Logical Studies

Inclusion: The Secret Behind the Aristotelian Categorical Syllogism

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

https://doi.org/10.30465/lsj.2023.43763.1419
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
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https://faculty.washington.edu/smcohen/433/Syllogistic.pdf
Logical Studies
Volume 13, Issue 2 - Serial Number 2
February 2023
Pages 87-118

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