Primitive and Common Predications, as in the Proposition and as in the Subject

Islamic philosophers used Primitive Predication and Common Predication in two different meanings: 1. as in the proposition 2. as in the subject. Primitive Predication and Common Predication, in the first meaning, are defined as “intentional identity” and as “extensional predication” and in the second meaning, as “intending the intension of the subject” and as “intending the extensions of the subject”. Primitive Predication and Common Predication, in the second meaning, are precisely the Natural and the Non-Natural propositions. In this paper, by examining various applications of Primitive Predication and Common Predication, we deal with the fundamental differences of the mentioned meanings and formalize them by Modern Logic. At the end, we show how Modern Logic can transform the differences into similarities.