Logical Studies

Abstract One of the methods of immediate inference in logic is the conversion. Logicians have identified three types of conversion: conversion, obverted contraposition, and contraposition. The present study, by means of a dichotomous division demonstrates that a further valid and new type of conversion can be posited which has been overlooked by logicians. In this newly identified form, after the conversion of subject and predicate, only the subject is complemented, in such a way that, assuming the truth of the original proposition, the converted proposition is likewise true. This study names this newly identified type “complemented subject conversion” and establishes its logical variations due to the various forms of categorical propositions, whether predicative or conditional. Accordingly, the complemented subject conversion of affirmative propositions (both universal and particular) yields a particular negative proposition, while in the case of a universal negative proposition, it’s a universal affirmative proposition. Particular negative propositions have no valid complemented subject conversion. By employing this innovative type of conversion, a greater number of true propositions can be inferred and derived from a given true proposition, which endows it with a logical value comparable to that of the other recognized types of conversion.

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.

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 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 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.

Abstract The nature of conditional propositions and their content analysis has been one of the extensive topics in logic. The questions and issues raised in the Western logical tradition regarding conditional propositions differ somewhat from what we know in the logical tradition of the Islamic world. In this article, relying on some significant works of traditional Western, particularly English-speaking logic of the 19th century, the most important topics related to conditional propositions are examined, such as the nature of the conditional proposition, various classifications of propositions, the modal interpretation of conditional propositions, the quantity and quality of conditional propositions, and the negation of conditional propositions. Western logicians have presented different views and pointed out aspects that have been less emphasized in the traditional logic of the Islamic world. Understanding the different views of traditional Western logicians on these topics acquaints us with the foundations of modern logic and provides an opportunity to critique traditional logic in the Islamic world.

Abstract Argumentative premises refer to propositions that do not require reasoning and are considered the basis of the five arts - argument, polemic, rhetoric, fallacy, and poetry to explain these premises, three types of categorizing have been presented, and this research in addition to presenting the evolution of these categories, presents the problems that exist in the mentioned criteria and expresses a new criterion for the categorizing of the argumentative premises, which seems useful to eliminate the fallacies that have explained in the text of this research; The premises of the reasoning are: "certainties, Strong Likelihood, Common Beliefs, Illusions, persuasions, Accepted, Imaginations, Fallacies" that the above terms can be classified based on their nature in such a way that Certainties and strong likelihoods are mutually exclusive because these two propositions are indicative of the level of belief derived from their correspondence with external reality; Similarly, common beliefs and illusions are mutually exclusive because they indicate the cognitive processes through which these propositions are derived; likewise, accepted truths, persuasions, and imaginations are also mutually exclusive because all three represent a degree of influence on the audience; fallacies are considered mutually exclusive with all the aforementioned bases of argument because fallacies are propositions that are mistaken for another basis of argument due to verbal or conceptual errors.

Abstract Aristotle defined a proposition as to be either true or false (ṣādiq aw kāẓib). But Avicenna, who mentioned the Aristotelian definition in all his books, except in his latest book, Pointers and Reminders, deviated from Aristotle’s and defined a proposition according to the truthfulness and lying of his “utterer.” (The compoisition which yields an assertion and which is one whose utterer is called “truthful” in what he says, or “a liar”). (Avicenna 1984, Inati’s translation, p. 77, ll. 222-223). This means that “ṣādiq” and “kāẓib” are the description of the utterer and not of the propostion itself, and this is contrary to the definition of Aristotle and of Avicenna himself in all previous works, which consider “ṣādiq” and “kāẓib” to be the description of the utterer and not the propostion. Some contemporaries have proposed reasons for Avicenna's shift from the first definition to the second one, and while reporting them, I show that the attribution of none of them to Avicenna is documented. On the contrary, I present a new reason that the probability of referring to Avicenna is not less, if not more, and that is that the words “ṣādiq” and “kāẓib” in ancient Arabic (before the Graeco-Arabic translation movement) did not mean what “true” and “false” and their equivalents mean in English and other languages, but that they meant “truthful” and “liar” and their equivalents mean in English and other languages.

Abstract This article aims to answer the question, what is the truth of topoi in rhetoric? To answer this question, two other questions must be answered. 1. How does the definition of topoi include all its examples? 2. What is the function of topoi in achieving rhetorical analogies? To answer these questions, with analytical descriptive method, we first examined the definitions provided by logicians. Then, by examining the various topoi, we came to the conclusion that these definitions are not comprehensive for all examples. In the following, to provide a clearer and comprehensive definition of topoi according to the types of topoi and the purpose of their classification, we came to the conclusion that topoi are general rules and formulas that the orator uses to produce arguments on a certain topic. This definition includes both common topoi and special topoi. Finally, to complete the definition process, how it works was explained by citing an example.

Abstract This research addresses and evaluates Mortezā Moṭahharī's perspective on the role of Aristotelian logic in identifying errors in thought, aiming to scrutinize and criticize his reductionist stance. Moṭahharī confines the utility of traditional logic exclusively to the formal rectification of human arguments, dismissing any responsibility for correcting material errors. He contends that logic fundamentally lacks the capacity to rectify the material errors of individuals, asserting that only through "attention" and "care" can one shield oneself from such errors. The analysis presented in this research reveals several shortcomings in Moṭahharī's argumentation: 1) His reductionist stance confines Aristotelian logic to formal reasoning structures; 2) He conflates the detailed examination of the "materials of argument" with determining the governing laws of said materials; 3) His interpretation of "material logic" as the exploration of the "psychological causes of material error" succumbs to the fallacy of "psychologism"; 4) The absence of general rules for recognizing the validity of reasoning materials results in skepticism; 5) "Attention" and "care" are deemed general conditions to avoid any mistake, not specifically material errors. These critiques collectively demonstrate the untenability of Moṭahharī's theory concerning the function of Aristotelian logic

Abstract Poetics is one of the five arts of logic. All of five arts are molded in the form of syllogism and from a material appropriate to each art. The material of poetics is imagined propositions, from which poetic syllogisms are composed. Logicians have different views on presenting the form of poetic syllogism. Al-Farabi and Avicenna, as two great logicians, have each taken a different path in this regard. Al-Farabi considers the form of poetic syllogism as one of the invalid modes of second figure and Ibn Sina considers it as one of the valid modes of first figure. In addition, Ibn Sina considers the example of a poetic proposition sometimes as the conclusion of a syllogism and sometimes as the minor premise of a syllogism. In this article, we have tried to explain why each of these two logicians has chosen a specific figure and mode of syllogism as the poetic syllogism, and regarding Ibn Sina, we will also explain the difference between the two examples that he has mentioned as examples of poetic syllogism.

Abstract The Muslim logicians have described the necessity term in the necessity signification as three different levels: The absolute necessity, The evident necessity as its general term, and the evident necessity as its specific term. Using the descriptive analytical method, this journal has proved that by conditioning these levels, this signification wouldn't include six groups of concepts: 1- external non-necessary concepts 2- non-predicated concepts 3- particular concepts 4-separable accidents 5- non-evident(as its general term) necessary accidents 6- non-evident(as its specific term) necessary accidents that are not evident accidents(as its general term). These concepts can't be included in expression signification as well because they wouldn't be placed in the signification of complete or partial accord. The logicians' models for a bipartite division of expression signification aren't flawless and don't point out a solution for the universality of the division. Therefore, this journal has introduced a new division for expression signification in which the third group(after two groups of complete and partial accord significations) is called "external signification" and it includes the signification of necessity as its subsequent.

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 In the tradition of Avicennian logic, there is a rule according to which there is a equivalence between two conditional hypothetical propositions that have the same quantity, different quality, the same antecedent, and the opposite consequent. This rule is called consequent negation. Avicennian logicians disagree about this rule. Some of these logicians have proved this rule and some have rejected these proofs. In this article, we have tried to show the disagreements about these proofs are connected with the ambiguities in the tradition of Avicennian logic about the nature of singular conditional hypothetical propositions. Some of the evidences in Avicennian logic indicate that the appropriate connective for formulating the relationship between the antecedent and the consequent in connected Singular conditional hypotheticals are inflectional, and some evidences show this relationship as conditional. In this article, we have shown that this issue has had a serious impact on the existing disputes about the consequent negation rule

Abstract Abstract
With regard to the division of carrying, into the primary essential predication and common technical predication , there have been differences of opinion in determining examples and matching with types, among others, there are opinions about the quality of predication the essentials together and on the essence. It is well-known that carrying genus and differentia on species of each other is a common technical predication. Allameh Tabatabai considers the predication of genus and differentia to each other common technical predication and the predication of genus and differentia to species as the primary essential predication, as some like Allameh Javadi Amoli have introduced the predication of genus and differentia to each other and the predication of genus and differentia to type as the primary essential predication. It is possible that Allameh Tabatabai's point of view may be criticized and challenged, but it seems that according to the basis of Allameh's point of view, the criticisms raised can be answered. In this article, while analyzing the basis of Allameh in predication the essentials on the essence, some problems raised at the level of the theory have been investigated.
Key words: Allameh Tabatabaei, primary essential predication common technical

Abstract Shams al-Din Samarqandi in his books Qistas al-afkar and Sharh al-Qistas presented two new analyses of the khariji, haqiqi and mental propositions which are different from those of his predecessors. He held relations among these propositions which have new consequences on the inferential relations between them. Samarqandi conditioned the khariji proposition on the "external existence" of its subject and predicate, also conditioned the haqiqi proposition on the "possibility" of the external existence of its subject and predicate, and considered the mental proposition unconditional to these two conditions. He has also regarded the khariji as implying the haqiqi and the haqiqi as implying the mental, all these in the affirmative propositions and the converse of these relations in the negatives, without distinguishing the universals from the particulars. These inferential relations claimed by Samarqandi are different from those expressed in the works of other Muslim logicians such as Afzal al-Din Khunaji and Qutb al-Din Razi, who seem to be the only Muslim logicians who have explicitly discussed this issue. In this article, we have analyzed and critiqued the claims of Samarqandi and shown that the inferential relations claimed by him do not correspond to the examples he gives for khariji, haqiqi and mental propositions, and are therefore not accurate enough.

Abstract Self-evident propositions as the foundation of Philosophy possess a significant position, but due to various reasons, they have been discussed only in margins. To explain the validity and inerrancy of these propositions, philosophers come up with different ideas. One of these Ideas was suggested by Misbah Yazdi in which he refers them to immediate(presential) knowledge in order to benefit from the unerring feature of this kind of knowledge. Among all self-evident propositions in formal logic, he only considers the inner experience and prime knowledge(Awwaliyat) as two true and eligible instances of self-evident, because among all only these two meet the criteria of being self-evident, and because He believes that sensory knowledge is the source of the mistake, thus he tries to separate self-evident propositions from sensory perception and tie them up to immediate knowledge in order to guarantee the truth of these propositions. But this theory seems to have some errors, in this article we try to explain his theory and then elaborate on the features of immediate knowledge to discover some objections to this novel but apparently incomplete theory.

Abstract In spite of the completeness of modern propositional logic which is accepted by logicans, the compeletness of Stoic logic is a subject that is dubted. In this paper, aftet investigating various systems which are reconstructed by modern scholars for Stoic logic, the compeletness of these systems is studied and it is shown that these systems may not be satisfied Stoic standards for valid arguments. Therefore, it is wrong that the completeness of these systems is ascribed to Stoic logic. Finally, it is negated that Stoic logic is compeleted in this sense that all valid arguments may be reduced to “indemonstred”s and it is shown that in addition to “indemonstrated”s and arguments which may be reduced to “indemonstrated”s, There are some other arguments which are accepted by Stoics as valid

Abstract This article is an comparative study between Mulla Sadra and Tabatabai common approach regarding the efficiency of the causal argumentation, in the realm of philosophy. Mulla Sadra relying on the theory of simplicity of existence, and on which is simple have not essential definition and therefore no argument, found that the causal argumentation is not useful to existence recognition. Sadra based on the rule Zavatol Asbab, says that the Aposteriori Demonstration sometimes completely invalid, and sometimes with poor performance valid. He then weaken or even condemn the role of argument in the realm of philosophy. Then resign to antilogical approach..
Tabatabai based on three cognitive science major rule, first, deny the causal argumentation then existence recognition too. Then design a new argument, the argument by the public obligations, Molazemate Ammeh. This problem shows the inability of the essential logic in the realm of existential philosophy. This article denes the efficiency of the causal argumentation, but believes that, the theory of argument by the public obligations, Molazemate Ammeh, is the worthwhile discovery, which compensates for shortcomings of the essential logic.

Abstract Some logicians earlier logicians, especially as long as the correlation provided or paid for. And even an independent treatises have been written on the subject. In contrast, others argue considered useless or less useful. Unfortunately, this issue has been raised in later works or abbreviated or omitted entirely. In many ways, provided the correlation is important in this debate as well as an understanding of the views of Muslim logicians was provided in the case and the arguments of the vote in comparison with the views of other ill-judged logicians. In this paper, counting and how to explain and prove they are connected Tlazmhay cases in the works presented logicians The review examines these issues, using the coding categories to see if there are other cases of correlation.

Abstract The verse 81 of Zokhrof says: "If God has a child, so I am the first of worshipers." Most of the interpretators believes that this verse contains an argument which can be expressed in a modes tollens form. But despite their attempt to proposal the form of this argument as they claim, no one of their formulized arguments do not match the verse and cannot keep the truth and validity. The difficulty of interpretation of this verse and the variety and difference of it is undoubtedly rooted from the word "first" (which can be interpreted in different meaning which none of them can support the validity of a modes tollens). In this research, after studying these proposal formulations according to modes tollens, a fortiori argument will be proposed and it is claimed that this form of argument, with an extra term, can better shows the content of the verse.

Abstract In this paper, Avicenna’s disjunctive propositions are treated from multiple aspects. In the first section of this paper, disjunction propositions are considered in Shifā, and it shown that there are differences between Avicenna’s and later interpretations, e.g Rāzī interpretation, in this point. In the next section, two general interpretations about Avicenna’s disjunctive propositions are studied and we reveal deficiencies of them. Based on “Confilict” concept as the main core of Avicenna’s view on disjunction propositions, this paper specifies Relevent-Modal interpretation more precise than others but it doesn’t precisely coincide with Avicenna’s view. Finally an alternative interpretation is suggested with respect to Stopper view on Stoic conditional and we show that this interpretation also has deficiency but it formulates Avicenna’s disjunctive propostions better than others.

Abstract Though going back to Aristotle and porphyre Tyrien,the matter of the four relstions between two concepts, as a distinctive division, is one of the most important innovations in Arabic logic. This devision, for the first time, appeared in Farabi, Ghazali, Razi, and Khunaji in different forms. The devisions of the first three sufferred respectively from the fallacies of ‘non-coherency’, ‘non-exclusivity’ and ‘overlap of the sub-classes of the division’, so the later Arabic logicians didn’t accept them; thus Khunaji’s devision, laking all the fallecies, found its way to the pedagogical books and and established itself in Arabic logic up today. Although it has encountered important paradoxes from the very outset, it could resist all of them and reach its today firmed and established position in Arabic logic. In this paper, we explore the background of the four relations and determine each logician’s contribution in developing the subject.