ON SOME AMBIGUITIES IN IBN SĪNĀ’S ANALYSIS OF THE QUANTIFIED HYPOTHETICAL PROPOSITIONS

Abstract In his analysis of the hypothetical (šarṭīyya) connected (muttaṣila) and disjunctive (munfaṣila) propositions (Al-qiyās, section V), Ibn Sīnā suggests that they can be quantified and presents in section VI a hypothetical system containing the conditional ones, which is exactly parallel to categorical syllogistic and makes use of the same conversion rules and the same proofs. In section VII, he provides four lists of hypothetical quantified propositions whose clauses are themselves quantified and says that the relations of the Aristotelian square of opposition hold for them. In addition, he says that some conditional universal affirmative propositions are equivalent to some universal negative ones with opposed consequents, and to some quantified disjunctive ones. The problem is that these claims are incompatible with each other, since they require two different readings of the universal affirmative conditional proposition, which Ibn Sīnā does not distinguish clearly. In this paper we solve the problem by distinguishing explicitly between these two readings and showing that the first one satisfies the conversion rule of the universal affirmative and the relations of the logical square, and validates all the admitted moods, while the second one satisfies the contraposition rule and the equivalences stated by Ibn Sīnā. This accounts for all Ibn Sīnā’s claims and makes the system coherent.