Whatness and Logical Structure of Equivalence Syllogism

The equivalence syllogism is apparently similar to a simple categorical conjunctive syllogism, the truth of which depends on the truth of its external premise of “what is equal to the equal of something is equal to that thing”. Therefore, some believe that, by using the phrase “result by itself” in the definition of syllogism, Aristotle aimed to derive some syllogisms such as the equivalence syllogism. It can be inferred from Ibn Sina’s words that the equivalence syllogism is a categorical conjunctive syllogism which has lost its syllogistic form, and whose terms lack a logical arrangement. This is because the premises of this syllogism share only a part of its middle term rather than its totality. Khwajah Nasir al-Din Tusi has tried to express the syllogistic configuration and logical arrangement of the terms of the equivalence syllogism. In doing so, he has presented two types of simple and compound categorical syllogisms. He has also responded to Fakhr al-Din Razi’s words in this regard. He believes that the equivalence syllogism lacks a repeated middle term and, hence, cannot be deemed a conjunctive syllogism. Rather, it should be viewed as a syllogism which results in a conclusion based on intellectual evidence. However, when commenting on Khawajah Nasir al-Din Tusi’s words, Qutb al-Din Razi, on the one hand, views the equivalence syllogism of a compound conjunctive nature and believes that it is problematic to introduce it as a simple conjunctive syllogism. On the other hand, in his comments on Sharh-i matali‘, similar to Fakhr al-Din Razi, he argues that the equivalence syllogism lacks the repetition of the middle term, and that its conclusion is evident based on its two internal and external premises. Khwunji designs a new structure for the equivalence syllogism and believes that its external premise is as follows: “Anything equal to B is equal to everything equal to B”. Of course, this view is not immune to criticism as well. Shahrzuri believes that, if the equivalence syllogism results in concluding “A is equal to C”, it will be out of the division of syllogism into conjunctive and exclusive types; when the conclusion is “what is equal to A is equal to C”, he considers it to be a simple categorical conjunctive syllogism. By rejecting the view that deems the equivalence syllogism lacking in the repetition of the middle term, Mulla Sadra introduces it as a kind of compound categorical conjunctive syllogism with independent conclusions and argues that the middle term has been repeated in both syllogisms. Mulla Sadra’s words, which are in agreement with those of Khwajah Nasir al-Din Tusi, present the correct view regarding the logical structure of the equivalence syllogism.