Traditional Logic
Seyed Ammar Kalantar
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 ...
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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.
Standard Mathematical Logic
amir khamseh
Abstract
Hindman’s Theorem states that for every coloring of natural numbers N with finitely many colors, there is an infinite set H such that the set of numbers which can be written as a sum of distinct elements of H is monochromatic. On the other hand, Brauer’s Theorem states that for all r,l,s≥1, ...
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Hindman’s Theorem states that for every coloring of natural numbers N with finitely many colors, there is an infinite set H such that the set of numbers which can be written as a sum of distinct elements of H is monochromatic. On the other hand, Brauer’s Theorem states that for all r,l,s≥1, there exists t=t(r,l,s) such that if the interval [1,t] is r-colored then there exists a,b>0 such that the set \{a,b,a+b,a+2b,…,a+(l-1)b\}⊆[1,t] is monochromatic. If A and B are sets, FS^A (B) is the set of all sums of j-many distinct elements of B, for all j∈A. Hindman-Brauer Theorem is the following statement: for every r-coloring of the set of natural numbers N, there is an infinite set H⊆N and a,b>0 such that FS^(\{a,b,a+b,a+2b,…,a+(l-1)b\}) is monochromatic. In this paper, we study the finite version of Hindman-Brauer Theorem and also Hindman-Schur Theorem and show that these results are provable in first order Peano Arithmetic. Also, we will see that these results are provable if we consider the apartness condition.
Gholam Ali Hashemifar; Mahdi Azimi
Abstract
Even though the principle of non-contradiction is one of the most important principles governing philosophy, especially since the time of Aristotle, some people have gone against this principle and challenged it. The present study mainly aims to show the historical course of the dialethism and the solutions ...
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Even though the principle of non-contradiction is one of the most important principles governing philosophy, especially since the time of Aristotle, some people have gone against this principle and challenged it. The present study mainly aims to show the historical course of the dialethism and the solutions provided by the dialetheists to believe in the possibility of the sum of contradictions from ancient times until now. The present study aims to show the historical course of the dialethism and the solutions presented by the dialetheists to believe in the possibility of the sum of contradictions. The main problem of this research is that what arguments and solutions have the prominent opponents of the principle of refusal of contradiction presented for their point of view, and it has used the descriptive method and critical analysis to reach the answer to this problem. In order to outline the thought process of defense of dialethism, first the background of the principle of non-contradiction is examined. Then, dialethism and its relationship with trivialism will be discussed, and after that, the background dialethism from ancient Greece to modern times will be reported in detail. The explanation of the logic of dialethism will be the end of this work.
Analytical Philosophy
Seyyed Mohammad Ali Hodjati; MOhammad Hassan Arjmandi
Abstract
The “Frege-Geach problem” is one of the most challenging problems against the non-cognitivist view. The crisis is rooted in Ayer’s view. While affected by the main thesis of logical positivists –i.e., the verifiability principle, Ayer showed that moral propositions are neither ...
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The “Frege-Geach problem” is one of the most challenging problems against the non-cognitivist view. The crisis is rooted in Ayer’s view. While affected by the main thesis of logical positivists –i.e., the verifiability principle, Ayer showed that moral propositions are neither analytic, necessarily true, nor experimental so that their truth rests on reality. He concluded that such propositions are deprived of propositional content and so truth-valueless. His suggested semantics is widely accepted among moral non-cognitivists and today is called ‘nonrepresentational semantics’, one of the negative principles in non-cognitivism. Using the linguistic-logical approach, Searle and Geach, independent from each other, formalized a problem by which non-descriptive semantics for moral judgments fundamentally have undergone criticism. However, this was not the end of the story since the process of responding to the challenge showed that the main source of the problem does not reside in what Geach said, but is rooted in a conspicuous semantics of complex moral judgments in which the moral judgments are embedded. Hence, the problem has confronted a more complicated form, the ‘embedded problem’.
Traditional Logic
davood heidari
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 ...
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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.
Philosophy of Logic
Majid Zamani Alavijeh
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 ...
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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.
Morteza Moniri
Abstract
In recent years, some books on the philosophy of mathematics have been translated into Persian. Unfortunately, in some cases, these translations are insufficient and even misleading. It seems that reviewing and criticizing these translations can help to correct and improve this situation. In this article, ...
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In recent years, some books on the philosophy of mathematics have been translated into Persian. Unfortunately, in some cases, these translations are insufficient and even misleading. It seems that reviewing and criticizing these translations can help to correct and improve this situation. In this article, after a brief review of the book "Philosophy of Mathematics" written by Colyvan, we will give a selective review of the translation of this book. Colyvan’s book Philosophy of Mathematics is an introductory text in the field of philosophy of mathematics. This book was written for both undergraduate and graduate courses in universities in Australia and the United States of America. Although the main audience of this book is philosophy students, it seems that it does not require much philosophical prerequisites and it can be used for mathematics students as well. The references for the translation and the original text are as follows:Colyvan, Mark (2017). An Introduction to the Philosophy of Mathematics, translated by Cumrun Shahbazi, Tehran: Naqd Farhang.Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics.
Standard Mathematical Logic
Katayoon Mehrabadi
Abstract
The validity of any argument depends on its compatibility with logical rules. Some arguments have a form of proof; But they have some types of logical errors inside, that is, they are pseudo-arguments; not proof. Theological works, as texts that have seemingly logical and valid arguments, are worthy ...
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The validity of any argument depends on its compatibility with logical rules. Some arguments have a form of proof; But they have some types of logical errors inside, that is, they are pseudo-arguments; not proof. Theological works, as texts that have seemingly logical and valid arguments, are worthy of evaluation in this regard. Therefore, logic provides a suitable scientific tool for validating them. In this research, three arguments from the book Kashf al-Mahjub are examined. This review is done both from the syntactic point of view, based on the first-order logic, and from the semantic point of view and deduction's materials. Finally, by specifying formal and semantic fallacies as well as determining the types of deductions of the arguments, it is shown that Hojwiri knew and mastered the principles of logic, and considered himself obliged to comply with its rules; But sometimes it has not been free from fallacies. It also turns out that his arguments are sometimes downgraded from argument to lecture.
Philosophical Logic
Mojtaba Afsharpour
Abstract
Aristotelian logicians proposed the interrelation of definition and argument as a solution to the challenge of recognizing the true essence of things and the lack of epistemological value in complete definitions. Mulla Sadra's emergence and his theory of the ideality of quiddity further highlighted this ...
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Aristotelian logicians proposed the interrelation of definition and argument as a solution to the challenge of recognizing the true essence of things and the lack of epistemological value in complete definitions. Mulla Sadra's emergence and his theory of the ideality of quiddity further highlighted this epistemological challenge. Understanding essence in its conventional sense does not lead to understanding the reality of an object, because species and genus are quiddity, whereas the reality of an object is its existence. Therefore, the pursuit of knowledge of species and essence is epistemologically worthless and cannot lead us to the reality of an object in the conceptual realm. However, the founder of Transcendent Wisdom also speaks of the interrelation of definition and argument in his various works, describing the definition and argument of an object as a bridge to each other. This article, using an analytical-descriptive method, seeks to answer the question: How does Mulla Sadra, who rendered complete definitions ineffective in recognizing the reality of objects and considered essence and its attributes as mental constructs, grant epistemological value to the interrelation of definition and argument? and concludes that by differentiating between essential and existential definitions, interpreting the existential definition as knowledge of the realization of being, providing an existential analysis of species, and substituting the knowledge of the realization of being for knowledge of the species and essence in definition of the essential nature, Sadra successfully grants epistemological value to the interrelation of definition and argument.
