Kamran Ghayoomzadeh
Abstract
Aristotle with introducing Modal logic in Organo and Essentialism and Essence in Organon and Metaphysics was one of the vanguard in metaphysical and logical challenging discussions. One of the most important subjects in history of logic and Aristotle’s philosophy is a presentation of consistent ...
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Aristotle with introducing Modal logic in Organo and Essentialism and Essence in Organon and Metaphysics was one of the vanguard in metaphysical and logical challenging discussions. One of the most important subjects in history of logic and Aristotle’s philosophy is a presentation of consistent interpretation of Aristotle’s modal logic and conforming it with accounts of Aristotle’s essentialism in Organon and Metaphysics. This interpretation and commentary is penetrating inside Aristotle’s remarks and comparing it with modern philosophy. In this Article, we criticize one of the interpretations in ‘de re’ and ‘de dicto’ form and then introduce a new other interpretation, which was exposed by Richard Patterson, with two substantial feature. The first feature is pertaining to the consistency of Aristotle’s modal logic. We can say this interpretation is the best explanation about this consistency among other interpretations. The second feature is coincidence between this interpretation with Aristotle’s essentialism in Metaphysics. We examine and then confirm that this interpretation with instruments of ‘strong necessity’ and ‘weak necessity’ in modal syllogisms with two necessity premises.
MohammadJavad Kiani Bidgoli
Abstract
From ancient Greece to the world today, the problem of induction has preoccupied the minds of thinkers, especially logicians and philosophers. The use of induction in various fields has multiplied the importance of the matter. There are different answers to this problem; Since induction has always been ...
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From ancient Greece to the world today, the problem of induction has preoccupied the minds of thinkers, especially logicians and philosophers. The use of induction in various fields has multiplied the importance of the matter. There are different answers to this problem; Since induction has always been considered as another type of argument alongside deduction, and deduction is justified by almost all logicians, some have tried to justify induction as a deduction; On the other hand, some groups have tried to resemble deduction and induction by discrediting and taking the validity of deduction. Other people have taken a different view of the issue and some have ruled out the issue. In this article, while stating the problem and the answers are given to it and categorizing the contents, we will deal with an answer from the second group and present and translate an article by Susan Haack, which is about justifying deductive reasoning. In her article, Susan Hawke, while expressing the challenges of induction, tries to contrast these challenges with deduction and show that deduction, like induction, has problems but has been freed from them by assuming some things, and he examines these presuppositions.
saeed Anvari
Abstract
منطقدانان قرون وسطی برای ضربهای منتج قیاس اقترانی حملی اسامی اختصاری انتخاب کرده بودند. این اسامی به نحوی انتخاب شده بود که نوع قضیة محصورة به کاررفته در صغری و کبری ...
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منطقدانان قرون وسطی برای ضربهای منتج قیاس اقترانی حملی اسامی اختصاری انتخاب کرده بودند. این اسامی به نحوی انتخاب شده بود که نوع قضیة محصورة به کاررفته در صغری و کبری و نتیجة قیاس را مشخص کرده و نشان میداد که ضربهای منتج اشکال دوم تا چهارم از چه طریق، به ضربهای شکل اول بازمیگردند و نیز روش رد و تبدیل ضربهای منتج آن اشکال به شکل اول چگونه است. به عنوان مثال نام ضرب اول قیاس، باربارا (Barbara) است. حروف صدادار به کار رفته در این اسم، بیانگر نوع قضیة محصورة در مقدمات و نتیجة این ضرب از قیاس است. در این مختصر این اسامی اختصاری و نکات مرتبط با آنها توضیح داده شده است. همچنین علت متفاوت بودن این اسامی در مورد شکل چهارم بیان شده و به تاریخچة تغییرات این اسامی در مورد شکل چهارم اشاره شده است. در پایان مقایسهای میان این روش و روش استفاده از قواعد کلی انتاج توسط منطقدانان مسلمان صورت گرفت و مزایا و معایب هر یک از این دو روش بیان گردید.
Meghdad Ghari
Abstract
In this note, we study the effect of adding fixed points to justification logics. By making use of the fixed point operators (or diagonal operators) introduced by Smorynski in his Diagonalization Operator Logic, we introduce fixed point extensions of Fitting's quantified logic of proofs QLP. We then ...
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In this note, we study the effect of adding fixed points to justification logics. By making use of the fixed point operators (or diagonal operators) introduced by Smorynski in his Diagonalization Operator Logic, we introduce fixed point extensions of Fitting's quantified logic of proofs QLP. We then formalize the Knower Paradox and various self-reference versions of the Surprise Test Paradox in these fixed point extensions of QLP. By interpreting a surprise statement as a statement for which there is no justification or evidence, we propose a solution to the self-reference version of the Surprise Test paradox. We show that one of the axioms of QLP (the Uniform Barcan Formula) could be the reason for producing contradiction in these paradoxes, and thus by rejecting this axiom we can avoid contradiction in the aforementioned paradoxes. By introducing Mkrtychev models for the fixed point extensions of QLP, we further show that these fixed point extensions (without the Uniform Barcan Formula) are consistent.
Amer Amikhteh; Seyyed Ahmad Mirsanei
Abstract
In this paper, a non-classical axiomatic system was introduced to classify all moods of Aristotelian syllogisms, in addition to the axiom "Every a is an a" and the bilateral rules of obversion of E and O propositions. This system consists of only 2 definitions, 2 axioms, 1 rule of a premise, and moods ...
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In this paper, a non-classical axiomatic system was introduced to classify all moods of Aristotelian syllogisms, in addition to the axiom "Every a is an a" and the bilateral rules of obversion of E and O propositions. This system consists of only 2 definitions, 2 axioms, 1 rule of a premise, and moods of Barbara and Datisi. By adding first-degree propositional negation to this system, we prove that the square of opposition holds without using many of the other rules of classical logic (including double negation elimination). We then show that the Propositional Substructural Logic SLe is the best logic to study Aristotelian Syllogisms. Also, based on the IFLe square of opposition, the rules of conversation and the rules of negation are completely proved in Muzaffar's logic. For this purpose, we used the monadic first-order logic with the same standard deductive apparatus of quantifiers in classical logic, plus the axioms of "some a is an a" and "some not-a is a not-a". Finally, to show that there is no existential commitment to general terms in categorical logic, the Strong Four-Valued Relevant-classical Logic KR4 was used. With the same existential interpretation of the quantifiers and the standard translation of the quarter quantified.
Seyed Mohammad Amin Khatami; Esfandiar Eslami
Abstract
In the early 19th century, the ''principle of bivalence'' of the Aristotelian logic was challenged. Of course, Aristotle himself was questioned the applicability of this principle to propositions concerning future contingents, and he answered it via something like as modalities of possibility. However, ...
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In the early 19th century, the ''principle of bivalence'' of the Aristotelian logic was challenged. Of course, Aristotle himself was questioned the applicability of this principle to propositions concerning future contingents, and he answered it via something like as modalities of possibility. However, Aristotle did not abandon the principle and it has not received much attention till the Renaissance. From Renaissance to the early 19th century, some philosophical considerations to this issue were developed. Rejecting the principle of bivalence implies alternative accounts of various kinds of logics such as many-valued logics in the context of logic. In this article, we first survey the development of many-valued logics by reviewing motivational ideas behind many-valued logics together with examining the aims and scopes of some of these logics. Then, we devote the rest of the paper to study various aspects of "truth value sets" and "interpretation of logical connectives" in many-valued logics to obtain a more comprehensive view on these logics.
