Gholamreza Zakiany; Mahin Bagheri; Mehdi Mirzapour
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 ...
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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..
Mohammad Hafi; Mahin Bagheri; Mehdi Mirzapour; Gholamreza Zakiani
Volume 9, Issue 2 , October 2018, , Pages 1-19
Abstract
The purpose of this research is to provide a new concept in Aristotelian categorical syllogism which is called groundability. A valid mood is called groundable if one would derive all the 24 valid moods in the Aristotelian’s syllogism by assuming only the valid mood and applying a chain of the ...
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The purpose of this research is to provide a new concept in Aristotelian categorical syllogism which is called groundability. A valid mood is called groundable if one would derive all the 24 valid moods in the Aristotelian’s syllogism by assuming only the valid mood and applying a chain of the following rules: simple conversion, reduction-ad-absurdum, sub-alternation, obversion and quantification negation. In this paper, we will prove that only the fifteen valid moods have the groundability property. Because Aristotle proves all the valid moods of other figures based on the four moods in the first figure, he considers these moods of the first figure as moods having the groundability property. We show that the groundability is not restricted to the first valid moods of the first figure--they are fifteen moods as stated. Thus, it can be shown that Aristotle's purpose from the self-evidence of the first figure is not the groundability of the four moods in the first figure. This important logical result in Aristotle's system is gained through the introducing the concept of the groundability of the moods in syllogism. We show that unlike the common view in the Aristotelian tradition, it is not the case that the groundability of the first figure must be the basis for explaining of being self-evidence of the four moods of the first figure. Regardless of what lies behind the evidence of the first figure valid moods, this paper will eliminate one of the options which is somehow a common wrong interpretation for answering the problem
Mahin Bagheri; Mehdi Mirzapour; Gholamreza Zakiani
Volume 9, Issue 1 , October 2018, , Pages 19-52
Abstract
Supposition theory is one of the most important logical- semantic theories which is put forward by medieval logicians in their logical texts and commentaries usually under the discussion topic "Properties of Terms". Since this theory has important consequences and results in logic, philosophy and theology, ...
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Supposition theory is one of the most important logical- semantic theories which is put forward by medieval logicians in their logical texts and commentaries usually under the discussion topic "Properties of Terms". Since this theory has important consequences and results in logic, philosophy and theology, in this paper we will investigate its conceptual and historical origin. We claim that there is a significant and deep (historical and conceptual) bound between the medieval theory of supposition and Aristotle’s theory of fallacies as he has stated in his treatise “sophistical refutations”. The case-by-base study of Aristotle’s fallacy in comparison to the semantical analysis of medieval logicians support this idea that supposition theory is the implicit semantic of Aristotle’s “sophistical refutations” which has been reinterpreted as an explicit and dependent field of study by medieval logicians, and also it has been extended throughout the late medieval ages due to different semantical problems.
