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Definition of inconceivable : Not conceivable; incapable of being conceived by the mind; not explicable by the human intellect, or by any known principles or agencies; incomprehensible; as, it is inconceivable to us how the will acts in producing muscular motion.

Synonyms:

unimaginable, unbelievable, unconceivable, shaky, likely, unacceptable, belief, insufferable, out of the question, unthinkable, unsubstantial, improbable, flimsy, unsufferable, weak, thin, unconvincing, incredible

unfeasible, impracticable, unobtainable, unworkable, impossible, unattainable, implausible, absurd

Usage examples:

• But all the same," he broke off, his eyes burning in his head, " all the same, to me it is inconceivable that any man, however sunk, could have been cruel to her!
• But that Gifford could have, apart from what Edith Morriston might have told him, any intimate knowledge of the tragedy was inconceivable. - "The Hunt Ball Mystery", Magnay, William.
• Is it a mere word, which presents no meaning as corresponding to any objective reality, or has the word a meaning notwithstanding its being an inconceivable one? - "A Candid Examination of Theism", George John Romanes.