نشریه منطق پژوهی
سال دوازدهم شماره 2 (پاییز و زمستان 1400)

Some objections to the mental existence that are proposed by the western philosophers are almost unknown to Muslim philosophers and therefore have not received flawless response yet. For example, the complicated formulae objection, being one of the most important and difficult of them, says that since no man can imagine the complicated things, they cannot be in our minds. The mental existence difficulties arising from the complicated things are of several kinds. Sometimes we must remember a complicated thing by means of memory and imagine it in our minds. Sometimes too we must first imagine a complicated argument, that is so long, in our minds to then have logical certainty about it. And sometimes too a complicated argument is so long that no ordinary man can imagine its details in his entire life and therefore it is only of computer-assisted proof. We will investigate here the very three kinds – that are connected with memory – and will try to analyze them mostly based on the views of Muslim thinkers. After criticizing the actual and potential views of Muslim philosophers, we will propose our own views about the three kinds in the end. On the suitable occasions, we will response to the possible objections too.

This article is concerned of the problem that weather Tarski’s definition of the ‘logical consequence’ in his seminal article ‘On the Concept of Logical Consequence’ (1936), as his article claims, captures the common concept of logical consequence or not. First of all, for understanding what defect had prevailing approach of logical consequence (proof- theoretical approach) that led him to attempt to present new definition of concept of logical consequence, I introduce proof-theoretical approach to logical consequence and examine its default and then explain two interpretations of his definition of the common concept of logical consequence. the First interpretation is that the common concept of logical consequence is the concept that all of ordinary and non-professional peoples in philosophy, logic and mathematics use. the Second interpretation is that what Tarski means by the common concept of logical consequence is the concept that for professional peoples in logic and mathematics is ‘common’ and already used in axiomatics. I defend the second interpretation and after descriptive-analytic examination of his suggested definition of this concept and presentation of example of it, I finally conclude that Tarski in his attempting for capture of the common concept of logical consequence has succeeded.

The Unity of the Encoding PropositionAbstract: There is a family of problems under the rubric of “the unity of the proposition”. They ask how is it that (ordinary) propositions are unit wholes over and above their constituting parts, how is it that they are representational and have truth values. In this paper, we propose the very same concern regarding the Meinongian encoding propositions; those propositions that contain the encoding mode of predication rather than the ordinary exemplificational predication. Embracing such a dual mode of predication lets us interpret propositions such as “the round square is round” not only as meaningful but also as true propositions. We demonstrate how to reduce exemplification to encoding. This should dissolve the classical problem of the propositional unity, yet providing a rather new formulation of it.

In his article "Truth", Peter Strawson, following Ramsey, raises the issue of the redundancy of the theory of truth. He considers the utterance of sentences containing the truth predicate to do something, and in his idiomatic sense, he does not consider it constative, but performative. Performative utterances are not true or false, but are characterized by felicitous or infelicitous, and are actions or deeds, not propositions or descriptions. Thus, in this article, after mentioning Strawson's critiques of the theory of truth and explaining his performative theory of truth and explaining Austin's performative utterances, we will deal with the three critiques of Strawson's conception and then examining the relationship between linguistic meaning and the performative theory of truth and explaining systematical of meaning, we prove that not just Strawson's performative theory of truth is incorrect, but that the conception of performative uses of language can also be defective. In this sense, the ordinary language philosophers also exaggerated the extent to which performative sentences are different from ordinary non-performative sentences. These philosophers mistakenly assumed that performative sentences do not represent descriptive and ordinary propositions that provide the sentences with straightforward truth conditions.

Predication is one of the main instruments in Logical analyses. Among all kinds of predication, ḥaml al-shay’ ‘alā nafsihī (predicating a thing of itself) is considered a contentious one in Islamic philosophy. One of these is what we can name by the help of post-Ṣadrīan terminology taking ḥaml al-shay’ ‘alā nafsihī as awwalī predication or take it as shāyi‘ predication, or by the help of mathematical terms, taking ḥaml al-shay’ ‘alā nafsihī as tautology. But with close inspection in Islamic predecessor’s ideas we can understand that it is naïve to think that ḥaml al-shay’ ‘alā nafsihī can be simply fallen under any of these kinds: awwalī predication, shāyi‘ predication, or tautology. In this article we try to show the problems of enforcing this predication into the framework of all the aforementioned predications. In our analyses, I am using “mā bihī al-ittihād” and “mā bihī al-Ikhtilāf” as two necessary conditions of each predication accepted by almost all of the Islamic thinkers, and used by them as a criteria for analyzing predications.

Common nouns, in most natural languages, are divided into two categories: Count nouns and mass/noncount nouns. There are both syntactical and semantical distinctions between mass terms and count terms. However, among these distinctions, a syntactical distinction is the most obvious. Mass nouns are modified by numerals. For example, in English, we can talk about “two dolphins” or “three trees.” but we can not speak about “bronze” and “water” in this way. On the semantic side, according to objectual interpretation, an individual object—a dolphin— can satisfy “x is a dolphin.” But an individual object can not satisfy “x is water.” At least in most times, a collection of particles, drops, molecules —and so on—can satisfy that sentence. A central question here is that what is the nature of this “collection”? Is this collection an abstract set or a concrete mereological fusion? Accordingly, there are two approaches based on set theory and mereology. First, in this paper, I considered challenges faced by these two approaches, then I showed that the mereological-based approach with some modifications would overcome these challenges.

Our main goal in this paper is to find modal companions for some subintuitionistic logics introduced by de Yongh and Shirmohammadzadeh. They introduced two types of neighbourhood frames, N-neighbourhood frames and NB-neighbourhood frames, in order to prove the completeness of these subintuitionistic logics. The structure of N-neighbourhood frames are similar to the neighborhood frames for non-normal modal logics. But the structure of NB- neighbourhood frames was introduced with a somewhat more complex definition than the neighbourhood semantics for non-normal modal logics. So in order to find out the modal companions of these subintuitionistic logics, we consider two types of translation, one from the language of intuitionistic propositional logic to the language of modal propositional logic, and the other from the language of intuitionistic propositional logic to the language of binary modal propositional logic, and compare the provability of a formula and its translation. Finally, using these two types of translations, we obtained the modal companions of desired subintuitionistic logics.

The aim of this article is to reconstruct the problems and answers which Aristotle raises in Zeta and eta of Metaphysics. Aristotle’s fundamental presupposition here is that definition has parts, and it corresponds to essence or form. This very presupposition leads to the main problems raised in Zeta and Eta. These problems are ordered at each other, and answering one leads to other. According to this articles reconstruction, Aristotle encounters to four main problems on compounds, unity of definition, matter as part of definition, and universality of definition. If definition should to have parts, parts also need to have some unity. then, what guarantees this having parts and yet having some unity? Aristotle’s answer is matter. now, Aristotle encounters with the problem of justification of matter’s entering into definition, because matter is unintelligible. For answering this difficulty, matter should have considered universalized and indeterminate, and this, in turn, leads to last problem, namely, the problem of universality of definition.

Bounded model theory can be considered as part of first-order model theory, which its aim is to study model-theoretic notions in a language consisting of an order relation where all quantifiers are restricted to the bounded ones. One can apply bounded model theory to study some problems in bounded arithmetic. Bounded arithmetic can be considered as a sub-theory of first-order Peano arithmetic in an extended language. Bounded arithmetic has some applications in computational complexity theory. There are already some related bounded model-theoretic concepts like bounded quantifier elimination and bounded model completeness which has been applied to bounded arithmetic and complexity theory. In this article, we review some known results and prove some new ones in bounded model theory and use them to obtain certain results in bounded arithmetic and complexity theory. In particular, we define the notion of bounded model companion and study its relations to some fundamental problems in complexity theory.

Following Fakhr Razi, Muslim logicians indentend two technical terms: haqiqi and khariji propositions, which prima facia are absent from Aristotle’s works as well as from the wrorks of his followers. We show that although Aristotle used haqiqi propositions for his absolute syllogisms, he utilised khariji ones for his modal syllogisms. However, he has a pssage that prohibits the use of khariji propostions in modal syllogisms. Now, what to do dealing with conflict between this explicit passage and those many exapmles? Some contemporary commentators proposed the possibility that the passage is from his students. Anyway, Aristotle’s modal syllogisms are sensetive to the division of propositions into haqiqi and khariji, although we couldn’t find any historian of logic who investiegatied carefully and completely the syllogisms form this perspective.Keywords:Arisotole, haqiqi proposition, khariji proosition, modal syllogism.Keywords:Arisotole, haqiqi proposition, khariji proosition, modal syllogism.Keywords:Arisotole, haqiqi proposition, khariji proosition, modal syllogism.

Interactions between logic, measure and probability theories have always possessed significant importance in logic and model-theory. In this regard, numerous logical frameworks were introduced to connect these subjects. Integration-logic is amongst important ones of them that was first introduced by Keisler and Hoover and then developed in various works such as Bagheri-Pourmahdian paper and turned into a suitable logical framework for working with structures equipped with measures and integration operator. Also in a paper by Mofidi-Bagheri, a more abstract framework for working with operators more general than integration was introduced. Moreover, in a more recent work on connections of logic and measures, different aspects of dynamical-systems and measures in model-theory was published by Mofidi in 2018. One of the characteristics of Bagher-Pourmahdian framework is its boundedness, i.e. it is assumed that interpretation of every relation is a bounded function. Despite some advantages of this assumption (such as simplifying working with relations and proving ultraproduct and compactness theorems), it causes substantial limitations in the expressive-power of logic and its ability to interact with various mathematical structures. In this paper, we aim to resolve this limitations by strengthening and generalizing the framework of integration-logic in a way that relations be interpreted with (not-necessarily bounded) functions in L^p-spaces and furthermore, showing that fundamental results of ultraproduct and compactness theorems still hold (of course with new proofs and more subtle techniques). This generalization can provide more interactions with structures such as L^p-spaces and (not-necessarily-bounded) random-variables which are central notions in analysis and statistics.

Theophrastus, a student and successor of Aristotle, in addition to describing his master's logical system, also tried to reform and expand it. Furthermore, he introduced forms of argument that were either not mentioned at all in Aristotle's works or that Aristotle merely referred to in passing. One of these forms proposed by Theophrastus is prosleptic syllogisms. Although brief references to this type of argument can be found in Aristotle's Organon, the elaboration of these arguments and their specific naming is related to Theophrastus.This particular form of argument does not fit into Aristotle's  system. Of course, for some of these types of arguments, equivalents can be found among the moods of Aristotelian syllogism. But not all of them can be reduced to categorical syllogism. It seems that the discussion of prosleptic syllogisms is beginning a second-order logic and a discussion of the relationship between concepts and universals.Key words: Theophrastus, prosleptic proposition, prosleptic syllogism, second order logic