Analysis and Demonstration of Equality Syllogism on the Basis of the Chapter of Four-fold Relations in the Traditional Logic

Two things which equal the same thing also equal one another. This well-known sentence had widely been accepted from the period of ancient Greeks and perhaps earlier as an evident axiom. By the introduction of Logic into the Islamic field، Ibn Sina and most of other Muslim logicians after him tried to affirm this chapter following the lead of Aristotelian syllogism or some other methods. However، it seems that their efforts haven’t been as fulfilled and have received criticism. Arguments for the above syllogism and other similar ones are also continued among the contemporaries. Nevertheless، it gives the impression that lack of enough attention to the contents of the premises of such syllogisms has led to the disappointment of any efforts in demonstrating them. Through the usage of the chapter of four-fold relations، in the analysis of these premises، the equality syllogism would easily be proved provided that the terms used in these syllogistics are universal. Furthermore، through the amalgamation of the chapters of syllogism and the four-fold relations a variety of other syllogisms corresponding to other relations other than equality would emerge all of which would be proved if we employ the previous method and within the traditional logic.