My son had an interesting critique of Brisker lomdus as it relates to the idea of something being categorized as having a certain "shem". As explained by R' Moshe Lichtenstein in his essay "What Hath Brisk Wrought":
In one common construct, an inquiry into the issue in question attempts to determine whether the law in a given case is linked to laws in other halakhic areas or whether it reflects the operating of an independent concept, often considering the inquiry to be satisfactorily concluded by proclaiming that the legal phenomenon under discussion reflects a “hallot shem (legal status or category) of X.” The categorization is taken as self-explanatory, and the question of why there should be such a category is dismissed without further ado.I think an example would illustrate the point better than a definition. The Rambam paskens (Hil Tshuvah 1:1) that viduy, confession, is an integral part of the tshuvah process without which the mitzvah is incomplete. Yet, the Rambam paskens (Ishus 5:5) that if a man is mekadesh a woman on the condition that he is not a rasha we assume the kiddushin is valid because perhaps in his heart the mekadesh did tshuvah (Kiddushin 49). How can tshuvah be done in the heart if verbal confession is an integral part of the process? R' Soloveitchik answered (Igros haGRI"D) that tshuvah sans viduy removes the person from having a "shem rasha". However, there is an additonal level to the mitzvah of tshuvah whereby tshuvah itself serves as a kapparah. This additional kiyum is incomplete sans viduy.
My son argued that the whole idea of a "shem" anything makes no sense. Either something is X or it is not -- it makes no sense for something not to be X but to have a "shem X".
I think his critique is valid as a substantive and not just a semantic point. I think he is correct in understanding that the whole reason Briskers use the terminology of "shem" is precisely to split hairs in the way he finds discomforting -- Briskers do think that something can not be X but be labelled with a "shem X" nonetheless.
Rather than a shortcoming, this ultimately proves to be the genius of Brisk -- through categorization items that appear unrelated can be shown to have a common underlying conceptual root and items that appear similar can be finely distinguished. Retuning to the example I used, the creation of a "shem rasha" shifts the discussion of the status of the sinner engaged in tshuvah from a moral question of whether he/she is good or evil (tzadik or rasha) to a legal question of whether the individual falls into the category of rasha. A person may indeed still be shy of moral absolution yet no longer fall into the legal class reserved for the rasha.
I thought the critique showed good insight for a H.S. freshman and took some thinking about to formulate a clear answer to (which I may not have succeeded in doing). Something to think about.