The Collaborative International Dictionary of English v.0.48:
Inapplicability \In*ap`pli*ca*bil"i*ty\, n. [Cf. F. inapplicabilit['e].] The quality of being inapplicable; unfitness; inapplicableness. [1913 Webster]WordNet (r) 3.0 (2006):
inapplicability n 1: irrelevance by virtue of being inapplicable to the matter at hand [ant: applicability, pertinence, pertinency]