thirdness

from The Century Dictionary.

• noun The character of being third; the third position in an ordinal series considered as a character of the object occupying it.
• noun 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.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun The quality of being or coming third.