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 ...
Read More
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 ...
Read More
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, ...
Read More
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.
Mahdi Mirzapour; Gholamreza Zakiani
Volume 2, Issue 2 , September 2011, , Pages 117-136
Abstract
It may be historically shown that the theory of distribution is among innovations of logicians of the later Middle Age such as William of Sherwood, Roger Bacon, Peter of Spain, William Ockham, and John Buridan. According to an applied approach, in the contemporary era, this theory has been used in educational ...
Read More
It may be historically shown that the theory of distribution is among innovations of logicians of the later Middle Age such as William of Sherwood, Roger Bacon, Peter of Spain, William Ockham, and John Buridan. According to an applied approach, in the contemporary era, this theory has been used in educational works in the field of general logic to establish validity of Aristotelian syllogism. Focusing on logical thoughts of the eminent thinker of the Middle Age, John Buridan (1295-1361), the present study proves that the theory of distribution is a consequence of the theory of reference; also, referring to Buridan's logical works, it shows that the two rules of "impossibility of the undistributed middle term" and "impossibility of the method of fallacy" which are some applications of the theory of distribution are among innovations of this logician of the Middle Age. And, in their logical textbooks, contemporary logicians have shown, at best, only different readings of the definition of distribution and its rules, and that is not the case that such rules have been invented by them. Meanwhile Peter Geach believes clearly that the theory of distribution is different from the theory of reference, however his view is logically and historically criticized; and it will be shown that it is not a defensible theory. In the conclusion, according to the philosophical-logical framework of Buridan, new definitions of "distributed" and "undistributed" terms will be provided which are based on his logical concepts and terms.
Mehdi Mirzapour
Volume 1, Issue 2 , September 2010, , Pages 119-150
Abstract
Aristotelian deduction rules, which are usually considered as “THE RULES OF THE CATEGORICAL SYLLOGISM” in the elementary logic text books, are proper tools which help beginners in logic to examine the validity of a categorical syllogism. Authors of Persian logic text books, influenced by ...
Read More
Aristotelian deduction rules, which are usually considered as “THE RULES OF THE CATEGORICAL SYLLOGISM” in the elementary logic text books, are proper tools which help beginners in logic to examine the validity of a categorical syllogism. Authors of Persian logic text books, influenced by the authors of English logic text books, rewrite these rules with only some minor changes and revisions in their books and apply them for the same aim. These revisions depend on many different factors including the authors’ personal interests and those English logic text books which were his main reference. The main aim of this article in the first step is to provide an analytical method for formalizing the rules of deduction which can lead us to find a mechanical and algorithmic method and in the next step, is to follow this computable and formal approach to analyze and criticize the deduction rules in Persian logic text books. In addition to categorizing “The rules of the categorical syllogism”, we will propose a new version of such formalized rules by appealing to the concept of “distribution”.
