Two - fold logicians of the 7th century, with reference to the difference in the syntax of generic and indefinite propositions, set out to treat it as one kind of predicative proposition and to change the t:.iyartite division into the quadripartite one. They started criticising the hvo outlooks of generic indefinite and individual propositions. There is Cl difference between generic propositions and indefinite propositions. Since the former is not reducible to the contirmation of the subject and predicate, its predicate is not included in its subject, and it,; real subject is not identical with the mentioned subject. There is no syntactical difference between the generic and individual propositions on the above - mintioned issues. Their differences pertain to the predicate. With regard to generic propositions, as distinguished from individual ones, the logicians of the 7th century realized the logical importance of second order concepts. The present article is an attempt to study the contribution of two - fold logicians of the 7th century to the development of logic.

The division of propositions into verity and actuality propositions is one of the innovations of Muslim logicians succeeding Ibn Sina, such as Fakhr Razi and his students, Afzal al-Din Khawnji, and Athir aI-Din Abhari. This division corresponds to Western philosophers' divisions of propositions into necessary and contingent ones (by Aristotle), analytic and synthetic ones, and a priori and a posteriori ones (by Hume and Kant). It also reveals Muslim logicians' view of these divisions. It was first criticized by such logicians as Khwajah Nasir and his students, however, all later logicians agreed with this division and attached great importance to it. In recent years, a number of classifications for verity and actuality propositions have been presented in modern logic (by Ha'iri Yazdi, Muradi Ufusi, Kurdi, and Vahid Dastjerdi). In this paper, by means of revealing the weaknesses of these classifications in our logicians' analyses of the issue, the writer has offered a new classification and demonstrated its correspondence with the elevated thoughts of Islamic logic.

In Islamic traditional textbooks modal operators sometimes come before propositions, sometimes before the predicates and sometimes at the end of propositions. This makes the interpretation of modality in each case as de re or de dicto difficult. Given Ibn SVnÏ's discussion of and sensitivity to this distinction, in this paper by examining the position of modality in the contradictories and converses of modal categorical propositions as well as their positions in modal syllogisms I will try to find a reasonable answer to this important issue.

Khunaji and his companions get influence from Fakhr al-Din Razi and classified quantified propositions into two kinds: factual and external.Abhari added the third kind which was named mental. Ṭusi and his companions refuted Khunaji’s viewpoint. Analysis and explanation of the historical development of classification of predicative proposition into factual, external and mental is the problem of this research. In the shade of analysis and historical explanation of this classification would be clear that this problem has two classifications under one name: bipartite and triadic. The present article is an attempt to study the contribution of two-fold logicians of the 7th century to the development of logic.

Deviding both the subjects and the predicates of the categorical propositions into actuality and verity, Afzal Al-Din Khunaji states the actuality-parts as adjectives, but verity-parts in three forms: as simple, as relational and as conditional. Since the adjectives are formulated in Modern Logic by conjunction, we can formulate actuality-parts as conjunctions. Verity-parts can be formulated at least in three forms: simple, truth-functional conditional and relevant conditional. The relations Khunaji has stated between the kinds of the verity- and actuality-propositions correspond, in most of the cases, to the analysis of verity-parts in simple form and, in some other cases, to their analysis by material conditional and, in few cases, to their analysis by relevant conditional. He, also, in some cases, takes as granted the existential import of universal affirmatives and, in some cases, ignores it. I conclude that Khunaji does not stand on a firm point and confus.

A controversy among the Muslim philosophers about the domain of the extensions was that is the subject of the verity-propositions contained the impossible extensions or only all of the actual and possible ones. From Ibn-Sina to Al-Khunaji, there are explicit texts to the former view; but later logicians, starting with Athir Al-Din Al-Abhari, were inclined to the latter. In this paper, we attampt to support Ibn-Sina and Al-Khunaji's view versus Al-Abhari's. For this, we take the extensions as sets of concepts. If an extension is a set of inconsistent concepts we'll regard it impossible and name its logic ‘the logic of the concepts’. For systematizing the logic, we introduce semantics similar to that of predicate logic and construct a formal system in the first-order language. We show that the logical system can be collapsed to a fraction of the second-order logic, concluding that Ibn-Sina and Al-Khunaji's view can be supported by the second-order logic.