"The Inhumanities" is Sheldon Cooper's dismissive catch-all term for every higher academic discipline which is not hard science (Physics) or a "soft science" (Geology, Zoology, Psychology). Sociology is a particularly loathed pseudo-discipline. Caltech has a Humanities faculty.
Amy uses this argument in The_Benefactor_Factor to persuade him to attend a University fund-raiser, on the grounds that if he doesn't, the cash wil only go to the sociology department.
"Oh, the Inhumanity.."