…and, conversely, from the cause to the effect—as when one infers from the scent that rises from a drink that it is intoxicating, and from its being intoxicating that it is forbidden, in line with the Prophet’s saying, peace and blessings be upon him, “Every intoxicant is wine, and every intoxicant is unlawful,” related by Muslim. Similarly, when an expiation for an oath is required in a particular commitment one concludes that the commitment is indeed an oath, and from its being an oath one knows that an īlāʾ (vow of conjugal abstention) is effected by it, and the inference is valid in the opposite direction as well.

Likewise, one infers from the spreading rays that the sun has risen, and from its rising that dawn has ended; from the returning shade that the sun has passed the meridian, and from that that the time for the ẓuhr prayer has begun—for shadows do not move back from west toward east until the sun declines from the zenith, and only what appears after that point is called fayiʾ (returning shade), whereas ẓill (shade) is a general term for what is present early and late in the day. If you prefer, you may instead infer from the lengthening of the shadows after they have reached their shortest that the sun has declined, and from that, again, that the time for ẓuhr has entered.

In the same way one reasons from the constellation al-Jady to the direction of north, and from that to the direction of the Kaʿbah, knowing that in those lands the Kaʿbah lies to the south while the celestial pole is to the north—sometimes directly in line with the Syrian Corner, as in the region of Ḥarrān and places on the same latitude, and sometimes inclined toward the east so that the side containing the Door tilts westward, as in the land of Iraq. Examples of this kind are plentiful.

To sum up: by the consensus of rational people, proof (dalīl) is broader than cause. Indeed, anything that entails another thing can, without restriction, serve as evidence for that other. One should not differentiate between one necessary concomitant and another, nor claim that some concomitants require a middle term so that they cannot be known except through it. Whenever one knows that this entails that, one infers the entailer from the entailed.

Thus, what they regard as an immediate concomitant may nevertheless be known only through a middle term that functions as evidence, as in the relation of effect to cause; and what they say is a concomitant through a middle term can sometimes be known without any such mediation, as their own example shows. They maintain that colorness belongs essentially to blackness and corporeality to animal because each is established without a middle term, whereas evenness and oddness are accidental to number. They argue: although we know that four is even and three is odd, we do not know this of every number; to learn that two hundred and sixty-two is even, and that one hu…