Logical Studies

Abstract In the present article, I try to study, analyze, and criticize some definitions of the concept of conceivability. In this relatively historical study, I have put particular importance on Descartes as the representative of definitions involving "conceiving". Then, I have discussed definitions involving "belief" and criticized them. After that, I have gone to definitions involving imaging (of a situation). In the conclusion, I have discussed definitions involving verification in the consistent, coherent, and possible worlds.

Abstract connective [statement] is among the foundations of Sinean logic. In the Logic of Shifa, it has been divided into evident and non-evident necessary as well as into various kinds of necessary in terms of necessity and necessary in terms of facts. Without knowing and understanding various kinds of necessary, the nature of necessary connective, its rules, its relation to various kinds of entailment in the modern logic, and the structure of necessary connective cannot be understood and known. Thus, in the present article, after providing Ibn Sina's definition for evident and non-evident necessary connective and analyzing and criticizing some views posed in this concern, I analyze views introduced by Ibn Sina and some later logicians about necessary connective in terms of necessity and in terms of facts (or, as put by Khwajah, verbal and true necessary).  Then, I examine  and criticize  some views posed in this regard which, I think, have gone in wrong direction and got far from Ibn Sina while speaking of Ibn Sina. According to the results of the present study, firstly, division of necessary into evident and non-evident in Ibn Sina's Shifa has nothing to do with division of conditional into necessary and accidental. Secondly, in dividing necessary into evident and non-evident, Ibn Sina has relied upon the factual world and the necessary relations existing in it. Thus, it should not be thought that such a division is merely based upon logical and merely formal relations. Thirdly, according to Ibn Sina, the necessary connective statement "if five is even, then it is a number" is true in terms of necessity and false in terms of facts. Thus, the reason provided by him for falsity of this connective statement concerns facts and should not be confused with the station of necessity. Fourthly, Ibn Sina's argument for falsity of the above connective statement in terms of facts is a continuous and integrated one consisting of various steps none of which should be regarded as an independent argument. Furthermore, this argument has been stated in the language of predicative logic (and not in the language of propositional logic) and has nothing to do with the fallacy of hiding in the relevance logic. Thus, the idea that division of necessary connective into evident and non-evident corresponds to division of connective into accidental and necessary is not consistent with the contents of Shifa and the present author's interpretation of it. Nor is the idea that Ibn Sina has regarded a necessary with impossible precedent as a necessary connective in terms of necessity and thought that it is false in factual world consistent with his distinction between two stations of necessity and facts.

Abstract Dialectical method has certain roots in the Greek philosophical thought before Plato. Such roots may be traced back from Heraclitus and Parmenides to Sophists. There, the first regular uses made of it may be found in Socrates. Though, Aristotle has mistakenly introduced Xenon of Elea as the founder of dialectical method. Plato inherited Socrates' method. But what is clear is the distinction which may be seen between dialectical methods of Socrates and Plato. The doctrine of Ideas gives much importance to this distinction. This distinction may be summarized in this way that the doctrine of Ideas is in conflict with Socratic ignorance. In other words, Socrates employed the dialectical method to show that his logical style prevents him from providing decisive statements based on knowledge; and that his duty is only "to correct", a correction for which no end may be found. Introducing the doctrine of Ideas, Plato made it completely different. And as this doctrine is introduced, it becomes clear that the end of the dialectical method is revealing the "Idea" of the subject discussed. The present article tries to show that: (1)     Roots of the dialectical method may be found in the Greek philosophical thought before Plato, and (2)     Probably Xenon of Elea has nothing to do with the dialectical method, and (3)     Doctrine of Ideas is Plato's (and not that of Socrates), and (4)     When this doctrine is added to the dialectical method, it is of a clear impact on the process of finding an end for the logical search; or, to put it more accurately, (5) dialectical method with, and without, the doctrine of Ideas are different from each other.

Abstract About 11 centuries after its emergence, Aristotle's Organon was translated into Arabic; and, based on such translations, scholars such as Farabi and Ibn Sina created logical works in the Islamic world.
Because of these works, logic emerged and flourished among Muslims. Through analysis and evaluation of the first translations of Organon, we may get familiar with, on the one hand, attention paid by Muslims to the Greek heritage in the first centuries of Islam and the extent of accuracy and correctness of such translations on the other. Abdolrahman Badawi has collected and edited the first Arabic translations of Aristotle's Organon together with Porphyry Isagoge in three volumes. When we compare the Arabic translation of Organon with the Greek text as well as English (Jenkinson), Persian (Adibsoltani) translations of the Prior Analytics (Book 2), we find almost 100 minor and major discrepancies. We have classified such discrepancies under shortages in translation, inconceivable Arabic, added phrases, changed examples, errors made in edition, and preference for the unoriginal text

Abstract In dealing with uninvited guests as natural propositions and propositions that are based on primary essential predication, the term “predication” has undergone some semantic changes; according to the elements of “unity” and “difference” three periods may be distinguished: (1) the period in which “what causes the unity” is external and “what causes the difference” is in the mind, (2) the period in which “the unifier”, in addition to its being in the outside world, may be in mind too and “the differing factor”, also, moves to the top level of mind or another mind, (3) the period in which “the unifier” and “the differing factor”, besides in viewed and viewer, may regularly be located in viewer and viewed. Without separating these periods, the theory of “distinction of the predications” in Mulla Sadra’s works cannot correctly be read. In this article, in fact, “what causes the unity” and “what causes the difference” will be analyzed in a historical development so that some parts of obscurities about this theory may be removed.

Abstract It may be historically shown that the theory of distribution is among innovations of logicians of the later Middle Age such as William of Sherwood, Roger Bacon, Peter of Spain, William Ockham, and John Buridan. According to an applied approach, in the contemporary era, this theory has been used in educational works in the field of general logic to establish validity of Aristotelian syllogism. Focusing on logical thoughts of the eminent thinker of the Middle Age, John Buridan (1295-1361), the present study proves that the theory of distribution is a consequence of the theory of reference; also, referring to Buridan's logical works, it shows that the two rules of "impossibility of the undistributed middle term" and "impossibility of the method of fallacy" which are some applications of the theory of distribution are among innovations of this logician of the Middle Age. And, in their logical textbooks, contemporary logicians have shown, at best, only different readings of the definition of distribution and its rules, and that is not the case that such rules have been invented by them. Meanwhile Peter Geach believes clearly that the theory of distribution is different from the theory of reference, however his view is logically and historically criticized; and it will be shown that it is not a defensible theory. In the conclusion, according to the philosophical-logical framework of Buridan, new definitions of "distributed" and "undistributed" terms will be provided which are based on his logical concepts and terms.