In the case that no argument was made to justify a claim, just a claim made, where's the validity in rejecting it? Based on what? "No argument" is not an argument --for or against. It doesn't lend truth or falsehood to a claim, so doesn't valid or invalidate.
My sister is taller than my mother. I am taller than my sister. Therefore, I am taller than my mother. - valid argument.
Therefore I am taller than my mother. - not a valid argument
Has nothing to do with whether I have a sister or whether I am actually taller than my mother.
By taking the claim as a "conclusion" of the die roll, do you mean that the claim is believed? i.e. upheld as true? That's how I interpreted it. And isn't belief an implicit argument, that the claimant holds what is claimed up as true? Isn't that --the possiblity of it being true --what is being rejected?
Yes, yes, upheld as true or at least claimed to be upheld as true. No, the possibility of it being true is not being rejected. That would be quite irrational (in most cases).
The very act of rejecting implies that falsehood was recognized, just as the act of believing implies that truth was recognized.
Yes, and I hope for the last time, the falshood is in the argument (or lack there of). I nor anyone else have direct access to "truth". Either it is demonstrated that something is true or it is not. If it is not a claim of it being true is rejected.
What is "the conclusion" of the claim? I might have misunderstood.
It doesn't even matter. Pick any example you want - like:
My sister is taller than my mother. I am taller than my sister. Therefore, I am taller than my mother. - valid.
My sister is taller than my mother. I am taller than my sister. Therefore, I am shorter than my mother. - invalid.
You can instantly say that one of them is not valid. Yet you know absolutely nothing about whether or not I actually have a sister, if she is taller than my mother or if I'm taller than her. Absolutely nothing. No "truth value" anywhere.