thirdness

Century Dictionary and Cyclopedia

1. n. The character of being third; the third position in an ordinal series considered as a character of the object occupying it.
2. n. 2. The mode of being of that which is such as it is by virtue of a triadic relation which is incapable of being defined in terms of dyadic relations.

Wiktionary

1. n. The quality of being or coming third.