Logical Studies

Abstract One of the questions in ontological pluralism is whether or not to accept the generic quantifier. But if we accept the generic quantifier due to reasons that are for the acceptance of the generic quantifier, then ontological pluralism will face problems due to other reasons, for example, it is as if pluralism and monism are just notationally variant of each other and there is no genuine and important difference between them. In other words, the acceptance of generic quantifier offers a kind of monistic counterpart for pluralism, and this monistic counterpart causes three basic problems for pluralism. Of course, these three problems are considered to be one of the most important criticisms of ontological pluralism. In the following article, these three problems are discussed. After clarifying each of them, we have criticized and rejected them. Our key in rejecting these three problems is the assumption that the generic quantifier is not an elite and fundamental quantifier and can only be defined based on restricted quantifiers. Therefore, it has been shown that ontological pluralism, if accepts the generic quantifier and if it does not consider this generic quantifier as elite, it will not face any problem.

Abstract Different kinds of nonstandard conditionals of modal nature, are studied in conditional logic or Dyadic Modal Logic. Preference structures are one of the important categories of semantic models for these logics. Deontic conditionals and nonmonotonic conditionals are two kinds of these nonstandard conditionals, such that these models have been introduced as one of their main semantics.
In this paper we have a brief review of the literature of preference models in these two branches. Then we compare the subjects studied under the topic of preference models in both fields and have an analysis about the meaning and the acceptance of the axioms of conditional logics, when the conditionals either read as deontic conditionals or as nonmonotonic ones.
In addition, we present some examples to show that in the both fields, preference models have shortcomings in expressing the correct and intuitive reasoning. We offer some extended semantics from nonmonotonic literature to overcome these shortcomings.

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 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 The present article is one of the first written in the Western world on the relationship between logic and ontology (or metaphysics in general). Bocheński shows that Gottlob Frege, the father of mathematical logic, by placing truth instead of inference as the subject matter of logic, brought logic very close to ontology and metaphysics, to the point that some of Frege's followers, such as Heinrich Scholz, considered logic and ontology to be one and the same. On the other hand, of course, a group such as Ernest Nagel remained faithful to tradition and considered logic and ontology to be completely distinct from each other. In explaining this historical controversy on the relationship between logic and ontology, Bocheński points out that the roots of this controversy are in Aristotle's two books on syllogisms and polemics (originally titled Prior Analytics and Topics). In Prior Analytics, Aristotle expresses his logical results (i.e., the moods of syllogism) in the form of truths and laws, while in Topics, he had proposed logical results in the form of rules of debate and of dialogue between two opponents (the questioner and the answerer). Bocheński claims that the logical tradition after Aristotle, from the Stoics to before modern logic, all saw logic in the form of Aristotele’s Topics, i.e. as rules of debate and dialogue, unlike mathematical logicians such as Leibniz, George Boole, and Frege, who saw logic in the form of Aristotele’s Prior Analytics, i.e. as axioms and laws.

Abstract The book Philosophy of Mathematics written by Linnebo is one of the recent and useful books in this field. This book is written for undergraduate and graduate students of philosophy and mathematics. One of the remarkable aspects of this book is the simultaneous attention to classical and new philosophical perspectives on mathematics. Unfortunately, the Persian translation of this book contains many mistakes and inadequacies that make it almost impossible to understand the subject through it. In this article, we will selectively review this translation to show only some of the mentioned shortcomings. It seems that the scientific and philosophical community should show more responsibility in criticizing the existing translations and providing the basis for better translations. In addition to reviewing the translation, we will also have a look at some of the contents of the book. The address of the original book and its translation is as follows:
Linnebo, Øystein (1399). Philosophy of Mathematics, translated by Mohammad Hossein Vaghar, Etelaat Publications.
Linnebo, Øystein (2017). Philosophy of Mathematics (Princeton Foundations of Contemporary Philosophy), Princeton University Press.

Abstract To accurately understand a statement and arrive at the speaker's intentions and beliefs, specific rules and principles are needed. After reaching that information, it must be analyzed logically in order to think about and use it in arguments. This analysis in logic is carried out by analyzing propositions. "Proposition" has various dimensions and components that are subject to philosophy's interpretation. Philosophers' interpretations are of great importance and can be effective in analyses and logical structures of assents, in addition to being used in sciences such as epistemology. Using the method of content analysis, when Ibn Sina's writings in this field are examined, it is found that there are three types of propositions with specific rules: the verbal proposition (sentence), the rational proposition (proposition), and the accepted proposition (assent). "Copulative" is the most fundamental component in a sentence, which indicates the "predicative relation" in the proposition, a relationship that results from a subjective relation and is an attribute of the subject. In the assent, "judgment" is attributed to that relationship.

Abstract Kripke’s reading of Wittgenstein introduces a sceptical paradox: neither objective facts nor private intentions determine future rule‐applications, and the final authority rests with the community.
This paper offers an internal, post‐Kripkean reconstruction of the sceptical solution: the communal criterion of correctness is preserved, while the individual’s mental guidance is redefined as the inner dimension of that very social mechanism of meaning.
The proposed framework, called the Dynamic Network of Particular Beliefs, develops a form of socially embedded dispositionalism—a communalized version of dispositionalism—in which the mind’s similarity‐based tendency constitutes the inner continuation of communal behaviour at the individual level, rather than an external addition to it.
Meaning arises from the intertwining of two components:(1) the individual’s network of particular beliefs, shaped through socially validated linguistic practices; and (2) the mind’s natural tendency to extend similarities, which integrates new cases into familiar clusters without recourse to explicit rules or interpretive regress. The community remains the final arbiter, thereby securing normativity and corrigibility. In the immediate act of linguistic use, the sense of similarity performs the guidance, while particular belief provides the historical structure of that guidance.
Accordingly, the theory moves from Kripke’s attributional model to a belief‐based one, unifying individual guidance and social normativity within a single dynamic structure—one in which the notion of family resemblance is elevated from a merely descriptive motif to an explanatory mechanism of linguistic guidance.

Abstract The central problem of this article is the semantic transformations of the “matter (mādda) of the proposition” in Islamic logic, for which at least four major positions have been advanced: (1) Ibn Sīnā (Avicenna) defines the matter of propositions as the nafs al-amr relation of predicate to subject and reduces it to the triad necessity/possibility/impossibility, while treating constraints such as permanence (dawām), non-permanence (lā-dawām), non-necessity (lā-ḍarūra), and temporal or qualificational conditions (fixed time, indeterminate time, and the like) under modality (jihah), not under matter; (2) Afḍal al-Dīn al-Khūnajī, by adding non-permanence and non-necessity alongside permanence and necessity, brings the number of matters to four; (3) Athīr al-Dīn al-Abharī enumerates thirteen matters, thereby increasing the inventory but blurring the boundary between matter and modality; (4) Naṣīr al-Dīn al-Ṭūsī, criticizing Abharī’s multiplication and returning to the Avicennian three, restricts matter to nafs al-amr relations among concepts (nisab nafs al-amriyya bayna al-mafāhīm). On the basis of texts representing these four views, together with other logicians,

Abstract Ḥillī, with mastery of logic and uṣūl and with a comparative and critical perspective toward earlier logicians, undertook an important reconsideration of the classification of the categorical proposition. He expanded the traditional fourfold structure of propositions (singular, generic, indefinite, and definite) into a more comprehensive fivefold system by distinguishing between the generic and the general proposition. Ḥillī’s innovation, through a precise redefinition of the distinction between the generic proposition (where the subject is considered in terms of its abstract quiddity) and the general proposition (where the subject is considered in terms of applying universality to individuals), opened the way for applications in uṣūl, logic, and jurisprudence. This innovation, however, was overlooked due to the dominance of the logical school of Khūnajī and his followers, but it was later revived in the works of subsequent uṣūlīs in the form of the conceptual distinction between the actual proposition (ḥaqīqī) and the external proposition (khārijī). Adopting a historical approach, this article analyzes the dimensions of Ḥillī’s innovation in revising the classification of categorical propositions, and after explaining the reasons for the neglect of his scheme and the lack of reception among logicians, it advances the hypothesis that Ḥillī’s innovation was particularly appreciated among later uṣūlīs due to its methodological and jurisprudential applications.

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 Aristotelian logic is categorical logic, and its central topic is syllogisms with categorical premises. Avicennian logicians have the same approach. Although Aristotle wanted to deal with syllogisms with conditional premises, nothing has been received from him. Muslim logicians, however, have dealt with conditional propositions, although the central topic of their logic, under the influence of Aristotle, was categorical logic, and hence have tried to analyse conditional propositions in the same way as categorical propositions. Most of them have accepted the reduction of conditional propositions to categorical propositions. In this paper, the amount of logical similarity between these two kinds of propositions is investigated. Some similarities are evident; however, some distinctions are also evident, so we cannot say that all judgments belonging to categorical propositions apply to conditional propositions. Therefore, the Avicennian logician’s approach to considering conditional propositions as essentially predicative is mistaken and leads to treating the relations of “condition” and “predication” as the same, whereas they are completely different.