#### Supplement to Ibn Sina's Logic

## Appendix B: Quantified Hypotheticals

### B.1 Quantified Conditional Propositions with Quantified Parts

#### B.1.1 Universal affirmative conditional

1. | (a-\(\mathbb{C}\))aa | Always, if every A is B, then every C is D
( kullamā kāna kull A B fa-kull C D) |

2. | (a-\(\mathbb{C}\))ai | Always, if every A is B, then some C is D
( kullamā kāna kull A B fa-baʿḍ C
D) |

3. | (a-\(\mathbb{C}\))ia | Always, if some A is B, then every C is D
( kullamā kāna baʿḍ A B fa-kull C
D) |

4. | (a-\(\mathbb{C}\))ii | Always, if some A is B, then some C is D
( kullamā kāna baʿḍ A B fa-baʿḍ C
D) |

5. | (a-\(\mathbb{C}\))ee | Always, if no A is B, then no C is D
( kullamā kāna lā šayʾ min A B
fa-lā šayʾ min C D) |

6. | (a-\(\mathbb{C}\))eo | Always, if no A is B, then not every C is D
( kullamā kāna lā šayʾ min A B
fa-lā kull CD) |

7. | (a-\(\mathbb{C}\))oe | Always, if not every A is B, then no C is D |

8. | (a-\(\mathbb{C}\))oo | Always, if not every A is B, then not every C is D |

9. | (a-\(\mathbb{C}\))ae | Always, if every A is B, then no C is D |

10. | (a-\(\mathbb{C}\))ao | Always, if every A is B, then not every C is D |

11. | (a-\(\mathbb{C}\))ie | Always, if some A is B, then no C is D |

12. | (a-\(\mathbb{C}\))io | Always, if some A is B, then not every C is D |

13. | (a-\(\mathbb{C}\))ea | Always, if no A is B, then every C is D |

14. | (a-\(\mathbb{C}\))ei | Always, if no A is B, then some C is D |

15. | (a-\(\mathbb{C}\))oi | Always, if not every A is B, then some C is D |

16. | (a-\(\mathbb{C}\))oa | Always, if not every A is B, then every C is D |

Note that the *luzūmī-ittifāqī* distinction
is often expressed by syntactic variations on the above forms, which
typically involves prefixing the verb *yalzamu* (or its
negation) to a declarative clause (e.g., for (1) “Always, when
every A is B, it necessarily follows that every C is D”).

*Laysa* is often used for negation instead of
*lā*.

#### B.1.2 Universal negative conditional

1. | (e-\(\mathbb{C}\))aa | Never, if every A is B, then every C is D
( laysa albattata in/iḏā …
fa-…) |

2. | (e-\(\mathbb{C}\))ai | Never, if every A is B, then some C is D |

3. | (e-\(\mathbb{C}\))ia | Never, if some A is B, then every C is D |

4. | (e-\(\mathbb{C}\))ii | Never, if some A is B, then some C is D |

5. | (e-\(\mathbb{C}\))ee | Never, if no A is B, then no C is D |

6. | (e-\(\mathbb{C}\))eo | Never, if no A is B, then not every C is D |

7. | (e-\(\mathbb{C}\))oe | Never, if not every A is B, then no C is D |

8. | (e-\(\mathbb{C}\))oo | Never, if not every A is B, then not every C is D |

9. | (e-\(\mathbb{C}\))ae | Never, if every A is B, then no C is D |

10. | (e-\(\mathbb{C}\))ao | Never, if every A is B, then not every C is D |

11. | (e-\(\mathbb{C}\))ie | Never, if some A is B, then no C is D |

12. | (e-\(\mathbb{C}\))io | Never, if some A is B, then not every C is D |

13. | (e-\(\mathbb{C}\))ea | Never, if no A is B, then every C is D |

14. | (e-\(\mathbb{C}\))ei | Never, if no A is B, then some C is D |

15. | (e-\(\mathbb{C}\))oi | Never, if not every A is B, then some C is D |

16. | (e-\(\mathbb{C}\))oa | Never, if not every A is B, then every C is D |

#### B.1.3 Particular affirmative conditional

1. | (i-\(\mathbb{C}\))aa | Sometimes, if every A is B, then every C is D
( qad yakūnu iḏā …
fa-…) |

2. | (i-\(\mathbb{C}\))ai | Sometimes, if every A is B, then some C is D |

3. | (i-\(\mathbb{C}\))ia | Sometimes, if some A is B, then every C is D |

4. | (i-\(\mathbb{C}\))ii | Sometimes, if some A is B, then some C is D |

5. | (i-\(\mathbb{C}\))ee | Sometimes, if no A is B, then no C is D |

6. | (i-\(\mathbb{C}\))eo | Sometimes, if no A is B, then not every C is D |

7. | (i-\(\mathbb{C}\))oe | Sometimes, if not every A is B, then no C is D |

8. | (i-\(\mathbb{C}\))oo | Sometimes, if not every A is B, then not every C is D |

9. | (i-\(\mathbb{C}\))ae | Sometimes, if every A is B, then no C is D |

10. | (i-\(\mathbb{C}\))ie | Sometimes, if some A is B, then no C is D |

11. | (i-\(\mathbb{C}\))ao | Sometimes, if every A is B, then not every C is D |

12. | (i-\(\mathbb{C}\))io | Sometimes, if some A is B, then not every C is D |

13. | (i-\(\mathbb{C}\))ea | Sometimes, if no A is B, then every C is D |

14. | (i-\(\mathbb{C}\))oa | Sometimes, if not every A is B, then every C is D |

15. | (i-\(\mathbb{C}\))ei | Sometimes, if no A is B, then some C is D |

16. | (i-\(\mathbb{C}\))oi | Sometimes, if not every A is B, then some C is D |

#### B.1.4 Particular negative conditional

1. | (o-\(\mathbb{C}\))aa | Not always, if every A is B, then every C is D
( laysa kullamā … fa-…) |

2. | (o-\(\mathbb{C}\))ia | Not always, if some A is B, then every C is D |

3. | (o-\(\mathbb{C}\))ai | Not always, if every A is B, then some C is D |

4. | (o-\(\mathbb{C}\))ii | Not always, if some A is B, then some C is D |

5. | (o-\(\mathbb{C}\))ee | Not always, if no A is B, then no C is D |

6. | (o-\(\mathbb{C}\))oe | Not always, if not every A is B, then no C is D |

7. | (o-\(\mathbb{C}\))eo | Not always, if no A is B, then not every C is D |

8. | (o-\(\mathbb{C}\))oo | Not always, if not every A is B, then not every C is D |

9. | (o-\(\mathbb{C}\))ae | Not always, if every A is B, then no C is D |

10. | (o-\(\mathbb{C}\))ao | Not always, if every A is B, then not every C is D |

11. | (o-\(\mathbb{C}\))ie | Not always, if some A is B, then no C is D |

12. | (o-\(\mathbb{C}\))io | Not always, if some A is B, then not every C is D |

13. | (o-\(\mathbb{C}\))ea | Not always, if no A is B, then every C is D |

14. | (o-\(\mathbb{C}\))ei | Not always, if no A is B, then some C is D |

15. | (o-\(\mathbb{C}\))oa | Not always, if not every A is B, then every C is D |

16. | (o-\(\mathbb{C}\))oi | Not always, if not every A is B, then some C is D |

### B.2 Quantified Disjunctive Propositions with Quantified Parts

#### B.2.1 Universal affirmative disjunction

1. | (a-\(\mathbb{D}\))aa | Always, either every A is B or every C is D
( dāʾiman immā an yakūna … aw
…) |

2. | (a-\(\mathbb{D}\))ai | Always, either every A is B or some C is D |

3. | (a-\(\mathbb{D}\))ia | Always, either some A is B or every C is D |

4. | (a-\(\mathbb{D}\))ii | Always, either some A is B or some C is D |

5. | (a-\(\mathbb{D}\))ee | Always, either no A is B or no C is D |

6. | (a-\(\mathbb{D}\))eo | Always, either no A is B or not every C is D |

7. | (a-\(\mathbb{D}\))oe | Always, either not every A is B or no C is D |

8. | (a-\(\mathbb{D}\))oo | Always, either not every A is B or not every C is D |

9. | (a-\(\mathbb{D}\))ae | Always, either every A is B or no C is D |

10. | (a-\(\mathbb{D}\))ao | Always, either every A is B or not every C is D |

11. | (a-\(\mathbb{D}\))ie | Always, either some A is B or no C is D |

12. | (a-\(\mathbb{D}\))io | Always, either some A is B or not every C is D |

13. | (a-\(\mathbb{D}\))ea | Always, either no A is B or every C is D |

14. | (a-\(\mathbb{D}\))ei | Always, either no A is B or some C is D |

15. | (a-\(\mathbb{D}\))oi | Always, either not every A is B or some C is D |

16. | (a-\(\mathbb{D}\))oa | Always, either not every A is B or every C is D |

#### B.2.2 Universal negative disjunction

1. | (e-\(\mathbb{D}\))aa | Never, either every A is B or every C is D
( laysa al-battata immā … wa-immā
…) |

2. | (e-\(\mathbb{D}\))ai | Never, either every A is B or some C is D |

3. | (e-\(\mathbb{D}\))ia | Never, either some A is B or every C is D |

4. | (e-\(\mathbb{D}\))ii | Never, either some A is B or some C is D |

5. | (e-\(\mathbb{D}\))ee | Never, either no A is B or no C is D |

6. | (e-\(\mathbb{D}\))eo | Never, either no A is B or not every C is D |

7. | (e-\(\mathbb{D}\))oe | Never, either not every A is B or no C is D |

8. | (e-\(\mathbb{D}\))oo | Never, either not every A is B or not every C is D |

9. | (e-\(\mathbb{D}\))ae | Never, either every A is B or no C is D |

10. | (e-\(\mathbb{D}\))ao | Never, either every A is B or not every C is D |

11. | (e-\(\mathbb{D}\))ie | Never, either some A is B or no C is D |

12. | (e-\(\mathbb{D}\))io | Never, either some A is B or not every C is D |

13. | (e-\(\mathbb{D}\))ea | Never, either no A is B or every C is D |

14. | (e-\(\mathbb{D}\))ei | Never, either no A is B or some C is D |

15. | (e-\(\mathbb{D}\))oi | Never, either not every A is B or some C is D |

16. | (e-\(\mathbb{D}\))oa | Never, either not every A is B or every C is D |

#### B.2.3 Particular affirmative disjunction

1. | (i-\(\mathbb{D}\))aa | Sometimes, either every A is B or every C is D
( qad yakūnu immā an yakūna … aw
…) |

2. | (i-\(\mathbb{D}\))ai | Sometimes, either every A is B or some C is D |

3. | (i-\(\mathbb{D}\))ia | Sometimes, either some A is B or every C is D |

4. | (i-\(\mathbb{D}\))ii | Sometimes, either some A is B or some C is D |

5. | (i-\(\mathbb{D}\))ee | Sometimes, either no A is B or no C is D |

6. | (i-\(\mathbb{D}\))eo | Sometimes, either no A is B or not every C is D |

7. | (i-\(\mathbb{D}\))oe | Sometimes, either not every A is B or no C is D |

8. | (i-\(\mathbb{D}\))oo | Sometimes, either not every A is B or not every C is D |

9. | (i-\(\mathbb{D}\))ae | Sometimes, either every A is B or no C is D |

10. | (i-\(\mathbb{D}\))ao | Sometimes, either every A is B or not every C is D |

11. | (i-\(\mathbb{D}\))ie | Sometimes, either some A is B or no C is D |

12. | (i-\(\mathbb{D}\))io | Sometimes, either some A is B or not every C is D |

13. | (i-\(\mathbb{D}\))ea | Sometimes, either no A is B or every C is D |

14. | (i-\(\mathbb{D}\))ei | Sometimes, either no A is B or some C is D |

15. | (i-\(\mathbb{D}\))oi | Sometimes, either not every A is B or some C is D |

16. | (i-\(\mathbb{D}\))oa | Sometimes, either not every A is B or every C is D |

#### B.2.4 Particular negative disjunction

1. | (o-\(\mathbb{D}\))aa | Not always, either every A is B or every C is D
( laysa dāʾiman immā … wa-immā
…) |

2. | (o-\(\mathbb{D}\))ai | Not always, either every A is B or some C is D |

3. | (o-\(\mathbb{D}\))ia | Not always, either some A is B or every C is D |

4. | (o-\(\mathbb{D}\))ii | Not always, either some A is B or some C is D |

5. | (o-\(\mathbb{D}\))ee | Not always, either no A is B or no C is D |

6. | (o-\(\mathbb{D}\))eo | Not always, either no A is B or not every C is D |

7. | (o-\(\mathbb{D}\))oe | Not always, either not every A is B or no C is D |

8. | (o-\(\mathbb{D}\))oo | Not always, either not every A is B or not every C is D |

9. | (o-\(\mathbb{D}\))ae | Not always, either every A is B or no C is D |

10. | (o-\(\mathbb{D}\))ao | Not always, either every A is B or not every C is D |

11. | (o-\(\mathbb{D}\))ie | Not always, either some A is B or no C is D |

12. | (o-\(\mathbb{D}\))io | Not always, either some A is B or not every C is D |

13. | (o-\(\mathbb{D}\))ea | Not always, either no A is B or every C is D |

14. | (o-\(\mathbb{D}\))ei | Not always, either no A is B or some C is D |

15. | (o-\(\mathbb{D}\))oi | Not always, either not every A is B or some C is D |

16. | (o-\(\mathbb{D}\))oa | Not always, either not every A is B or every C is D |