I'm just claiming that adding such acceptance would affect the tilt of the scale, and the tilt would be more towards authenticity than it had been before the addition. Does that help?
No, because you're simply restating the same fallacy over and over again using different words. You simply don't understand how categorical logic works, nor what it means to prove something.
Pause to consider what "authentic" means in the case of the cloth. "Authentic" means 2,000 years old. If you claim it is authentic, you must prove it's 2,000 years old. It doesn't matter what you can prove it
isn't. Proving authenticity means proving what it
is -- specifically that it is 2,000 years old.
There is another age on the table, and that's the 700-year age established by radiocarbon dating and other factors. You seem to have gotten it into your head that solely by undermining one specific age (700 years), you accumulate proof for some other specific age (2,000 years). That's simply not how proof works.
The scale analogy is suitable only when there are exactly two possible outcomes. That's the only way you can say that the question, in the language of the scale, "tilts" one way or the other when evidence is rebutted. But the two possible outcomes here are not "700 years old" and "2,000 years old." Those may be the only two outcomes you're
considering, but they aren't the only two outcomes that are possible. You've just plucked the 2,000-year age out of the air because that's the specific age you need in order for your belief in authenticity to hold. An age that is salient because of the
belief is not also immediately salient in terms of the
evidence.
In the scale analogy, you can introduce categories to cover multitudes of individual outcomes. But all the individual possible outcomes must fit into one or the other category, so that you continue to have two pans. That is, if one pan of the scale is "700 years old," then in order to fit the two-possible-outcomes limitation, the other pan has to be "
not 700 years old." That way all possible outcomes fall into one category or the other. Then
and only then can you say that undermining the 700-year age tilts any sort of scale. But the direction toward which it tilts is merely "not 700 years," not "2,000 years." There are quite a lot of dates that aren't 700 years but which also aren't 2,000 years.
If you show that the 700-year age is untenable for one reason or another, you can't immediately assert that it must be 2,000 years old. The cloth may eventually fail to be a 700-year-old forgery, but you won't have eliminated the possibility that it's, say, a 1,000-year-old forgery or a 1,500-year-old forgery.
