Lesson 10 · Propositions I: what a qaḍiyya is, and its kinds
Sources: S4 slides 2–6; Book pp. 58–59. (This English translation leaves out the book's chapter on propositions, so this unit follows the slides and the standard rules of al-Muẓaffar's Arabic original.)
1. What a proposition is
The slide's name for it: "Proposition, প্রস্তাবনা, قضية".
Qaḍiyya: a statement that can, in itself, be described as true or false. (S4: "যে স্টেইটমেন্টকে সত্য বা মিথ্যে দিয়ে অভিহিত করা যায়।")
This is exactly the khabar of Lesson 5. Commands, questions, wishes and the rest of inshāʾ are not propositions.
The slide's question: is a Qurʾānic verse or a ḥadīth a proposition?
- A verse or ḥadīth that reports something is a proposition. Taken in itself, as a statement, it is the kind of thing that can be true or false. That it is certainly true comes from outside the sentence: from the truthfulness of the One who said it, or of the Messenger ﷺ. This is why the definition says "in itself": it looks at the statement alone, not at the speaker.
- A verse or ḥadīth that commands, forbids or supplicates is inshāʾ, so it is not a proposition at all.
So "আল্লাহ্ যার ভালো চান তাকে দ্বীনের জ্ঞান দান করেন" (slide 3) is a proposition, and a true one, while "Establish the prayer" is not a proposition.
2. The three kinds
| Kind | S4's name | What it does | Example |
|---|---|---|---|
| Ḥamliyya (categorical) | Unitary proposition (القضية الحملية) | affirms or denies a predicate of a subject | "Asif is a student." |
| Sharṭiyya muttaṣila (connected conditional) | Attached conditional (الشرطية المتصلة) | affirms or denies that one statement follows from another | "If the sun is up, it is day." |
| Sharṭiyya munfaṣila (separated conditional) | Detached conditional (الشرطية المنفصلة) | affirms or denies that two statements are incompatible | "A number is either odd or even." |
Parts
- Ḥamliyya: mawḍūʿ (subject: "Asif"), maḥmūl (predicate: "a student"; the slides call it the "object"), and the rābiṭa (the copula, "is"; Arabic usually leaves it unsaid).
- Sharṭiyya: muqaddam (antecedent: "the sun is up") and tālī (consequent: "it is day"). Each part is itself a proposition, but inside the conditional it is only a taṣawwur (Lesson 1).
3. Kinds of muttaṣila
- Luzūmiyya (real link): the consequent really follows from the antecedent. "If the sun is up, it is day."
- Ittifāqiyya (coincidental): the two just happen to be true together. "Whenever a human speaks, a donkey brays." There is no link; only the luzūmiyya can be used in a proof (book pp. 58 and 65).
4. Kinds of munfaṣila (book pp. 58–59)
| Kind | Both true? | Both false? | Example |
|---|---|---|---|
| Ḥaqīqiyya (real) | no | no | "A number is either even or odd." |
| Māniʿat al-jamʿ (excludes joining) | no | yes | "This thing is either a tree or a rock." (It could be a horse.) |
| Māniʿat al-khuluww (excludes neither) | yes | no | "Zayd is either in the water or not drowning." (He can be in the water and not drowning.) |
The ḥaqīqiyya is the proposition form of the contradictories of Lesson 4: no joining and no third option.
5. Affirmative and negative (S4 slides 5–6)
Every proposition is mūjiba (affirmative) or sāliba (negative). The important point is what gets negated.
| Kind | Affirmative | Negative |
|---|---|---|
| Ḥamliyya | Asif is a student. | Asif is not a student. |
| Muttaṣila | If the sun is up, it is day. | It is not the case that if the sun is up, it is night. |
| Munfaṣila | A number is either even or odd. | It is not the case that a number is either odd or two. |
A conditional is negated by denying the link (muttaṣila) or denying the incompatibility (munfaṣila), not by negating one of its parts. So "If a person is not wise, he is not content" is an affirmative muttaṣila, even though both parts are negative: it still asserts a link.
ʿAqīda link. Two of the most used propositions in ʿaqīda:
- "Had there been within them gods besides Allah, they would both have been ruined" (al-Anbiyāʾ 21:22) is an affirmative luzūmiyya muttaṣila. Lesson 15 shows how it becomes a proof.
- "Every existent is either necessary in itself or possible in itself" is a ḥaqīqiyya munfaṣila, the starting point of the argument from contingency (imkān). So is "The world is either eternal or originated."
Quiz 10
- Proposition or not? a) "Allah is the Lord of the worlds." b) "O Allah, guide us." c) "Is there any creator other than Allah?" d) "The world is eternal."
- A ḥadīth reports something, and it is certainly true. Why does it still fit the definition "can, in itself, be true or false"?
- Ḥamliyya, muttaṣila or munfaṣila? Name the parts.
- a) "Whoever does an atom's weight of good will see it."
- b) "A human is either a believer or a disbeliever."
- c) "Muḥammad ﷺ is the Messenger of Allah."
- Luzūmiyya or ittifāqiyya? a) "If it rains, the ground gets wet." b) "Whenever I wear my blue shirt, the bus is late."
- Which kind of munfaṣila? a) "A word is either a noun or not a noun." b) "This object is either white or black." c) "Zayd is either in Dhaka or not in Dhaka's New Market."
- Write the negative of: a) "If the sun is up, it is day." b) "A number is either even or odd."
- Is "If a man does not pray, he is not safe from punishment" affirmative or negative? Why?
- Review: "walking" for human: khāṣṣa or ʿaraḍ ʿāmm?
Show answers
- a) yes · b) no (a supplication) · c) no, as a question, though it implies a denial · d) yes (a false one)
- The definition looks at the statement in itself. As a sentence it is the kind of thing that could match reality or not; its certainty comes from outside it, from the truthfulness of the one who said it.
- a) muttaṣila (a conditional in meaning: "if anyone does..., he will see it"); antecedent and consequent · b) munfaṣila; its two sides · c) ḥamliyya; subject "Muḥammad", predicate "the Messenger of Allah"
- a) luzūmiyya · b) ittifāqiyya
- a) ḥaqīqiyya · b) māniʿat al-jamʿ (it could be red) · c) māniʿat al-khuluww: both can be true (he is in Dhaka but not at New Market), but both cannot be false (outside Dhaka yet inside New Market is impossible)
- a) "It is not the case that, if the sun is up, it is day." (S4's version negates "it is night" instead.) b) "It is not the case that a number is either even or odd."
- Affirmative: it asserts a link between its two parts. Negative parts do not make a conditional negative.
- ʿAraḍ ʿāmm.