[The absence of reasoning.] Intuition. [False or vicious reasoning; show of reason.] Sophistry.
sophistry, paralogy, perversion, casuistry, jesuitry, equivocation, evasion; chicane, chicanery; quiddet, quiddity; mystification; special pleading; speciousness; nonsense [more]; word-fence, tongue-fence.
false reasoning, vicious reasoning; petitio principii, ignoratio elenchi; post hoc ergo propter hoc; non sequitur, ignotum per ignotius.
sophism, solecism, paralogism; quibble, quirk, elenchus, elench, fallacy, quod-libet, subterfuge, subtlety, quillet; inconsistency, antilogy; "a delusion, a mockery, and a snare" [Denman]; claptrap, mere words; "lame and impotent conclusion" [Othello].
meshes of sophistry, cobwebs of sophistry; flaw in an argument; weak point, bad case.
[Verbs] judge intuitively, judge by intuition; hazard a proposition, hazard a guess, talk at random.
reason ill, reason falsely; misjudge [more]; paralogize.
beg the question, reason in a circle, cut blocks with a razor, beat about the bush, play fast and loose, blow hot and cold, prove that black is white and white black, travel out of the record, parler a tort et a travers, put oneself out of court, not have a leg to stand on.
unreasonable, illogical, false, unsound, invalid; unwarranted, not following; inconsequent, inconsequential; inconsistent; absonous, absonant; unscientific; untenable, inconclusive, incorrect; fallacious, fallible; groundless, unproved.
deceptive, sophistical, jesuitical; illusive, illusory; specious, hollow, plausible, ad captandum, evasive; irrelevant [more].
at the end of one's tether, au bout de son latin.