AD REM

In the Latin phrase ad rem, rem is the accusative of the noun res, which can mean ‘object, being’ or ‘legal dispute’. (Gaffiot, Res)
Accordingly, the argument ad rem can be defined in two ways.

Ad rem₁. In the first sense of res, « reality », the argument ad rem is an argument that focuses on « the reality of things ». It is probably in this sense that Whately equates the argument ad rem with Locke’s argument ad judicium.
From an essentialist perspective, this ad rem argument can also be understood as an argument about the being of things.

Ad rem₂. On the other hand, res can refer to « a judicial case, a dispute ». For example, res clearly refers to a debate in the expressions nihil ad rem ‘that is not the question’ and quid ad rem? ‘what does it matter’.
In this sense, the ad rem argument is an argument based on a fact, res, that is, relevant to a cause [causa], see Matter.

On the articulation ad rem – ad judicium – to the matter – to the letter (ad litteram), see Ad judicium.