What is the difference between intellect (عقل) and intelligence (ذكاء)? And are disbelievers—who are characterized by intelligence and excel in inventions—among those mentioned in the noble verse: "Had we but listened or used our intellect, we would not have been among the inhabitants of the Blazing Fire"?

Scholars have defined reason ('aql) as a faculty that distinguishes between good and evil. It is called 'aql because it restrains (ya'qil) its possessor from falling into perdition. As for intelligence (dhaka'), it is the swiftness of discernment and understanding, and the perfection of reason. Allah the Almighty has denied reason to disbelievers in several verses, such as His saying: "Indeed, the worst of living creatures in the sight of Allah are the deaf and dumb who do not use reason" (8:22), and His saying: "Deaf, dumb, and blind — so they do not use reason" (2:171). The intent is that they did not use their reason to infer the Oneness of Allah. So, reason was denied to them because they did not benefit from it in faith, just as hearing and sight were denied to them for the same reason. This does not negate their comprehension of worldly sciences and their inventions. For Allah the Almighty said: "They know only the outer appearance of worldly life, while they are heedless of the Hereafter" (30:7). Thus, He denied them beneficial knowledge for their Hereafter, and affirmed for them only knowledge of the outer appearance of worldly life.