1) Fallaciousness 2) Impotence 3) Invalidness 4) Nullity 1) Illogic 2) Illogicality 3) Illogicalness 4) Invalidness 5) Lack of validity 
• (n.) Want of health; infirmity. • (n.) Want of validity or cogency; want of legal force or efficacy; invalidness; as, the invalidity of an agreement or of a will.
In`va·lid'i·ty noun [ Confer French invalidité , Late Latin invaliditas want of health.] 1. Want of validity or cogency; want of legal force or efficacy; invalidness; as, the invalidity of an agreement or of a will. 2. Want of health; infirmity. [ Obsolete] ...
[n] - illogicality as a consequence of having a conclusion that does not follow from the premisses
invalidness noun illogicality as a consequence of having a conclusion that does not follow from the premisses
lack of validity.