(Argumentum) ad res / ad rem
Latin for: “(argument) on the matter”. Denotes a factual argument – in contrast to an ad hominem argument, which is directed in an unobjective manner against the person making an argument.
“Ad res” or “ad rem”
Both “res” (e.g. nominative and accusative plural), and “rem” (accusative singular) are correct Latin forms that can follow the preposition “ad”, and there are good arguments for the use of both variants in this context.
Since the form “ad res” is by far the most commonly used, it is also preferred on this site. From this, however, one cannot conclude that this form is generally preferable over “ad rem”.
Validity
The term res refers solely to the fact that an argument addresses the “matter” being discussed, and serves to distinguish it from ad hominem arguments, which target the person rather than the argument.
Even such arguments “on the matter”, however, can be fallacious or unfair. From being ad res does not follow that an argument is valid.