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 One of the important questions about definite descriptions is the difference between referential and attributive uses of these descriptions. Donnellan objects Russell and Strawson's theories of definite descriptions because they both fail to explain referential use, but nowhere do they give us a set of necessary and sufficient conditions for distinguishing any use. Kripke also believes that the difference between referential and attributive uses is in fact the difference between the speaker's reference and the semantic reference. The speaker's reference and the semantic reference coincide in attributive use, but in referential use, they may be different. According to the theory of speech acts, Kripke's account may not be quite correct, however, the difference between speaker's reference and semantic reference is similar to the difference between the speaker's meaning and the meaning of the sentence, although Kripke adopts a strange way of expressing it, because reference, contrary to meaning, is a speech act. But Searle's solution is based on his theory of indirect speech acts; That is, the speaker says something, he means what he says, but he also means something else. In Searle's account, the speaker's primary illocutionary act which is not literally expressed in his utterances, is done indirectly by performing his secondary illocutionary act which is expressed literally. According to Searle, all Donnellan's referential uses are mere uses where the speaker uses a definite description that expresses the secondary aspect under which the reference is made.

Abstract When formalizing the Islamic legal reasoning system, we encounter various categories of justifications which require different logical operators. For instance, certain ones possess a certain epistemic value; thus, accepting them necessitates accepting the accompanying causal and logical ramifications. However, there are other types of justifications that hold significance only within a legal system. These justifications may not necessarily have any direct bearing on truth or knowledge but are instead concerned with establishing the rules of institiuation
This article presents an axiomatic logical framework based on the "Count As" logic (logic of institutions) and non-monotonic logic, as well as the justification logic. This framework can represent the logical properties of two category of valid justifications in the Islamic Legal Reasoning, namely, Amaarat and Osul-al-Amaliyyah. In fact, the legal consequences of both as well as the rational consequences of Amaarat are valid, but the rational consequences of Osul-al-Amaliyyah are not accepted. Our framework can represent this difference.

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 In Classical Logic, it is not possible to conclude from "If P then Q" that "It is not the case that if P then ∼Q". This argument, whose conditional counterpart is known as Boethius' thesis, is abundantly attested in the realm of causal, conceptual, and logical relations. Aristotle's thesis "It is not the case that if P then P" is not a theorem in this logic. Furthermore, in Classical Logic, each of the two propositions P and Q is derived from "It is not the case that if P then ∼Q", against which there is a lot of evidence. The Non-Truth Functional System of Propositional Logic is an answer to these problems, in which causal, conceptual, and logical relations are analyzed, formulated, and evaluated in accordance with natural intuition without exception.
In article "Hajhosseini's Non-Truth Functional Logic", Asadollah Fallahi makes three specific criticisms of this system: "The number of inference rules are reducible", "Every propositional variable is a theorem, and this system and its extension are trivial" and "The extension of the Non-Truth Functional System reduces to classical logic". In this article, we show that the first criticism is based on some incorrect proofs. Also, the second criticism arises from the incorrect definition of some non-truth functional combinations or the incorrect proof of some arguments. Finally, the third criticism is solved by reducing the rules of distributivity. For our answer to his repeated criticisms we refer to the article "Critical Review of a Criticism on the Theory of Truth-Functional System".