In reality, ad hominem is unrelated to sarcasm or personal abuse. Argumentum
ad hominem is the logical fallacy of attempting to undermine a speaker's
argument by attacking the speaker instead of addressing the argument. The mere
presence of a personal attack does not indicate ad hominem: the attack must be
used for the purpose of undermining the argument, or otherwise the logical fallacy
isn't there.
[...]
A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be
a mammal."
B: "You evidently know nothing about logic. This does not logically follow."
B's argument is still not ad hominem. B does not imply that A's
sentence does not logically follow because A knows nothing about logic. B
is still addressing the substance of A's argument...
This is too beautiful, thorough, and precise to not post. HT to sfk on HN.
(By the way, B's argument is wrong because A's argument is not really ad hominem... but if it were, he would be right when he says it should be rejected. That's what we should do with fallacious arguments in general: reject them)
Stephen Bond writes the definitive word on ad hominem in "the ad hominem fallacy fallacy":
This is too beautiful, thorough, and precise to not post. HT to sfk on HN.