We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of (...) import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

The Persian philosopher Atn al-Abharwriting mann al-sRevealing Thoughts’s various logics of complex terms with modern treatments.

In this article, the author studies some central concepts in Avicenna's and sī's modal logics as presented in Avicenna's Al-Ish r t wa'l Tan īh t ( Pointers and Reminders ) and in sī's commentary. In this work, Avicenna introduces some remarkable distinctions in order to interpret Aristotle's modal syllogistic in the Prior Analytics . The author outlines a new interpretation of absolute sentences as temporally indefinite sentences and argues on the basis of this that Avicenna seems to subscribe to (...) the Principle of Plenitude. He also shows that he has no valid proof of the modal conversion rules and that he uses some rather ad hoc distinctions to show that Aristotle's modal syllogistic is correct. The author also notes some interesting differences between Avicenna's and sī's approaches to modal logic. (shrink)

In this paper, I raise the following problem: How does Avicenna define modalities? What oppositional relations are there between modal propositions, whether quantified or not? After giving Avicenna's definitions of possibility, necessity and impossibility, I analyze the modal oppositions as they are stated by him. This leads to the following results: The relations between the singular modal propositions may be represented by means of a hexagon. Those between the quantified propositions may be represented by means of two hexagons that one (...) could relate to each other.This is so because the exact negation of the bilateral possible, i.e. ‘necessary or impossible’ is given and applied to the quantified possible propositions.Avicenna distinguishes between the scopes of modality which can be either external or internal . His formulations are external unlike al-F̄ar̄ab̄;’s ones. However his treatment of modal oppositions remains incomplete because not all the relations between the modal propositi.. (shrink)