Lesson 17 · Induction (istiqrāʾ) and analogy (tamthīl)

Source: Book pp. 71–74.

The syllogism gives certainty because it moves from a general rule to what falls under it. But where do general rules come from? And what about reasoning from one case to a similar one? These are the other two kinds of proof from Lesson 12.

1. Induction (istiqrāʾ)

Istiqrāʾ: the mind's move from particular cases to a general rule.

You examine many kinds of animal and find that each moves its lower jaw when it chews, and you conclude: "Every animal moves its lower jaw when it chews."

• Complete: "Every shape is either curved or angular; every curved shape is bounded; every angular shape is bounded; ∴ every shape is bounded." Every case is covered, so nothing can escape the rule.
• Incomplete: the jaw rule fails for the crocodile, which moves its upper jaw. One unexamined case is enough to break it.

The puzzle. Almost all our general rules (fire burns, every human dies, two is half of four) rest on incomplete induction, since nobody can examine every fire or every human. Yet we feel certain of them. Is that certainty unjustified?

The book's answer: it depends on what the induction rests on.

1. Bare counting of cases. Weak: one counterexample destroys it. Most logicians set this kind aside.
2. Counting plus finding the cause (taʿlīl). While examining the cases, you discover why the attribute is there. Then the rule holds wherever the cause holds, and certainty is reached. "Water flows from higher to lower ground" needs only a few observations once the cause is understood. The book calls this the method of inference, or the scientific method. (If the supposed cause turns out to be wrong, the law must be revised.)
3. Axioms. "The whole is greater than its part" is known once its terms are understood. This is not really induction at all.
4. Identical cases. Prove that one triangle's angles equal two right angles, and you have proved it for every triangle, because in the respect that matters all triangles are one and the same.

So it is unfair to say every incomplete induction gives only probability. Induction built on bare counting does; induction built on a discovered cause, or on identical cases, can give certainty.

ʿAqīda link. Induction is everywhere in the Islamic sciences:

• Mutawātir maʿnawī: many reports, each different in wording and detail, all carrying one shared meaning (such as the Prophet's ﷺ miracles taken together). The shared meaning is established with certainty, by the whole, even when single reports are not mutawātir.
• The aims of the Sharīʿa: al-Shāṭibī argued that the protection of religion, life, intellect, lineage and property is established by an induction over countless texts, not by one proof text.

2. Analogy (tamthīl)

Tamthīl: giving one thing the ruling of another because they are alike.

The jurists call this qiyās, which is where the confusion with the logician's qiyās (the syllogism) comes from: one Arabic word, two technical meanings in two sciences (a manqūl, Lesson 4).

Its four pillars (in the standard fiqh example)

Without a known ruling on the root, or without a real common factor, there is no analogy.

How strong is it?

• By itself, only probability. Two men may look alike, walk alike and dress alike; that one is a criminal does not make the other one a criminal.
• More shared features raise the probability, but still do not reach certainty.
• Certainty only if the common factor is shown to be the complete cause of the ruling in the root, and it is found in the branch. At that point the analogy becomes a syllogism, with the cause as the middle term:

Nabīdh intoxicates. Every intoxicant is forbidden. ∴ Nabīdh is forbidden. (Figure 1)

Proving that a feature is the complete cause is the hard part. In the Sharīʿa, the book says, the cause can only be known from the Sharīʿa itself.

A note on the book's position. The author is a Shīʿī scholar, and his remark that juristic qiyās is "destructive to religion" reflects his school, which rejects it except where the cause is stated in the text. The Sunni schools of uṣūl accept qiyās as the fourth source of law (after the Qurʾān, the Sunna and ijmāʿ) and have detailed methods for establishing the ʿilla (masālik al-ʿilla); the Ẓāhirīs reject it. The logical point stands for everyone: an analogy is only as strong as the proof that its common factor is the real cause.

ʿAqīda link: reasoning about the unseen. Can we reason from the seen (al-shāhid) to the unseen (al-ghāʾib), for example from created knowers to Allah?

• Ashʿarī and Māturīdī kalām allows it only through a strict link: a shared cause, condition, definition or evidence. Mere likeness is not enough.
• Ibn Taymiyya held that with regard to Allah only the a fortiori form is fitting (qiyās al-awlā), based on "to Allah belongs the highest description" (al-Naḥl 16:60): any perfection found in a creature, free of every defect, belongs to the Creator even more fittingly.

Either way, both sides reject a plain tamthīl that would make Allah like His creation.

Quiz 17

1. Complete or incomplete induction? Certainty or probability?
   • a) A teacher checks every exam paper in the class and finds that all passed.
   • b) Someone sees a hundred white swans and concludes all swans are white.
2. What is the crocodile's role in the book's argument?
3. Of the four bases for induction, which ones can give certainty, and why?
4. Name the four pillars of analogy in: "Rice is like wheat in being sold by measure of volume (kayl), so ribā applies to it as it applies to wheat."
5. Why does analogy by itself give only probability? When can it give certainty?
6. Turn this analogy into a syllogism: "Nabīdh is forbidden like khamr, because it intoxicates."
7. What does "qiyās" mean to a logician, and what does it mean to a jurist?
8. What is qiyās al-awlā, and which verse is it based on?
9. Review: fill in the hidden premise: "No one who eats food is a god, and ʿĪsā ate food."