Tertium quid

In the Christological debates of the fourth century, it was used to refer to the followers of Apollinaris who spoke of Christ as something neither human nor divine, but a mixture of the two, and therefore a "third thing".

In American political history, the Tertium Quids, or Quids, were moderate members of Jefferson's Democratic-Republican Party. The word implies that their political position was apt to embrace true republicanism and the comparable conservatism of the Federalist Party, particularly on foreign policy. The Quids arose in 1804 during Thomas Jefferson's first term in office. They were led by Virginia's John Randolph of Roanoke. They stood by the party's original stance for strict construction of the Constitution and opposed Jefferson's pragmatic approach to governing.

In sociology, it describes a category of degraded moral consideration.

In Souls of Black Folk, W.E.B. Du Bois used the term "tertium quid" to refer to the identity of African Americans in a racist society, where non-white people are viewed as a devalued category between man and animal.

"The second thought streaming from the death (slave)-ship and the curving river is the thought of the older South, the sincere and passionate belief that somewhere between men and cattle, God created a tertium quid, and called it a Negro—a clownish, simple creature, at times even lovable within its limitations, but straitly foreordained to walk within the Veil."[5]

The term is used in the Supreme Court of the United States case Wal-Mart Stores, Inc. v. Samara Brothers, Inc. 529 U.S. 205 (2000). In this Lanham Act case, the Court, when discussing product packaging vs. product design, referred to the type of trade dress in its earlier Two Pesos, Inc. v. Taco Cabana, Inc. decision as "some tertium quid" that may be a mutation of product packaging and product design—a "third thing."

In literature, it can describe an adulterer, often in a cuckolded relationship.

Kipling employs the term in his story "At the Pit’s Mouth" for an adulterer: "Once upon a time there was a Man and his Wife and a Tertium Quid."

Talbot Mundy, a contemporary of Kipling, makes use of the term in King of the Khyber Rifles to describe a cuckold, "And what kind of man must Rewa Gunga be who could lightly let go all the prejudices of the East and submit to what only the West has endured hitherto with any complacency—a "tertium quid"? "

Also, Robert Browning uses the term "Tertium Quid" in his long narrative poem The Ring and the Book for a section presenting third, more balanced viewpoint on the 1698 Roman murder case his poem discusses, different from the opinions expressed in the sections "Half Rome" and "The Other Half Rome", which strongly sympathize with, or equally deplore, the accused.