The Collaborative International Dictionary
Incompossibility
Incompossible \In`com*pos"si*ble\, a. [Pref. in- not + compossible: cf. F. incompossible.] Not capable of joint existence; incompatible; inconsistent.
Ambition and faith . . . are . . . incompossible.
--Jer. Taylor.
-- In`com*pos`si*bil"i*ty, n. [Obs.]
Wiktionary
incompossibility
n. The quality of being incompossible.