I understand exactly what you're saying, but the qualification is divergent from your initial statement, from which this discussion arose, and to which you returned in the second paragraph cited above:
"we shouldn't really care how someone formed their beliefs when evaluating the veracity of a claim"
A condition of evaluating the veracity of an utterance is to register the utterance as intelligible, for which the aforementioned considerations to context are necessary, i.e. 'how someone formed their beliefs'.
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I feel like this is circular: you state your claim, I state my rebuttal, you concede in qualification, and then you return to your original claim.
I need to know how you came to that conclusion, which is slightly ambiguous here, in the sense that I can't understand the claim independently of the linguistic practice in terms of which your intended meaning is given.
In the case of basic and well-worn facts about the natural world, I think I understand their utterance - although I could be unaware of a particular convention or idiom - because I am already very aware of the linguistic practices which endow them which intersubjective force (if I was a peasant in the Holy Roman Empire, I would doubtlessly have no idea what you were attempting to convey or do).
Alright, since you could not verify the Earth being round without knowing my belief structure...
2+2 = 4
You don't know my belief structure. Is it true?
I'm not asking you if you know that off the top of your head, I'm asking if you could go out and check to see if it's actually true!
That's what I mean by evaluating a claim - can you verify it? I'm sorry, but it's asinine to say that you cannot verify it because you don't know how I came to the conclusion. You seem to be arguing something about sharing my language as maintaining your point. I'm past that. If you understand the claim, you can test it.