Logical Studies

Abstract It is obvious that things are subject to change in our world. For example, the nib of a pencil may be broken; however, the pencil is the same pencil as before, with the only change that its nib is now broken. However, the problem is not so simple. During the history of metaphysics, there have been those- such as Parmenides, Melissus, Zenon, McTaggart, Geach, Russell- who rejected change and motion in such a customary sense. On the other hand, philosophers’ mainstream has tried to represent views and sound arguments for the existence of motion and change, for instance, Aristotelian-Avicennian approach is one of the most important of them. The peripatetic account relies on the distinction of essence and accidence and develops its theory of motion. In this paper we try to show that both positive and negative approaches mentioned above are defeated; their defeat is not due to the weakness of their arguments but is rooted in the wrong logic selected for the base of their metaphysics. This paper is an endeavor to show the advantage of paraconsistent logic relative to classical logic in explaining the problem of change.

Abstract The analytic- synthetic distinction is one of the most important topics in modern philosophy, the scope of which has been traced in contemporary analytic philosophy. This distinction has led to disputes and conflicts among philosophers, so that in a general classification, analytic philosophers can be divided into friends and foes of this distinction. There are few works in Persian in the field of analytic philosophy. About the mentioned distinction, there is almost no serious writing or even translation that only focuses on this distinction. But not long ago, in 2019, a book titled The Nature and Role of Analytic and Synthetic Propositions in Logic and Epistemology was written by one of the seminary and university scholars. This book is the selected work in the year book of the seminary. Having said that, it should be expected that the first book in this topic will be an accurate and serious book. What follows is focused on the critical review on this book. Of course, this review should be accompanied by clarifications and reconstructions, which this article has tried in this direction as well.

Abstract In this article, we discuss absolutely unprovable propositions from the point of view of Brouwerian intuitionism. According to Brouwer’s definition, a proposition is absolutely unprovable if the creative mind as an ideal mathematician has a proof that both the proposition itself and its negation are unprovable from a constructive point of view. Brouwer has shown that the existence of such propositions is impossible. In his book on Brouwer and Intuitionism, Mark van Atten has described and elaborated Brouwer’s short proof on this matter. The Persian translator of this book has reconstructed and explained this proof in two different ways. In this paper, we present a more appropriate reconstruction of Brouwer’s proof. In the meantime, we will deal with Gödel’s work in generalizing Brouwer’s result from propositional logic to first-order predicate logic. In addition, we will point out that such formalizations of intuitionistic ideas in the formal language of logic cannot do justice to Brouwer’s ideas.

Abstract Mirza Qomi's explanation about practical reason is important in three ways: (1) He is considered one of the most serious critics of Aristotelian logic and the way of reasoning in this logic, and he has followed a different path from the defenders of this logic. (2) The logic governing Mirza Qomi's thought is considered a psychological logic. and (3) by presenting a different explanation of the nature of reason, he considers imitation as a type of reason and opens the chapter of reference to imitation in practical matters.
It is shown that Mirzai Qomi considers every persuasive thing as a reason. By deviating from formalism in Aristotelian logic, Mirza believes in the multiplicity of forms in argument and believes that the manner of the mujtahid's reasoning determines the form of the argument a posteriori; Therefore, as a priori, no form can be accepted as the form of argument. According to Mirza, there is no logical certainty and logical certainty is also a kind of psychological certainty. If absolute certainty is a psychological matter, three requirements arise: (1) The distinction between specific suspicion and general suspicion disappears and all suspicions become equally valid. Therefore, (2) there is no difference in the validity of suspicions from which source they come? and (3) persuasive imitation has no difference from the epistemological point of view with psychological certainty, and rather it is considered a partial imitation of certainty; Therefore (4) we can use imitation in practical matters.

Abstract Counterfactual emotions, such as envy and regret, play a foundational role in shaping human behavior, influencing moral judgment, and guiding social interaction. Because they arise from the comparison between actual states and imagined alternative scenarios, these emotions serve as powerful cognitive mechanisms that motivate individuals to reassess their decisions, modify their actions, and anticipate future consequences. Consequently, they are of substantial importance to the advancement of research in artificial intelligence and multi-agent systems, where modeling human-like affective reasoning remains a central challenge. In this article, we formalize the counterfactual emotions of envy and regret using the Counterfactual Emotions (CFE) framework [2]. Furthermore, we examine their intensity through quantitative constructs such as the “degree of importance,” “degree of inadequacy,” and “degree of counterfactual avoidability” introduced in [1]. This study provides a theoretical and computational foundation for developing intelligent agents capable of understanding, representing, and adapting to the complex emotional and ethical dimensions of human interaction.

Abstract Even though the principle of non-contradiction is one of the most important principles governing philosophy, especially since the time of Aristotle, some people have gone against this principle and challenged it. The present study mainly aims to show the historical course of the dialethism and the solutions provided by
the dialetheists to believe in the possibility of the sum of contradictions from ancient times until now. The present study aims to show the historical course of the dialethism and the solutions presented by the dialetheists to believe in the possibility of the sum of contradictions. The main problem of this research is that what arguments and solutions have the prominent opponents of the principle of refusal of contradiction presented for their point of view, and it has used the descriptive method and critical analysis to reach the answer to this problem. In order to outline the thought process of defense of dialethism, first the background of the principle of non-contradiction is examined. Then, dialethism and its relationship with trivialism will be discussed, and after that, the background dialethism from ancient Greece to modern times will be reported in detail. The explanation of the logic of dialethism will be the end of this work.

Abstract Ali Sadad Bey is the first traditional logician in the Islamic world to have had a scholarly encounter with mathematical modern logic. He authored "Mizan al-Uqol, fi al-mantik va al-ousol"an Ottoman Turkish textbook on comparative logic. In this book, he first briefly presents the contents of traditional logic, secondly introduces and criticizes the new teachings of English logicians George Boole, William Hamilton, and DeMorgan, and thirdly includes discussions on the foundations and methodology of science.Sedad believed logical studies in the Islamic world had progressed beyond those in Europe, attributing skepticism in Western philosophy to backwardness in logical studies.He aimed to illuminate the historical roots of this perceived deficiency and to demonstrate the superiority of Avicennan logic compared to its European counterparts.Mizan al-Uqol is regarded as a turning point in the history of logic in Türkiye, both setting trends and generating a range of positive and negative reactions within the Turkish intellectual community.

Abstract The logic {LP} is a paraconsistent logic that bears strong structural and semantic similarities to the LP logic introduced by Graham Priest. It is defined using Nmatrices, a semantic tool that plays a significant role in the study of paraconsistent logics by allowing for the analysis of contradictory statements without collapsing the entire logical system. In this paper, we first present the semantic framework of this logic and then develop a proof theory for it based on Gentzen-type sequent calculus. We show that this proof system is both sound and complete with respect to the proposed matrix semantics. Another focus of this study is the analysis of certain distinctive features of the {LP} logic, where noticeable differences from the original LP logic emerge. In particular, we examine the non-standard behavior of the conjunction operator in this logic, which functions in such a radically different way from common logics that the term “conjunction” barely seems appropriate.

Abstract For Aristotle both words and propositions signify. However, the question is what the significate is and under what conditions a specific word or proposition can have a single signification. This issue leads to a discussion of homonymy and "to be spoken of in many ways." Of the 20th-century Aristotelian scholars, Irwin argues that the significate is essence, while Shields contends that the significate is meaning, which has multiple degrees ranging from shallow meaning (the lexical) to deep meaning (the essence). This paper argues that the main factor in the signification of words and propositions is that the significate must have real unity. The real unity of the signified of words, determined based on the doctrine of Categories, can occur in two forms: "in virtue of one," such as human, and "with reference to one," such as being. On the other hand, the true unity of the significate of propositions relates to the real unity of the conditions under which a proposition can be true. Therefore, in Aristotle's discussion of signification, we are seeking real unity, and ordinary linguistic meaning is not his ultimate goal. The significance of this discussion lies in this fact that the signification of words is one of Aristotle's important tools in philosophical discourse.