Document Type : Research

Authors

• Gholamreza Zakiany ¹
• Mahin Bagheri ²
• Mehdi Mirzapour ³

¹ Associate Professor of Philosophy Department, Allameh Tabatabai University,Tehran.Iran

² M.A in Philosophy-logic, Allameh Tabatabai University. Tehran.Iran

³ Ph.D in Computer Science, Montpellier University, France

Abstract

In this research, we firstly reconstruct the Aristotelian categorical syllogism using the concept of inclusion(=subset). Then, we prove the soundness of the equation “Aristotelian syllogism= Inclusion properties + Proof by contradiction + Existential import”.  The proof of this equation will be formed by reconstructing the Aristotelian syllogism. There is a consensus view among the old logicians in favor of the usage of existential import as an assumption. Also, the proof by contradiction is considered as a general logical principle. Consequently, it can be concluded that the inclusion and its properties are the core important elements of the Aristotelian categorical syllogism. In the end, after introducing the concept of complexity of syllogism based on the properties of inclusion, we point out the concepts of self-evidency and groundability and their relationship in the Aristotelian categorical syllogism setting. We clarify that the relation of being self-evident and groundability is not equality and the groundability is a more general concept with respect to being self-evident.

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Keywords

• Categorical Syllogism
• Properties of the Inclusion
• Complexity Function
• Groundability
• Self-evidency. Distributed Terms