dybmh
ויהי מבדיל בין מים למים
The argument in this thread for V:
Not V -> Not A
A
Therefore V (Modus tollens)
If I understand and recall correctly, and I'd need to double check.
If (Not V --> Not A) then ( A --> V ).
Or.
(Not V --> Not A) --> ( A --> V ).
If so, then (Not V --> Not A) is irrelevant to the truth value of the propostion. It is only false if ( A --> V ) is false. In all other cases it is assumed to be true per "implication".
Considering ( A --> V ), the same rules apply. If A is true or false is irrelevant. ( A --> V ) is only false if V is false, "A" doesn't matter.
So, it's not so much circular, but nothing is proven about V from the proposition Not V -> Not A. And this makes sense. A negative implication doesn't produce a positive assertion. All you've done is Not V --> V. This says nothing about V.