INCONSEQUENCE
illogicality, illogicalness, illogic, inconsequence
(noun) invalid or incorrect reasoning
inconsequence
(noun) having no important effects or influence
Source: WordNet® 3.1
Etymology
Noun
inconsequence (countable and uncountable, plural inconsequences)
The state or quality of being inconsequent.
Source: Wiktionary
In*con"se*quence, n. Etym: [L. inconsequentia: cf. F. inconséquence.]
Definition: The quality or state of being inconsequent; want of just or
logical inference or argument; inconclusiveness. Bp. Stillingfleet.
Strange, that you should not see the inconsequence of your own
reasoning! Bp. Hurd.
Source: Webster’s Unabridged Dictionary 1913 Edition