The first definition's broad term al-madhkūr permits discussion of concepts and judgments alike. The second raises a question: does every mere conception have a contradictory in quite the same sense as a complete proposition?
Conceiving “tree” does not itself assert its existence. Judging “this tree exists” yields a definite claim whose contradictory is “this tree does not exist.” A definition centered on excluding the opposite of an affirmed judgment therefore needs explanation when applied to conceptual awareness. This illustrates why even apparently small changes in a technical definition affect its range of application.