irrational, unreasonable, absurd, specious, fallacious, sophistical, inconsequent, unsubstantial, incorrect, inconsistent, false, flawed, casuistic, unscientific, paralogistic, contradictory, untenable, unsound, preposterous, invalid, self-contradictory, Kafkaesque, unproved, groundless, baseless, implausible, hollow, irrelevant, inconclusive, fatuous, senseless, incongruous, prejudiced, biased, unconnected, without foundation, not following, out of bounds, without basis, without rhyme or reason*, nutty*, screwy*, not ringing true*, wacky*, far out*, dopey*, having the cart before the horse*, Jesuitical*; see also fallible, wrong 2.
Antonyms sound, reasonable, logical*.