The Semantics and Pragmatics of the Conditional in al-Fārābī’s and Avicenna’s Theories

In this paper, I examine al-Fārābī's and Avicenna's conceptions of the conditional. I show that there are significant differences between the two frames, despite their closeness. Al-Fārābī distinguishes between an accidental conditional and two “essential” conditionals. The accidental conditional can occur only once and pragmatically involves succession. In the first “essential” conditional, the consequent follows regularly the antecedent; pragmatically it involves likeliness. The second “essential” conditional can be either complete or incomplete. Semantically the former means “if and only if”; pragmatically it means “necessarily if and only if”. The latter is expressed by ‘if, then’ and means entailment; pragmatically, it involves necessity and the inclusion of the antecedent into the consequent. As to Avicenna, he rejects explicitly al-Fārābī’s complete conditional and distinguishes between the luzūm (real implication) and what he calls ittifāq. He quantifies over situations (or times) to express the various conditionals. The two universals A_C and E_C are expressed by “In all situations, if…, then…”, while the two particulars I_C and O_C are expressed by “In some situations, if…, then..”. This gives them a modal connotation, and makes the universals close to strict implications. Pragmatically, A_C presupposes the truth of the antecedent, but there is no such presupposition in E_C, while what is presupposed in both I_C and O_C is a (possible) conjunction.

Despite these differences, in both systems, the conditional is not truth functional, unlike the Stoic conditional.