![]() 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. ![]() 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. Following different approaches, Arab logicians have tried to establish the validity of the equivalence analogy. However, this syllogism requires an external premise which can justify the transfer of the equality relation from the premises to the conclusion. ![]() In his view, a syllogism is a statement in which nothing is required for arriving at a conclusion except the premises of the syllogism. Thus it appears that the equivalence analogy 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. ![]() This form of syllogism is greatly similar to the first form of Aristotelian categorical syllogism because Φ is the primitive term Ψ is the middle term, and Θ is the final term, and the conclusion is established between the two side terms. The Equivalence Analogy which was first propounded in Euclid's book of Principles consists of two premises (Φ=Ψ and Ψ=Θ) and a conclusion (Φ=Θ).
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