Amer Amikhteh; Lotfollah Nabavi
Abstract
The uninorm logic UL is a fuzzy, substructural and semi-relevant logic. The Gentzen-style system for UL is obtained by removing the contraction rules and weakening from the Gentzen-style system of Godel fuzzy logic. The UL lacks "excluded middle", "positive paradox" and "negative paradox". The truth ...
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The uninorm logic UL is a fuzzy, substructural and semi-relevant logic. The Gentzen-style system for UL is obtained by removing the contraction rules and weakening from the Gentzen-style system of Godel fuzzy logic. The UL lacks "excluded middle", "positive paradox" and "negative paradox". The truth function of uninorm is a relevance weakening of the t-norm function. In this article, we introduce the new logic ULΔ. ULΔ is obtained by adding Δ to UL. ULΔ, an expansion of classical logic, is a normal semilinear modal logic; i.e. it is strongly sound and complete w.r.t. a linearly ordered algebra. And with the theorem of (p→q)∨Δ(q→p) it is distinguished from other standard systems of modal logic. Δφ is intuitively interpreted as "true that φ" or more precisely "classically true that φ". In this paper, we introduce the semi-classical logic ULΔ with four approaches, axiomatizations, hypersequent calculi, algebraic semantics and standard semantics. metatheorems we are considering include Delta deduction, strong soundness, strong standard completeness and definability of classical logic.
Mahdi Azimi
Abstract
In Priori Analytics, II. 25, Aristotle proposes a sort of reasoning called apagpge. Scholars differ about its translation, definition, and formulation. Ross believes that it is a semi-demonstrative, semi-dialectical first-figure syllogism, with a probable conclusion derived from a more probable minor ...
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In Priori Analytics, II. 25, Aristotle proposes a sort of reasoning called apagpge. Scholars differ about its translation, definition, and formulation. Ross believes that it is a semi-demonstrative, semi-dialectical first-figure syllogism, with a probable conclusion derived from a more probable minor premise and apodictic major premise, which is applicable as a method of discovery. Peirce holds that it is same as Abduction, or an anticipation of it. But Farabi, without any discussion about apagoge, put the Arabic translation of epagoge, i.e. induction, in the place of apagoge, which inspire the hypothesis that apagoge in Priori Analytics, II. 25 is distortion of epagoge. On my analysis, Peirce and Farabi’s interpretations both are abductions that, assuming strangeness of Priori Analytics, II. 25, propose explanatory hypotheses apposite to economy and consistency, while Ross rejects the assumption at all. Peirce’s theory on the Aristotelian origin of abduction, with its problems and alternatives, would be questionable; and this result may be important for the Histories of Logic and science.
Masoud Alvand; Morteza haji Hosseini; Amir Karbasi zadeh
Abstract
classical logic has had some problems in explaining issues such as semantic paradoxes, vagueness problem, and quantum phenomena and have led logicians to seek non-classical logical formulations in which such problems do not arise. However, the undeniable growth of mathematics and its widespread influence ...
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classical logic has had some problems in explaining issues such as semantic paradoxes, vagueness problem, and quantum phenomena and have led logicians to seek non-classical logical formulations in which such problems do not arise. However, the undeniable growth of mathematics and its widespread influence in other disciplines has often led non-classical logicians to emphasize adherence to mathematical reasoning with the principles of classical logic by separating mathematical reasoning from non-mathematical. Against this approach, Williamson shows that the strategy of separating mathematics from non-mathematics and adhering to non-classical logic in non-mathematical fields disrupts the applicability of mathematics, and non-classical logicians need to think about solving this problem. In this essay, while expressing Williamson's arguments on the tension between advocating non-classical logic and the applicability of mathematics and emphasizing some of them, we show that, unlike Williamson, scientific activity based on deductive inference does not follow classical logic completely and therefor the tension sometimes subsides.
GHOLAMALI MOGHADDAM
Abstract
The separation of ontological issues from ontology is one of the most important issues in epistemology. The rules of logic are responsible for analyzing and explaining the laws of detection Unknown conception and Unknown ratification. In traditional logic, the proposition, as the subject of the logic ...
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The separation of ontological issues from ontology is one of the most important issues in epistemology. The rules of logic are responsible for analyzing and explaining the laws of detection Unknown conception and Unknown ratification. In traditional logic, the proposition, as the subject of the logic of assertion, is Logical Secondary intelligible and has a formal and anecdotal truth. Formal logic is responsible for providing the instruments of composition between the theorems. The theorem content, the type of its connection with outside world and its Semantic issues are outside from this domain. It seems that the modal discussions in traditional logic, in some cases, have provided the interference of matter and form and entry of some objective rules into the subjective proposition. Actuality, permanence and faculty are Different from the formal. These are related to the process of objective objects in the external world. Adding these modals to the theorem structure has caused confusion, complexity, discrepancy, and ambiguity in traditional modal logic. In this article, we have demonstrated by analytical way that traditional logic can be criticized for adding modals to the proposition structure and, and for limiting the modal logic in certain modals.
Seyyed Mohammad Ali Hodjati; Kasra Farsian
Abstract
Dialetheism is the view that some (and not all) contradictions are true. Since in classical logic the principle of impossibility of contradiction (the Law of Non-Contradiction, i.e., LNC) is widely accepted, the challenge between dialetheism and classical logic surely occurs. In this paper we have tried ...
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Dialetheism is the view that some (and not all) contradictions are true. Since in classical logic the principle of impossibility of contradiction (the Law of Non-Contradiction, i.e., LNC) is widely accepted, the challenge between dialetheism and classical logic surely occurs. In this paper we have tried to explain the main problem of dialetheim and also examined Graham Priest’s arguments against LNC and his advocating to paraconsistent logic. Accordingly, Priest’s examples of dialetheic propositions in some systems such as Law, Natual and Formal Languages and Actual world are examined and criticized. The result is that if Priest’s argument be sound dialetheism may be acceptable. Dialetheism is the view that some (and not all) contradictions are true. Since in classical logic the principle of impossibility of contradiction (the Law of Non-Contradiction, i.e., LNC) is widely accepted, the challenge between dialetheism and classical logic surely occurs. In this paper we have tried to explain the main problem of dialetheim and also examined Graham Priest’s arguments against LNC and his advocating to paraconsistent logic. Accordingly, Priest’s examples of dialetheic propositions in some systems such as Law, Natual and Formal Languages and Actual world are examined and criticized. The result is that if Priest’s argument be sound dialetheism may be acceptable.
mohammad amin baradaran nikou; gholamreza zakiany; malek hoseini; hasan miandari
Abstract
The structure of Aristotle’s Science is deductive. It needs the premises that cannot be deduced. Therefore, knowledge of the premises of science is an important stage in scientific research. Aristotle, in Analytics and Topics, suggests induction and dialectic for this stage. Aristotle's ...
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The structure of Aristotle’s Science is deductive. It needs the premises that cannot be deduced. Therefore, knowledge of the premises of science is an important stage in scientific research. Aristotle, in Analytics and Topics, suggests induction and dialectic for this stage. Aristotle's commentators disagree about this. For example, Bolton prefers induction and Irwin prefers dialectic. Aristotle, according to Bolton’s interpretation, is an empiricist; he starts his researches from particular sense data and then discovers the general principles of science by induction. Irwin believes that scientific researches of Aristotle, as a rationalist philosopher, begins from special kind of reputable opinions (ενδοξα) and then the principles of science are known by a specific dialectic. This paper shows the differences between two interpretation of Bolton and Irwin; observing the issue of the methodology for recognizing the principles of science. Then, we investigate some important difficulties of their interpretations and, finally, suggest some ideas for a better interpretation.
Parisa Shakourzadeh; Abdurrazzaq Hesamifar
Abstract
This article studies the possibility of talking about ontology in Wittgenstein’s Tractatus Logico- Philosophicus. In the first step, we will consider various earlier readings of the first part of book, so called the "world" part and we will examine the theories of advocates and opponents of this ...
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This article studies the possibility of talking about ontology in Wittgenstein’s Tractatus Logico- Philosophicus. In the first step, we will consider various earlier readings of the first part of book, so called the "world" part and we will examine the theories of advocates and opponents of this idea that tractatus includes some ontological views. In the next step, by analyzing and comparing the sentences of the first part of the book, we will try to gain an explicit understanding of the concept of world and other ostensibly ontological categories. After studying two prominent concepts of objects and facts, the findings of the inquiry suggest that the ontological and realistic readings of book are wrong and what they recognize as ontological part of the book, is actually a discussion about logic. ThusThe world in Tractatus is the logical space and the territory of thought, not our actual and concrete world as it seems initially.
Mohammad Saeedimehr; Ahmad Hosseini Sangchal
Abstract
Before offering his own theory of the logical predication, Sadr al-Din Dashtaki first criticizes two alternative theories; the first interprets logical predication as the attribution of something (predicate) to something (subject), and the second takes it as expressing the conceptual difference between ...
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Before offering his own theory of the logical predication, Sadr al-Din Dashtaki first criticizes two alternative theories; the first interprets logical predication as the attribution of something (predicate) to something (subject), and the second takes it as expressing the conceptual difference between the subject and the predicate and their essential identity. He then proposes the “conventional difference and existential identity” as the criterion of the logical predication. This theory is constituted of several elements including his peculiar analysis of the derivative words. Dashtaki discovers that both theories of simplicity and complexity of the derivative words are inconsistent with his theory of predication and thus, introduces a new analysis of the derivative words. This analysis pays way to differentiating between attribution of the root to the subject and the identity of subject and predicate. This complex net of principles helps Dashtaki to provide a plausible analysis of special sorts of propositions like existential propositions and hypothetical propositions (la Batti).
Mohammad Golshani; Omid Etesami; Shahram Mohsenipour
Abstract
Cohen’s method of forcing is one of the main tools in set theory for constructing models of ZFC. In this paper, we consider different methods of introducing forcing, and show that they are all equivalent. First we introduce the method of forcing using partial orders and state some of its basic ...
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Cohen’s method of forcing is one of the main tools in set theory for constructing models of ZFC. In this paper, we consider different methods of introducing forcing, and show that they are all equivalent. First we introduce the method of forcing using partial orders and state some of its basic properties. Then we consider the method of Boolean-valued models and show that it is equivalent to the first approach using partial orders. We do this by showing that each forcing notion can densely be embedded into a complete Boolean algebra. Then we introduce the topological approach to forcing and compare it with the partial order approach to forcing. We show that the forcing relation defined in a topological manner is the same as the forcing relation defined using partial orders and hence these two methods are essentially identical. Finally we consider the categorical approach to forcing and compare it with the method of Boolean-valued models. We show that for a given complete Boolean algebra, the category of sheaves over it is essentially the same as the Boolean-valued model constructed using that Boolean algebra.
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
Medieval logicians chose acronyms for valid syllogism moods. These names were chosen in such a way as to determine the type of propositions used in the minor and major premises and the result of the syllogism. Moreover, it showed how the valid moods of the second to fourth figure return to the moods ...
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Medieval logicians chose acronyms for valid syllogism moods. These names were chosen in such a way as to determine the type of propositions used in the minor and major premises and the result of the syllogism. Moreover, it showed how the valid moods of the second to fourth figure return to the moods of the first figure and the method of rejecting and converting the valid moods of those figures to the first figure. The vowels used in this name indicate the type of proposition. For example, the name of the first mood of the analogy is Barbara. The vowels used in this acronym indicate the type of proposition enclosed in the premises and the conclusion of these moods of syllogism. In this article, these acronyms and their related points are explained. Also, the reason for the difference of these names is stated in the fourth figure, And the history of the changes of these names is mentioned in the fourth figure. Finally, a comparison between this method and the method of using the general rules of inference by Muslim logicians has been made, And the advantages and disadvantages of each of these two methods are stated.
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.
Seyyed Ammar Kalantar
Abstract
In this article I discuss Aristotle’s view on εστί (“is”) being a verb in de interpretaine and the significations which he explicitly attributes to “is”, and in several points the views of some of Aristotle’s commentators, including Ammonius, Boethius, ...
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In this article I discuss Aristotle’s view on εστί (“is”) being a verb in de interpretaine and the significations which he explicitly attributes to “is”, and in several points the views of some of Aristotle’s commentators, including Ammonius, Boethius, al-Farabi, and Aquinas, are reported and criticized. Therefore, first Aristotle's definition of verb is examined, including its most important feature, “additionally signifying time”. In fact, "is" is due to having this feature is a verb, and thus the first signification of "is" becomes clear. After that, I discuss other two significations of "is", namely “additionally signifying combination” and "determination of truth", and the relation of these three significations to each other. Finally, it is concluded that according to Aristotle, "is" (with two objects) does not signify a categorical thing, but only additionally signifies combination. And since "is" is additionally signifying time, it can be said that for Aristotle in de interpretaione "is" is additionally signifying temporal combination.
