Document Type : Research Paper
Author
Iranian Institute of Philosophy
Abstract
I aim to demonstrate that this distinction between the logics of ḥaqīqī and khārijī propositions is incompatible with the history of logic in the Islamic world. This is because Sinawi logicians examined the relationship between ḥaqīqī and khārijī propositions and mixed ḥaqīqī-khārijī syllogisms. It is clear that we cannot express the relationships among and mixtures of some propositions in two different logics and we have to do it in a unified logic. To solve this problem, it seems that the language and theory of classical and free predicate logics should be strengthened in a way that allows for expressing and proving relationships among, and mixtures of ḥaqīqī and khārijī propositions. To this end, there are at least three possible approaches: first, combining classical and free predicate logics; second, strengthening classical predicate logic by adding the predicate of "khārijī existence"; and third, strengthening free logic by adding "modal logic". We will see that the first approach is successful, and in the second approach, it is possible to define khārijī propositions in terms of ḥaqīqī ones by strengthening classical predicate logic. However, in the third approach, it is not possible to define ḥaqīqī propositions in terms of khārijī propositions by strengthening free predicate logic. Therefore, we conclude that the modal approach to analyzing ḥaqīqī and khārijī propositions, as previously used, is incomplete or imprecise and must be completed or precisized, based on one of the two approaches presented in this article.
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