Its use in Chapter 6 of 'Alice Through the Looking-Glass' - 'When _I_
use a word, it means just what I choose it to mean--neither more nor
less.' - is well known.
But, for all the nonsense that surrounds it, the phrase seems there to
be taken to mean something mundane. What is that meaning?
In ATLG, Humpty-Dumpty's 'argument' is that, since there are [leap
years aside!] 364 times more days on which one may receive an
'unbirthday present' than those offering the possibility of a
'birthday present', 'unbirthday presents' are much the better thing
altogether.
In other words that it 'stands to reason' that they're better. Cannot
rationally be disputed. A level of certainty. translated into legal
terms, that no properly instructed jury could find otherwise. Or (to
use a phrase now (I believe) enshrined in common law jurisdictions
outside the US), to decide otherwise would be 'Wednesbury
unreasonable' (applying the 'no properly instructed jury' idea to the
acts of public authorities). (Or, in terms of the bell curve, the
contrary argument is jammed right into one of those long asymptotic
tails.)
Alternatively, it's an argument that denies a premise of the
proponent's earlier reasoning; for instance, where A and B are arguing
about the merits of a particular TV show in the greatest of detail;
and, when B comes up with a load of inconsistencies in A's argument, A
comes back with, "It's only a TV show, for Christ's sake!" (If it's
not that - and it doesn't really fit - there ought to be a name for
that sort of argument - other than expletives au choix!)
Of course, 'nice knock-down argument' may be a literary quotation or
allusion 'patent to the mob' - in which case, I'd be happy to accept
humiliation as the price of elucidation.