Lesson 2 · Certainty, ignorance, axioms, and how thinking moves

Source: Book pp. 5–9 (plus p. 38 on why proofs must end in axioms).

1. Degrees of assent

Faced with a statement, your mind is in one of four states. There is no fifth.

Ẓann and wahm are two faces of one state. If you are 70% sure "it will rain" (ẓann), you hold "it will not rain" at 30% (wahm).

ʿAqīda link. "Indeed, ẓann avails nothing against the truth" (Yūnus 10:36). The core of the creed calls for firm assent; doubt (shakk) about it is not faith.

2. Ignorance (jahl)

Ignorance is the absence of knowledge in something that could know. It works like blindness: we do not call a rock blind, and we do not call it ignorant either.

• Simple ignorance (jahl basīṭ): you do not know, and you know that you do not know. "I don't know whether Mars moves."
• Compound ignorance (jahl murakkab): you do not know, and you do not know that you do not know. You think you know. Two ignorances stacked: about reality, and about yourself. The book calls it the ugliest kind.

Compound ignorance can only occur in taṣdīq, because it always comes with a belief. Ignorance in taṣawwur is always simple.

Why compound ignorance is not knowledge. Knowledge is the presence of the thing's image. Someone who believes the earth is flat holds the image of something else, not of the real earth. Seeing a shadow and believing it is a man does not make it a man.

ʿAqīda link. "...while they think they are doing well" (al-Kahf 18:104). Compound ignorance is harder to cure than simple ignorance, because the person feels no need to learn.

Book slip (p. 6): "it is only conception-ignorance that can be divided in this fashion" should read assent-ignorance. The very next sentence says conception-ignorance is always simple.

3. Ḍarūrī and naẓarī knowledge

• Ḍarūrī (also badīhī; axiomatic): reached without thought.
  • Taṣawwur: the concepts of existence and non-existence.
  • Taṣdīq: the whole is greater than its part; two contradictories cannot both be true; the sun has risen; one is half of two.
• Naẓarī (also kasbī; acquired): needs thought.
  • Taṣawwur: the concepts of spirit, of electricity.
  • Taṣdīq: the earth turns on its axis.

So knowledge splits two ways at once: taṣawwur or taṣdīq, and ḍarūrī or naẓarī. That gives four boxes.

Book slip (p. 6): "the whole is greater than the sum of its parts" should read "the whole is greater than its part" (al-kull aʿẓam min al-juzʾ).

Axiomatic does not mean everyone knows it. To see an axiom a person needs:

1. Attention. Someone not paying attention misses even the obvious.
2. A sound mind. Illness or a bad upbringing can make a person doubt the plainest truths.
3. Sound senses. Only for axioms that rest on the senses.
4. Freedom from shubha (a confusing argument). The book's example: some theologians posited a ḥāl, a state between existence and non-existence (the theory of aḥwāl, associated with Abū Hāshim al-Jubbāʾī). A sound mind rejects it as contradicting an axiom even before it can refute the argument.
5. Non-intellectual effort. Hearing a report from so many people that they could not have agreed on a lie (tawātur), running an experiment, travelling to see something. This takes effort but not reasoning, so the knowledge is still ḍarūrī.

ʿAqīda link. The Qurʾān's transmission and the existence of the Prophet ﷺ reach us by tawātur: ḍarūrī knowledge, not conjecture. And the law of non-contradiction sits under every proof in kalām; whoever denies it cannot argue at all.

Why axioms matter (p. 38). If every claim needed a proof, proofs would run back forever. Every chain of proof has to end in ḍarūrī premises.

4. What thinking is

Thought (fikr, naẓar) is "a movement of the intellect between the known and the unknown." It runs in five stages:

1. Facing the problem.
2. Knowing what kind of problem it is.
3. Moving from the problem to what you already know.
4. Moving among what you know: searching and arranging what is relevant.
5. Moving from the arranged knowns to the answer.

Stages 3 to 5, the three movements, are thought proper. Usually it all happens faster than a blink.

Intuition (ḥads). The mind leaps at once from the problem to the answer, without the search. The book calls it the first degree of inspiration (ilhām). Judgments reached by ḥads count as axioms, so one proposition can be ḍarūrī for one person and naẓarī for another.

5. What logic studies

Ḍarūrī knowledge is your capital; naẓarī knowledge is the profit. Logic is the rulebook for the trade: how to arrange what you know so it yields what you do not.

A proof can be studied for its form (how the premises are arranged; that is our focus) or for its matter (how certain the premises are; the full book treats this separately).

Quiz 2

Review from Lesson 1

1. Taṣawwur or taṣdīq?
   • a) "Is the Qurʾān created?"
   • b) "The mercy of Allah"
   • c) "This hadith is fabricated", when you have judged it false
2. Which stage of perception is unique to humans, and what does logic protect it from?

Lesson 2

3. Name the state (yaqīn, ẓann, wahm, shakk) and say whether it counts as assent:
   • a) You are completely sure Allah is One.
   • b) You think Zayd is probably at home.
   • c) That same person's state towards "Zayd is not at home".
   • d) You cannot decide at all whether a narrator is reliable.
   • e) You are completely sure a claim is false.
4. Simple or compound ignorance?
   • a) A student says, "I don't know what tawātur means."
   • b) Someone is certain a fabricated hadith is authentic.
   • c) Why can compound ignorance only occur in taṣdīq?
5. Ḍarūrī or naẓarī?
   • a) The concept "existence"
   • b) "The world is originated (ḥādith)"
   • c) "Makkah exists", for someone who has never been there
   • d) "One is half of two"
   • e) The concept "soul (rūḥ)"
6. After hearing a clever argument, a man starts denying that two contradictories cannot both be true. Which condition for grasping axioms has failed? Does his denial make the statement non-axiomatic?
7. Why must every chain of proof end in axioms?
8. A friend sees the answer to a puzzle instantly; you need ten minutes of working. What did your friend use, and how can the same proposition be ḍarūrī for one person and naẓarī for another?