Conditional-Predicative Conjunctive Syllogisms and Division of Propositions into Actuality, Mental and Factual

The necessity of the compatibility in all elements of logic is something that has never been denied among Muslims intellectuals. Throughout the history of logic, any possible inconsistency in the rules of logic, albeit small, has led to a careful study by Muslim logicians. In the continuation of this process, the present text introduces an important inconsistency in the current views of the logicians. In contemporary opinion, the division of predicative proposition into three categories: actuality, mental, and factual (with differences in interpretation) has been endorsed by most Islamic logicians and philosophers. It is claimed that this division is independent of the rest of the rules of logic and can be accepted without changing the syllogism expressed in the logical tradition. In this paper, it is presented that elements of the conditional-predicative conjunctive syllogisms can only be accepted if the predicative propositions are factual. This claim is proved by examining the conditional- predicative conjunctive syllogism by sharing an incomplete part and the middle term is a part of conditional consequence. This part of the syllogism in the tradition of Avicennian logic is considered the most obvious example of conditional-predicative syllogism with a shared incomplete part. Careful examination of the evidence in the books of the Avicennian logicians has shown the validity of our claim.