Logical Studies

Abstract Since the Elements of Philosophical Logic, written by Dr. Lotfollah Nabavi, is the first Persian book in the difficult area of philosophical logic, it is not flawless supposedly. So, we have tried in this paper to criticize the writer’s own specific views in the book. In the Tense logic chapter, for example, he falsely considers the Avicennian permanence inevitably general than the necessity because of neglecting the distinction between the eternal necessity and the essential necessity and the division of the latter to temporal and atemporal. In Epistemic logic, he falsely attributes the negative introspection to Socrates and neglects that the positive introspection is counter–intuitive and suffering from the infinite regress. In Free logic, he wrongly considers the existence predicate incompatible with the logical rules of Aristotelians and regards its use in syllogism to be problematic. In addition, problems such as repetition, contradiction, obversion rule, and proposition’s having two components can also be responded in the existence predicate. Some of the author's own answers and resolutions are also problematic: the problem of non-comprehensiveness; the problem of unity of meaning in "existent" and "real"; and the problem that converting a proposition such as "there is no impossible in essence/by means of the other" to "no impossibility is in essence/by means of the other" is not truth-maintainer. In Relevant logic, many of the author's phrases in explaining that Paraconsistency does not result in Dialetheism are controversial as well.

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".

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 Abstract According to Zalta's Neo-Meinongean object theory, objects are either ordinary or abstract. Ordinary objects, though abstract, exemplify - rather than encode - their properties. However, it seems that objects such as mythical objects violate this inclusive and exclusive categorization. Mythological approaches claim that mythical entities have an actual existence and can be realized in distinct fictional and concrete objects. This cannot be explained by Zalta's logic. However, it can be explained by adding the class of ordinary abstract objects, which on the one hand exemplify the properties and on the other hand necessarily have these properties. This modification can explain how fictional objects can realize mythical objects. Furthermore, applying the distinction of the nature of ordinary abstract object from concrete ordinary object to Zalta's logic explains how a concrete object can be the realization of a mythical one. Thus, this extended logic, with the corresponding changes in the syntax and semantics of Zalta's logic, is able to formalize mythological findings.

Abstract The science of logic, with a history as long as human thought, was compiled by the Greek thinker Aristotle (322-384 BC) in separate books, and his early commentators divided it into nine parts under the title "Organon" and this work in the beginning of Islam was gradually translated into Arabic by Syriac Christians. Kennedy, Farabi and especially Avicenna converted Aristotle's nine-part logic into two parts with logical reasoning. By changing the position of chapters and content of logic based on scientific reasons, increasing and changing the topics related to categories, theorems, contradictions and reverse theorems, and dozens of other cases, they created a fundamental transformation in logic. Al-Ghazali is a follower of Ibn Sina in compiling his logic into two parts, but he is essentially an Islamic theologian and jurist, and he approaches logic with this attitude. In the interaction between Aristotelian logic and jurisprudence and Islamic principles, he presented logic with words, concepts, and practical examples of Islamic sciences and jurisprudence principles, and gave it a logical direction by reasoning and rationalizing the principles of jurisprudence, especially jurisprudence analogy. Gharali's logical and principled works are different from the works of the past, because in addition to using words in Islamic sciences that change logical concepts, he considers analogy and reasoning as the basis of logic, and he extracts analogy from the Qur'an and uses reasoning as the only means of understanding of the Qur'an. This article tries to describe this interaction with a descriptive-analytical method.

Abstract In an article titled " Non-contradiction Paradox", Mahdi Azimi mentioned Mulla Sadra's words are in response to the non-contradiction Paradox. Azimi says that Mulla Sadra examines the statement “the aggregation of the pair of contradictories is impossible” then using the subject-predicate structure Mulla Sadra tries to solve the paradox by distinction between two type of predication called ‘awwali’ and ‘shayi’. Azimi considers the paradox to be the result of its structure and proposes the structure □~(A&~A) for the statement “the aggregation of the pair of contradictories is impossible”. In this structure, there is no need for a subject for a paradox to occur. But firstly, he rejects the subject-predicate structure for that statement without any reason. Secondly, Muslim philosophers mention the proposed structure along with the previous structure for the principle of Non-contradiction but the proposed structure does not produce a paradox that requires a solution. Thirdly, with a closer look, there is a paradox on the proposed structure. Fourthly, □~(A&~A) is not a complete translation of the principle of Non-contradiction.

Abstract Aristotle gives a definition of "universal" that Łukasiewicz considers non-comprehensive because it does not include null universals. In addition, Aristotle's definition of a particular can be understood in two ways: (1) a particular can only be predicated on one thing, (2) a particular cannot be predicated. This double conception, which is repeated with great frequency in the words of Aristotle's commentators, on the one hand, calls into question the opinion of Koons and Pickavance - who believe that a particular in Aristotle's view is unpredicable; And on the other hand, it is a conflict that must be resolved. In this essay, it will be shown that, firstly, Łukasiewicz's objection is not relevent and Aristotle's definition also includes null universals; And secondly, the conflict that seems to arise from the definition of particular can be resolved by distinguishing two types of predication, "in the manner of one name" and "not in the manner of one name".

Abstract The relationship between term-subject and subject in the attrebutive theorem is (‘عقدالوضع’-Aghd Al-Vaz). According to Al-Razi pruport, the modal of that relationship in Al-farabi’s viewpoint is contingency but Al-Tousi says Al-Farabi’s viewpoint is possibility modal. So at last, two of them don’t accept Al-Farabi’s holistic view. On the other hand both of them say that Avicenna, however, accepts actuality modal for ‘Aghd Al-Vaz’ in every theorem and this is the true modal. So Al-Farabi doesn’t talk about the modal of Aghd Al-Vad completely but it is understood that he looks at the relationship as a kind of theorem which accepts modals. Therefore, Avicenna doesn’t accept actuality modal for all theorems. So in this article, first of all we are going to check that possibility modal and contingency modal as a modal of Aghd Al-Vaz is accepted by both Al-Farabi and Avicenna; in the second step we are going to show that the critic of Al-Razi and Al-Tousi in Al-Farbi is not seemed true.

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 This paper is a reflection on the nature of Meinongian Propositions (MP), within which properties are ascribed to non-existent objects, preserving the possibility of their being true. Ordinary theories of the propositional unity, I demonstrate, provide explanations to the nature of MP, only in pain of misrepresenting their truth value, violating our intuitions about their constituents, or doubling our ontological commitments. Cognitive accounts e.g. that of Soames, later Russell or Priest, are to work.
This paper is a reflection on the nature of Meinongian Propositions (MP), within which properties are ascribed to non-existent objects, preserving the possibility of their being true. Ordinary theories of the propositional unity, I demonstrate, provide explanations to the nature of MP, only in pain of misrepresenting their truth value, violating our intuitions about their constituents or doubling our ontological commitments. Cognitive accounts e.g. that of Soames, later Russell or Priest, are to work.
This paper is a reflection on the nature of Meinongian Propositions (MP), within which properties are ascribed to non-existent objects, preserving the possibility of their being true. Ordinary theories of the propositional unity, I demonstrate, provide explanations to the nature of MP, only in pain of misrepresenting their truth value, violating our intuitions about their constituents or doubling our ontological commitments. Cognitive accounts e.g. that of Soames, later Russell or Priest, are to work.