MANTEQ-PAZHUHI (LOGICAL STUDIES)
Year:2011 | Volume:1 | Issue:2|Papers Count:8

In this article we investigate the relation between two Hegel’s books “The Phenomenology of the Spirit [or Mind]” and “The Science of Logic”. We try to answer this question that which of these books is conceptually prior to and a basis for understanding the other? Does “The Phenomenology of the Spirit” makes clear Hegel’s claims in “The Science of Logic” or does the latter form a frame for understanding the former’s content? We will show that what has been appeared in Hegel’s writings confirms none of these choices. Moreover, accepting each of them has some implausible consequences.

Opponent of the quantified modal logics believe that one of the most important objections to these logics is that they entail essentialism. Saul Kripke tries to overcome this challenge by showing that according to his first system, essentialism is acceptable without any inconsistency. In his revised system, Kripke leaves, to some extent, his previous interpretation of essentialism and tries to propose a more plausible justification in defense of quantified modal logic. In addition to explaining the meaning of essentialism, this article gives a detailed explanation of Kripke’s debate in his first and revised systems.

This article examines the concept of contradiction, law of non-contradiction and dialetheism in non-classical logic. The main purpose of this paper is examining different definitions of the concept of contradiction and the influence of such differences in accepting or rejecting the low of non-contradiction. Here I try to show, by appealing to an especial conception of contradiction, that how it is possible to make dialetheism plausible. In section 1, basic terms are introduced. Section 2 covers different definitions of contradiction. This section shows that according to diverse conceptions of contradiction, we could have different notions of dialetheism. In section 3, I review most important arguments of the proponents of the low of non-contradiction and try to refute them on the basis of the definitions of section 2. Finally it will be showed that new approaches to dialetheism is due to using semantic instead of ontology, multi-valued logic, vagueness and alternates theory of truth.

Eleven centuries after its appearance, Aristotle’s Organon was translated into Arabic and by acquainting with such translations, some elite scholars, e.g. al-Farabi and Ibn Sina, started to write and publish logical writings in the Islamic world. These writings caused rising and developing the logic among Muslims. Analyzing and assessing the first Arabic translations of the Organon make us acquainted, on the one hand with the Muslims attention to the Greek philosophical heritages in the earlier centuries and on the other hand with the amount of these translations accuracy. Abdul-Rahman Badawi has gathered and edited the first Arabic translations of Aristotle’s Organon and Porphyry’s Isagoge in a three volume book. After comparing Arabic translation of Syllogism to its original Greek and to English (Jenkinson) and Persian (Adib-Soltani) translations of the Prior Analytics, we found almost one hundred differences between them. We have categorized these differences under some titles as preference and cost of translation, unintelligible Arabic, supplemented statement, translation mistakes, change and replacement of examples, errors of editing and added explanations. In addition to indicating the significance of the translation age, we touch, in the introduction of this article, some other subjects such as Organon translation, Syllogism’s translator, Badawi’s translation, methodology of comparing different translations and preferences of Arabic translation.

Franz Brentano was one of the most influential philosophers of the second half of nineteenth and early twentieth century. His major role in the history of philosophy can be shown through two aspects. One is that in virtue of his philosophy, we can make a link between the analytic and continental philosophies, and the other is that his doctrines and analyses can still be an origin for most of the philosophical investigations, as it was one century ago; although, because of the glorious personality of his direct and indirect students, his thoughts and insights have been not achieved immediately. Recent efforts in order to re-find and re-understand his philosophy show that Brentano has many valuable ideas in many different areas of philosophical investigations. These efforts show, more precisely, that his thoughts can still be a significant starting point for philosophical inquiry. Brentano’s works, like other influential philosophers’, covers a wide range of philosophical subjects including philosophical psychology, ontology, epistemology, syllogistic logic, ethics, philosophical theology, history of philosophy and many others. This article only focuses on the Brentano’s impact on syllogistic logic. His revision of formal logic has been done around the axis of a fundamental thesis according which all of the subject-predicate judgments should be reduced to existential judgments. We will explore, in this article, the procedure of this thesis development in Brentano’s thought and also its consequences for syllogistic logic. To have a complete understanding of Brentano’s revision of Aristotelian logic, it is required to have some acquaintances with several subjects not directly related to formal logic; e.g. ontology and epistemology.

One of the most important applications of Gödel's completeness theorems is based on their roles the arguments of impossibility of formalization of human mathematical mind in capture of an algorithm or a finite formal system. Two main arguments have been proposed in this way of reasoning. In both of these arguments, it has been claimed that: the fact according to which human being can understand the truth of the unprovable Godelian sentence, shows the superiority of human being’s ability in mathematical reasoning to all machines’. But there are some important debates on both arguments. After explaining these two arguments, we will investigate the extensive contentions and challenges between mechanists and anti-mechanists. By explaining and analyzing Godel's incompleteness theorems and their connection to human arithmetical knowledge, we will show that there is no plausible argument, based on Gödel's incompleteness theorems, which can show the superiority of human being’s ability in mathematical reasoning to the machines’.

Aristotelian deduction rules, which are usually considered as “THE RULES OF THE CATEGORICAL SYLLOGISM” in the elementary logic text books, are proper tools which help beginners in logic to examine the validity of a categorical syllogism. Authors of Persian logic text books, influenced by the authors of English logic text books, rewrite these rules with only some minor changes and revisions in their books and apply them for the same aim. These revisions depend on many different factors including the authors’ personal interests and those English logic text books which were his main reference. The main aim of this article in the first step is to provide an analytical method for formalizing the rules of deduction which can lead us to find a mechanical and algorithmic method and in the next step, is to follow this computable and formal approach to analyze and criticize the deduction rules in Persian logic text books. In addition to categorizing “The rules of the categorical syllogism”, we will propose a new version of such formalized rules by appealing to the concept of “distribution”.