Abstract
The Arabic logicians include the study of the hypothetical syllogisms in their counterparts of the Prior Analytics, that is, in the treatises called al-Qiyās. In al-Fārābī’s frame, they are also evoked in al-Maqūlāt (the counterpart of the Categories ).
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Notes
- 1.
See [59] for a fuller analysis of the conditional in al-Fārābī’s theory.
- 2.
The expression “qad yakūn” has been translated in several ways. W. Hodges translates it as “sometimes”, K. El-Rouayheb translates it as “Once”.
- 3.
- 4.
- 5.
See also ([128], 42).
- 6.
This formula and all formulas below are expressed by considering only one situation. But they are also valid with two or more situations.
- 7.
We could also add “p” to “p ⊃ q”, since it is also a universal proposition and for the symmetry of the whole formula, but this addition is not required to validate the mood, for the “augment” (as Professor Wilfrid Hodges calls it) added to the first proposition is sufficient to validate it.
- 8.
All these are equivalent to “P ≡ Q” too, but Avicenna does not mention that in this part of the text.
- 9.
Here the word ‘not’ is added by N. Shehaby .
- 10.
This rule is stated as follows (for First-Order Logic ) by contemporary logicians: “If a sentence φ can be inferred in FOL from a set Γ of premises , then it can also be inferred from any set Δ of premises containing Γ as a subset” (See [20]).
- 11.
Some followers of Avicenna have also been shown by Wilfrid Hodges to use modern “Model-Theoretic” methods . See [88] for more details.
- 12.
Avicenna adds the conditions “as long as it is C” and “as long as it is A” to the propositions of this mood in his full analysis of the proof (pp. 114–115), but this does not alter the whole structure of the proof, which is the usual presentation of the reductio ad absurdum.
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Chatti, S. (2019). The Hypothetical Logic. In: Arabic Logic from al-Fārābī to Averroes . Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-27466-5_5
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