Definition of "illogic"

I think this is a very illogic way of reasoning.

1896, JAMA: The Journal of the American Medical Association

Because everything started precisely by the influence of that country that practically became our enemy; and it's very illogic that somebody would try to escape by getting into the mouth of the wolf.

2012, Marko Dorantes, Somewhere Somehow, page 131

The problem with using dreams as story material is the very illogic nature of them, the juxtaposition of images and actions without regard for the laws of physics, psychology, or anything else.

2015, Deborah J. Ross, Ink Dance: Essays on The Writing Life

And right often have I, the modern, been perturbed and vexed by the foolishness, illogic, obtuseness, and general all-round stupendous stupidity of myself, the primitive.

1907, Jack London, Before Adam

Mr Qaddafi, with a characteristic mix of bluntness and illogic, declared that his ideology was ‘theoretically’ a genuine democracy, but in reality, ‘the strong always rule.’

2011 February 25, “Endgame in Tripoli”, in The Economist