From G.H.Moore’s Zermelo’s Axiom of Choice :
In 1890 Schröder had already introduced a notion of consistent and inconsistent classes in his Algebra der Logik, well before the modern discovery of paradoxes in set theory and logic, and had utilized such inconsistent classes under certain conditions.
1890 is seven years before Cantor’s first published treatment of inconsistent classes in the second installment of Beiträge.
Since Schröder is working with and extending the methods of algebraic logic developed by Boole, I am guessing that these inconsistent classes are collections such as “the collection of all thoughts”, or somesuch.
There is an original German language PDF of Schröder’s Algebra of Logik online at archive.org, however a search inside this PDF for inkonsistent does not produce any matches.
Q: What were Schröder’s inconsistent classes and how did he demonstrate their inconsistency?