قياس مساوات و تحليل چگونگي اعتبار آن در منطق سنتي( همراه با نقد و بررسي رويكردهاي مختلف و ارايه رويكردي نوين)

Syllogism of Equality and its Validity in Traditional Logic (A Critical Study of Various Approaches and the Introduction of a New Approach)

قياس مساوات كه نخستين بار در كتاب اصول ايوكليدس (اقليدس) مطرح شد، از مقدمات ?=? و ? =? به نتيجه ?=? ميرسد. اين شكل از قياس، اما از اين جهت كه ? حد نخستين، ? حد ميانين و ? حد واپسين است و نتيجه بين دوحد كناري برقرار ميگردد، شباهت بسياري به شكل اول قياسهاي حملي ارسطويي دارد و بهمين دليل بنظر ميرسد بايد جزيي از قياسهاي حملي شكل اول باشد ولي اشكال مهمي در ميان است و آن اينكه قياس مساوات از تعريف قياس نزد ارسطو تبعيت نميكند. قياس از نظر وي گفتاري است كه در آن، براي بدست آمدن نتيجه، به چيزي جز مقدمات آن قياس، نيازي نباشد. اما اين قياس به يك مقدمه خارجي نياز دارد؛ مقدمه‌‌يي كه انتقال رابطه تساوي از مقدمات به نتيجه را موجه نمايد. منطقدانان مسلمان در رويكردهاي مختلفي تلاش نمودند تا اعتبار قياس مساوات را تامين نمايند. نوشتار حاضر به ارزيابي اين رويكردها ميپردازد و ضمن اثبات ناكامي آنها به بيان رويكردي نوين در اين موضوع اشاره ميكند و نشان ميدهد كه مساوات و اندراج (حمل)، هر دو از نوع روابط متعديند. روابط متعدي، قابل انتقال از مقدمات به نتيجه‌اند ولي روابط غيرمتعدي از قبيل نصف بودن يا دوبرابر بودن قابليت چنين انتقالي را ندارند. از اينرو درستي قياس مساوات و شكل اول از قياس اقتراني حملي ارسطويي را ميتوان تابعي از امكان تعدي در روابط مساوات و اندراج تلقي كرد.

The syllogism of equality which was first propounded in Euclid’s book of Principles consists of two premises (? = ? and ? = ?) and a conclusion (? = ?). This form of syllogism is greatly similar to the first form of Aristotelian categorical syllogisms because ? is the primitive term; ? is the middle term, and ? is the final term, and the conclusion is established between the two side terms. Thus it appears that the syllogism of equality must be a part of categorical syllogisms of the first form; however, the important problem here is that the basis of this syllogism does not follow Aristotle’s definition of syllogism. In his view, a syllogism is a statement in which nothing is required for arriving at a conclusion except the premises of that syllogism. However, this syllogism requires an external premise which can justify the transfer of the equality relation from the premises to the conclusion. Following different approaches, Muslim logicians have tried to establish the validity of the syllogism of equality. Here, the writers evaluate these approaches and, while demonstrating their shortcomings, refer to a new approach in this regard and prove that equality and subsumption (predication) are both of the type of transitive relations. Such relations are transferable from the premises to the conclusion, whereas non-transitive relations, such as a capacity equal to half of something or twice as much as it lacks this feature. Therefore, the correctness of the syllogism of equality and the first form of Aristotelian categorical conjunctive syllogism can be considered to be dependent on the possibility of transition in equality and subsumption relations.