inconsequence

[L. inconsequentia: cf. F. inconséquence.]
The quality or state of being inconsequent; lack of just or logical inference or argument; inconclusiveness. Bp. Stillingfleet.

Strange, that you should not see the inconsequence of your own reasoning!

noun

Lack of importance: inconsequentiality, inconsequentialness, indifference, insignificance, insignificancy, unimportance. See concern/unconcern.

The noun has one meaning:

Meaning #1: having no important effects or influence
  Antonym: consequence (meaning #3)