Lesson 11 · Propositions II: quantity, contradiction, conversion
Sources: S4 slides 7–9, with the standard rules of al-Muẓaffar's Arabic original.
1. Quantity (kamm)
A categorical proposition is sorted by its subject (S4 slide 7: "four categories of each proposition"):
| Kind | S4's name | Subject | Example |
|---|---|---|---|
| Shakhṣiyya (personal) | Personal | a particular | "Asif is a student." "Asif is not a teacher." |
| Kulliyya (universal) | Encompassing | a universal, with "every" or "no" | "Every human will die." "No human can live under water." |
| Juzʾiyya (particular) | Non-encompassing | a universal, with "some" | "Some men are good husbands." "Some men are not politicians." |
| Muhmala (unquantified) | Undefined | a universal, with no quantifier | "The believer fears Allah." |
- The word that marks quantity ("every", "no", "some", "not every") is the sūr (wall).
- A muhmala counts as a juzʾiyya: without a quantifier, the most it guarantees is "some".
- (There is also the ṭabīʿiyya, a judgment on the concept itself, such as "human is a species". It says nothing about individuals and is not used in the sciences.)
The four quantified forms
Combining quality (affirmative or negative) with quantity (universal or particular) gives four forms. The letters A, E, I, O are a common memory aid:
| Code | Name | Form |
|---|---|---|
| A | mūjiba kulliyya (universal affirmative) | Every S is P. |
| E | sāliba kulliyya (universal negative) | No S is P. |
| I | mūjiba juzʾiyya (particular affirmative) | Some S is P. |
| O | sāliba juzʾiyya (particular negative) | Not every S is P. (Some S is not P.) |
Watch the English: "Every waqf is not for sale" (S5 slide 10) means "No waqf is for sale" (E), not "not every waqf is for sale" (O). The book writes O as "Not every S is P", which is clearer.
2. Contradiction (tanāquḍ)
Two propositions are contradictories when they differ in quality (and, if quantified, in quantity) so that one must be true and the other must be false.
S4 slide 8: Asif is a student ≠ Asif is not a student.
The eight unities. Two propositions only contradict if they agree in everything except quality. The classical list has eight; S4 gives the first seven.
| Must agree in | Without it, no contradiction |
|---|---|
| 1. Subject (S4: person) | "Zayd is standing" / "ʿAmr is not standing" |
| 2. Predicate (S4: object) | "Zayd is standing" / "Zayd is not sitting" |
| 3. Place | "Zayd is standing" (in the house) / "Zayd is not standing" (in the market) |
| 4. Time | "Zayd is asleep" (at night) / "Zayd is not asleep" (by day) |
| 5. Part and whole | "The man is black" (his skin) / "The man is not black" (his teeth) |
| 6. Potential and actual (S4: capacity and action) | "The wine in the jar intoxicates" (potentially) / "It does not intoxicate" (actually) |
| 7. Condition | "The writer moves his fingers" (while writing) / "He does not move them" (while not writing) |
| 8. Relation (iḍāfa), missing from S4 | "Zayd is a father" (of ʿAmr) / "Zayd is not a father" (of Bakr) |
The contradictory of each form (S4's two questions on slide 8):
| Proposition | Its contradictory |
|---|---|
| A: Every S is P | O: Not every S is P |
| E: No S is P | I: Some S is P |
| I: Some S is P | E: No S is P |
| O: Not every S is P | A: Every S is P |
| Shakhṣiyya: Asif is a student | Asif is not a student (quality only) |
| Muhmala: The believer fears Allah (= some) | No believer fears Allah |
Why not A against E? Because "Every human is a writer" and "No human is a writer" can both be false (some are, some are not). Those two are only contraries. Likewise "some are" and "some are not" can both be true. Only A/O and E/I split truth and falsehood exactly.
ʿAqīda link: the eight unities in a live debate. "Every bidʿa is misguidance" (the ḥadīth kullu bidʿatin ḍalāla) is an A. Its contradictory is the O "Not every bidʿa is misguidance". Some scholars speak of a "good bidʿa", others insist no bidʿa is good. Very often the two sides take "bidʿa" in different senses (the linguistic sense, anything new; or the sharʿī sense, a new thing in the religion with no basis). If the subject differs in meaning, the unity of subject is broken, and the two statements do not actually contradict. Checking the eight unities before declaring a contradiction saves many quarrels.
3. Conversion (ʿaks mustawī)
S4 slide 9 calls this "Opposite (العكس)". The book calls it conversion.
Conversion: swap the subject and the predicate, keep the quality, and keep the truth.
| Original | Converts to | Example |
|---|---|---|
| Shakhṣiyya | a particular (or itself, if both sides are particular) | "Asif is the teacher" → "The teacher is Asif" |
| A: Every S is P | I: Some P is S | "All humans are animals" → "Some animals are humans" |
| I: Some S is P | I: Some P is S | "Some footballers are Brazilians" → "Some Brazilians are footballers" |
| E: No S is P | E: No P is S | "No human is a rock" → "No rock is a human" |
| O: Not every S is P | no conversion | "Some animals are not human" ↛ "Some humans are not animals" |
Why these rules? A conversion may never claim more than the original. "Every S is P" puts all S inside P, but P may be bigger (Lesson 7: A > B), so you can only say "some P is S". "No S is P" means the two circles are apart, which works both ways. "Not every S is P" tells you nothing about whether every P is S, so it has no safe converse.
A bonus rule (contraposition). From "Every S is P" you may also infer "Every non-P is non-S". This is Lesson 7's reversal (A > B gives not-A < not-B).
Why conversion matters. It is the main tool for turning Figures 2, 3 and 4 into Figure 1 (Lesson 14). The slides' "make the proposition opposite" means exactly this.
Quiz 11
- Identify the quantity and quality (A, E, I, O, shakhṣiyya or muhmala):
- a) "Every soul shall taste death."
- b) "Some of the People of the Book are trustworthy."
- c) "Allah is Forgiving."
- d) "None of the idols creates anything."
- e) "The believer fears Allah."
- f) "Not every one who claims knowledge is a scholar."
- Write the contradictory of each: a) "Every prophet is truthful." b) "No soul knows what it will earn tomorrow." c) "Some Companions narrated ḥadīth."
- Why are "Every human is a writer" and "No human is a writer" not contradictories?
- Which unity is missing in each pair?
- a) "The moon is bright" (at night) / "The moon is not bright" (by day)
- b) "The child is a scholar" (potentially) / "The child is not a scholar" (actually)
- c) "ʿAlī is older" (than his son) / "ʿAlī is not older" (than his father)
- Convert, if possible: a) "Every messenger is a prophet." b) "No idol creates." c) "Some believers are scholars." d) "Not every scholar is a Companion."
- Why does "Every S is P" convert only to "Some P is S"?
- Two people argue: "Every bidʿa is misguidance" / "Some bidʿa is good". Using the eight unities, explain how they might not actually contradict.
- Review: what kind of munfaṣila is "A number is either even or odd"?
Show answers
- a) A · b) I · c) shakhṣiyya · d) E · e) muhmala (it counts as a particular) · f) O
- a) "Not every prophet is truthful." (O) · b) "Some soul knows what it will earn tomorrow." (I) · c) "No Companion narrated ḥadīth." (E)
- Both can be false at once (some humans write and some do not), so one is not necessarily true when the other is false. They are contraries, not contradictories.
- a) time · b) potential and actual · c) relation
- a) "Some prophets are messengers." (A → I) · b) "No creator is an idol." (E → E) · c) "Some scholars are believers." (I → I) · d) No conversion (O).
- Because P may be wider than S (absolute general and particular). Saying "every P is S" would claim more than the original gives.
- If one takes "bidʿa" in the sharʿī sense and the other in the linguistic sense, the subject is not the same, so the unity of subject is broken and there is no real contradiction.
- Ḥaqīqiyya.