I think what we have here is a definitional problem. What Obvious Child seems to mean by 'a convincing argument' is, "and argument that would convince a reasonable person". What LucyTheApe seems to mean is " An argument that must convince everybody".
Its like the difference between scientific fact and the common conception of a fact as a form of absolute incontrovertible truth.
It seems doubtful to me that there are any 'convincing' arguments for anything of the standard that LucyTheApe desires.
TTFN,
WK