.
p(A | B) = claim A is true given it is communicated wellp(A | ~B) = claim A is true given it is not communicated well. If (approximately) = p(A), then p(A) = p(A|B) = p(A|~B) (see below).p(B | A) = claim A is communicated well given it is truep(B | ~A) claim A is communicated well given it is not true
if p(A) = p(A|~B):p(A) = p(A|B)p(B) + p(A)p(~B)p(A)(1 - p(~B)) = p(A|B)p(B)p(A) = p(A|B)
If being communicated badly has no bearing on whether A is true, then being communicated well has no bearing on it either.
P(B | A) = p(A | B)P(B) / p(A | B)p(B) + p(A | ~B)p(~B) = p(A)p(B) / p(A)p(B) + p(A)p(~B) = p(A)p(B) / p(A) = p(B).
Likewise being true would have no bearing on whether it would be communicated well or vice-versa.
To conclude, although it is "up to you" whether B or ~B or how much it was in either direction, this does imply that how something sounds to you should have an immediate effect on your belief in what is being claimed, as long as you agree that this correlation in general is non-zero.
In my opinion, no relationship is kind of difficult to justify, an inverse relationship is even harder to justify, but a positive relationship is possible to justify (though to what degree requires more analysis).
Also, this means that statements of the form "I thought X was argued for poorly, but I'm not disagreeing with X nor do I think X is necessarily false" is somewhat a priori unlikely. If you thought X was argued for poorly, it should have moved you at least a tiny bit away from X.
If you deceptively argue against A on purpose, then if A is true, your argument may still come out "bad." If A isn't true, it may still come out good, even if you didn't believe in A.
If you state "A" and then intentionally write gibberish afterwards as an "argument", that's still in the deceptive case. Thus "communicated well" takes into account whether or not this deception is given away.
If A is true, then sloppy and half-assed arguments for A are still technically valid and thus will support A. At worst this can only bring you down to "no relationship" but not in the inverse direction.
Here is an argument why you are completely correct:
Idsfhdfuhnf sfdhg dfkd skhsfuyd sd sfssu sd suhfs s s sdklh soia8uf fmdfo.
Was that clear? Update your beliefs in your proposition accordingly.
The fact that you're being disingenuous is completely clear so that actually works the opposite way you intended.
What was the way I intended?
To be deceptive - this is why you would ask me what your intentions are as opposed to just reveal them.
Your intent was ostensibly to show that you could argue for something badly on purpose and my rules would dictate that I update away from my own thesis.
I added an addendum for that, by the way.
Believing things because someone told them to you "well" makes you a sucker for con men.
Not sure how convinced I am by your statement. Perhaps you can add to it a bit more?
What "the math" appears to say is that if it's bad to believe things because someone told it to me "well" then there would have to be some other completely different set of criteria, that has nothing to do with what I think of it, for performing the updates.
Don't you think that would introduce some fairly hefty problems?
You've never said what you mean by "told well", and indeed have declined to say from the outset, saying only that it is "entirely up to us to decide" what it means. If "told well" means "making sound arguments from verifiable evidence", well, of course one would generally update towards the thing told. If it just means "glibly told as by a used car salesman with ChatGPT whispering in his ear", then no.
"Up to you" means you can select better criteria if you think that would be better.
I think I need a bit more formal definition of "communicated well" to understand the claim here. A simple example is "I have purchased a lottery ticket this week". it is (I hope) pretty unambiguous and hard to misinterpret, thus "clearly communicated". However, you (should) have a pretty high prior that responses to this will contain more deceptive statements than normal conversation.
I DO think you're often correct for complex, highly-entangled propositions - it's easier to state and explain the truth than to make up consistent falsehoods. But that's a generalization, not a mathematical constant. It depends on the proposition and the communicator whether your core condition holds.
do I 'believe that whether or not something is "communicated well" has no relationship whatsoever with the underlying truth-values of the core claims'? Sometimes, with varying strength of that belief.
If I'm not mistaken, if A = "Dagon has bought a lottery ticket this week" and B = Dagon states "A", then I still think p(A | B) > p(A), even if it's possible you're lying. I think the only way it would be less than the base rate p(A) is if, for some reason, I thought you would only say that if it was definitely not the case.
I think, in this context, you should give a lot more weight to the "possible" of my lies. If someone else had made a similar statement in rebuttal of your thesis, I'd model p(A|B) < p(A), In other contexts, B could even be uncorrelated to truth, due to ignorance or misunderstanding.
My primary objection isn't that this is always or even mostly wrong, just that it's a very simplistic model that's incorrect often enough, for reasons that are very instance-specific, that it's a poor heuristic.
Remember that what we decide "communicated well" to mean is up to us. So I could possibly increase my standard for that when you tell me "I bought a lottery ticket today" for example. I could consider this not communicated well if you are unable to show me proof (such as the ticket itself and a receipt). Likewise, lies and deceptions are usually things that buckle when placed under a high enough burden of proof. If you are unable to procure proof for me, I can consider that "communicated badly" and thus update in the other (correct) direction.
"Communicated badly" is different from "communicated neither well nor badly." The latter might refer to when A is the proposition in question and one simply states "A" or when no proof is given at all. The former might refer to when the opposite is actually communicated - either because a contradiction is shown or because a rebuttal is made but is self-refuting, which strengthens the thesis it intended to shoot down.
Consider the situation where A is true, but you actually believe strongly that A is false. Therefore, because A is true, it is possible that you witness proofs for A that seem to you to be "communicated well." But if you're sure that A is false, you might be led to believe that my thesis, the one I've been arguing for here, is in fact false.
I consider that to be an argument in favor of the thesis.
Thank you for not needlessly using LaTeX.
Does this prove too much? I think you have proved that reading the same argument multiple times should update you each time, which seems unlikely
If you read it a second time and it makes more sense, then yes.
A short, simple thought experiment from "Thou Shalt Not Speak of Art":
From my perspective: I chose the top one over the bottom one, because I consider it better. You, apparently, chose the one I consider worse.
Me ◯⟶◯ Good
You ◯⟶◯ Worse
From your perspective: Identical, but our positions are flipped. You becomes Me, and Me becomes You.
However, after we Ogdoad:
You ◯⟶◯ Good
It becomes clear that the situation is much more promising than we originally thought. We both, apparently, get what we wanted.
Our Ogdoad merely resulted in us both being capable of seeing the situation from the other’s perspective. I see that you got to have your Good, you see that I get to have my Good. Boring and simple, right?
It should be. Let’s make sure that any other way can only mess things up. Our intuitions say that we ought to simply allow ourselves to enjoy our choices and not to interfere with each other. Are our intuitions correct?
You ◯⟶◯ Better
This is the perspective if I choose to see your perspective as superior than mine. If I consider yours authoritative, then I have made your choice out to be “better” than mine. Likewise, if you choose to do the same for me, you’ll see mine as better. The only situations that could result from this are:
All three easily seem much worse than if we simply decided to stay with our original choices. Number 1 and 2 result in one of us having an inferior choice, and number 3 results in both of us having our inferior choice.
Apparently, neither of us have anything to gain from trying to see one another’s preferences as “superior.”
"Speaking of art" is a phrase which refers not just to discussing one's preferences openly, but specifically doing so while assuming an air of superiority and judgementality. I.e., to be condescending to others about what they want or do not want.