Ibn Sina’s Logic > Appendix B: Quantified Hypotheticals (Stanford Encyclopedia of Philosophy/Summer 2024 Edition)

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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

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