نشریه منطق پژوهی
سال دوازدهم شماره 1 (بهار و تابستان 1400)

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.

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.

Although there are some differences about how to define or explain the concept of possibility, all ancient and recent logicians consider it as one of the modal operators in logic and philosophy. However, Kashi`s description of the concept is rather different. As a prominent student of Fakhr Razi, in “Hadaiq al-Haqaiq” he claims that other philosophers before him have defined possibility as denying the necessity of truth or falsehood of a proposition, though the consensus was on the denying of the necessity of the negative side. In this paper, by reviewing other philosophers` and logician`s ideas about the concept of possibility, we reflect on Kashi`s definition and claim that in this subject, he was under the influence of Fakhr Razi`s ideas in “al-Molakhas” and “Sharh Isharat”.

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.

The idea of ideal language is one of the most important and central issues in analytic philosophy. The major philosophers of the first stream of analytic philosophy, which began with Frege and developed in Russell and early Wittgenstein and logical positivists, not only welcome this idea, but also pursue its realization as a central goal. But the idea of the ideal language was declined by the second stream of analytic philosophy, which is also inspired by Frege's work and ideas and developed in Moore and later Wittgenstein. Here I will try, first, to show the influence of the classical modern philosophers (Descartes, Leibniz, and classical empiricists) on the philosophers of the first stream in development of the idea of the ideal language, and second, to explain how both streams -the first in supporting and the latter in rejecting the idea of the ideal language – were under the influence of aspects of Frege's thought about sense and its relation to reference, and finally to show the role of later Wittgenstein's view on the meaning and his concept of "family resemblance" in declining the idea of “ideal language”.

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.

In his famous article “What the Tortoise Said to Achilles”, Carroll explained how adding logical rules as propositions to an argument causes an infinite regress in the inference and makes the conclusion far from reach. As a solution, some logicians propose to consider logic as dispositional knowledge. Logical dispositions are potentialities that in presence of certain situations manifest as certain actions. An agent, who is familiar with logic, when facing an argument, reveals their ability and deduce. In defending the dispositional approach, some consider logic as a part of a universal language or as the language of thought; in this way knowing logic like knowing a language is considered as having some dispositions. In this paper, we show logic is not part of the universal language, since we could have several and different logics. Although the dispositional approach could prevent Carroll’s regress, it cannot explain some basic features of logic such as its apriority. Dispositions are neither a priori nor a posteriori, but logic is always considered as an archetype of apriority. Also, we can explain actions in accordance with logical rules as actions that are motivated by propositional knowledge we have; logic provides reason to act logically. Therefore, in presence of better explanations for the propositional approach and some disadvantages of the dispositional approach, the latter seems unsatisfactory.

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.

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.

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.

From the time physicists have proposed the quantum logic, this logic is formed somehow in relation with quantum mechanics and experiences based on it. In fact, quantum mechanics and experiences gained from it assumed an approval to this logic. One of the highlights of the quantum mechanics, is uncertainty principle, which is a doctrine to reject the divisibility in quantum logic. Also EPR is assumed as a doctrine to reject the quantum mechanics. In the case of rejection of quantum mechanics, does the quantum logic also be questioned? In this paper it is shown that the uncertainty principle is rejecting the divisibility principle and EPR The aim of this study is to show that the uncertainty principal rejects divisibility principal, and hidden-variable theory which comes after EPR paradox, known as a rival theory, (even in the case of rejection of standard quantum mechanics) doesn’t reject the quantum logic. The outcome of this is that in practice quantum logic is independent of quantum mechanics, and it might be applied in areas other than quantum mechanics.

Avicenna (Ibn Sīnā's) discusses in detail the modality and modal syllogistic, in his logical books. The earliest formal system of modal logic was developed by Avicenna, who ultimately developed a theory of "temporally modal" syllogistic. However, referring to his works, there is a kind of ambiguity in the meaning of narrowest possibility. Some Western logicians have also reported such ambiguity, sometimes leading to misunderstandings. Therefore, knowing the exact meaning of the narrowest possibility from Avicenna's perspective is important. In the book of Healing (Kitāb al-Shifā, Kitāb al-Burhan), it becomes clear that his definition of the narrowest possibility is the same as the definition of a future possibility. In the book of Oriental logic (Mantiq Al-Mashriqiyin) and the book of Pointers (Al-Isharat wa’l-Tanbihat), the narrowest possibility and future possibility are defined separately, but the definitions provided do not completely coincide. Two strategies will be proposed to resolve this ambiguity. Finally, it seems that there is no real distinction between the narrowest possibility and future possibility.