In the Latin phrase ad rem, rem is the accusative of the noun res, which can be taken to mean « object, being » or « legal case, dispute ». (Gaffiot, Res)

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 assimilates the argument ad rem to Locke’s argument ad judicium.

Ad rem2. On the other hand, res can refer to « the judicial case, the dispute ».
[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 relies on a fact [res] that is relevant to a cause [causa]. S. Matter

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