MANTEQ-PAZHUHI (LOGICAL STUDIES)
Year:2019 | Volume:10 | Issue:1 |Papers Count:12

Moore’ s sentences are sentences of the form “ p but I don't believe that p” or “ p but I believe that not-p” . These sentences are called the omissive and the commissive form of Moorean sentence, respectively. These sentences might be true, yet they are ‘ absurd’ to believe. It is usually claimed that absurdity only occurs when these sentences are formulated in the present tense, but if they are expressed in the past tenses or future tenses they would not be absurd. In this paper, we will analyze the Moore’ s sentences in various tenses: past, present, and future. In this respect we employ a logic which is a combination of hybrid tense logic and doxastic logic. Then by formalizing the Moore’ s sentences in various tenses we show that, contrary to popular belief, the past and future versions are not necessarily absurd. Finally, we give a necessary and sufficient condition for determining the absurdity of the Moore’ s sentences.

Aristotle, in Posterior Analytics, A. 2, introduces the principles of science. In Post An, A10, He describes three kinds of foundations of science. There seem to be some discrepancies between the classification in A. 2 and three kinds of the foundations in A. 10. It is also not clear which of these principles and foundations can have all the features of a premise of science. This paper represents the puzzles that arise in interpreting the texts in question. It describes the Aristotle’ s principles of science and suggests that only one kind of them can be considered as a premise of science; the principles that assume both the subject of science is and what it is. It is necessary to distinguish between Aristotle's premises of science, the foundations of science and the prior knowledge. The puzzles are solved with the help of this distinction and notes from other texts in Post An. So a consistent interpretation between A. 2 and A. 10 is achieved. The proper interpretation helps to understand Aristotle’ s epistemology correctly.

Logical realism, in a sense, is realism about the subject matter of logic. What is logic really about? Talk of logic is more or less synonymous with talk of the relation of logical consequence; the relation that holds between the premisses of an argument and its conclusion. However, in the history logic, this has not always been the case. Before placing logical consequence at the heart of logic, the Frege-Russell view was dominant in the philosophical community; a view according to which logic is primarily about logical truths. In this paper, we argue that logic is about logical consequence and not logical truth. Then we list a couple of motivations for investigating a metaphysics of logic. Proponents of logical realism typically base their theories upon logical truths as logical facts. In this article, we aim to turn the emphasis from logical truths to logical consequence(s) as the primary object(s) of logical realism and give a general outline on how to be a realist about logical consequence.

Continuous logic is generalization of first order logic to a many valued logic with an infinitary truth value set. Many of the results of classic logic and it's model theory have been generalized to continuous logic. Continuous logic not only has many uses in the mathematical analysis and in the model theory of mathematical analysis structures, but also has created new attitudes in classical model theory. Firstly, the present paper study the development of continuous logic from Ł ukasiewicz logic. Then we have a review on some of the most important basic results of continuous logic, including the completeness of the proof system and the compactness theorem. Finally, according to the concept of continuity with respect to the truth value set, we will introduce a kind of continuous logic that is based on continuous t-norm based fuzzy logics. This will lead to the introduction of two kinds of continuous logics based on Gö del logic and product logic. Then we developed some of the results of continuous logic suContinuous logic is generalization of first order logic to a many valued logic with an infinitary truth value set. Many of the results of classic logic and it's model theory have been generalized to continuous logic. Continuous logic not only has many uses in the mathematical analysis and in the model theory of mathematical analysis structures, but also has created new attitudes in classical model theory. Firstly, the present paper study the development of continuous logic from Ł ukasiewicz logic. Then we have a review on some of the most important basic results of continuous logic, including the completeness of the proof system and the compactness theorem. Finally, according to the concept of continuity with respect to the truth value set, we will introduce a kind of continuous logic that is based on continuous t-norm based fuzzy logics. This will lead to the introduction of two kinds of continuous logics based on Gö del logic and product logic. Then we developed some of the results of continuous logic such as the compactness theorem for these two logics. h as the compactness theorem for these two logics.

Classical first-order logic is the most common logic in mathematics applications as well as in the study of logical foundations. From a long time ago, the only link between logic and mathematical topology was limited to the concept of type spaces, and there were no other links between these two domains. Recently, the basic links between these two branches (i. e. logic and topology) have been created, which have led to many applications in both areas of logic as well as in topology. In this article, we will study some of the most important links between these two branches of mathematics as well as their applications. One of the key concepts in mathematical logic and model theory is the concept of stability, which has a completely combinational statement. In this paper, we show that this concept is equivalent to a topological concept for a certain set of functions, and using this we prove a fundamental theorem of Shelah stability theory. We also describe the relationship between the concept of dependence and a topological property of a set of functions, and provide topological proofs of some of the important achievements of model theory. Some of the results of this paper are new.

The possibility, or lack thereof, of drawing a sharp distinction between the observable and unobservable entities, as a main debate between the scientific realism and antirealism, is still one of the most controversial problems in philosophy of science. One of the arguments offered in favour of realism states that there is in principle no such a determinate distinction. On the other hand, the consistency of scientific antirealism relies on the distinction between the observable and the unobservable. If such a distinction is shown to be untenable in an objective manner, then as a consequence the antirealistic viewpoint would be inconsistent. Antirealists, in order to save the consistence of their viewpoint, point out to the (alleged) vagueness of the notion of “ observable” and thus try to retain the distinction despite the apparent problems around it, as is the case in some well-known solutions for the paradox of vagueness. In this paper we will give a new interpretation of Linear Logic as it may shed a new light on the problem of vagueness and accordingly contribute to the studies pertained to the problem of the distinction between the observable and unobservable entities. We will show that if the offered approach to the problem of vagueness would be correct then to appeal to the vagueness of the notion of observabilty would not be helpful for the antirealistic viewpoint.

Suhrawardi claims that there can be no one-premissed syllogism, and he makes a reason for this. The issue of the current article is the genealogy of that claim and the logical evaluation of this reason. Our hypothesis is that, historically, the conflict over the possibility or impossibility of the one-premissed reasoning goes back to the Stoics: Chrysippus was the leader of the opposition; and the Antipater of Trasus was the leader of conservativism. This conflict by Alexander Aphrodisias came into the Prepatetic logic, and merged with Aristotle's Syllogistic, and, consequently, the stoical problem of "one-premissed reasoning" was confused with the Aristotelian question of "one-premissed syllogism. " Ibn Sina is the source of the transmision of this issue from Alexander to Suhrawardi. Suhrawardi's argument, if he views the refusal of the one-premissed reasoning, is, of course, incorrect; but if he is to refuse the one-premissed syllogism, he can have a good deal of truth.

According to Beall and Restall pluralism, classical logic, relevant logic and intuitionistic logic are all correct. In this type of pluralism, logic is considered to be normative; in the sense that one who accepts the truth of the premises of a valid argument, is bounded to accept the result of that argument. Some philosophers try to show that accepting Beall and Restall pluralism is incompatible by the acceptance of the normativity of logic. However, Blake-Turner and Russell have proposed telic pluralism that is not based on the normativity of logic; claiming that their arguments is not threatened by the collapse argument. In this article, by examining telic pluralism, we have determined that Blake-Turner and Russell’ s pluralism lacks strong arguments in defense of non-normativity of logic. On the other hand, we try to present a version of the Priest’ s collapse argument that still can be used against telic pluralism.

One of the most perplexing issues in Arabic Logic is the particular quantifier for conditionals. Before discussing particular quantifier at cogent conditionals, Ibn-Sina deals with particular quantifier at categorical propositions and its divisions. But, as we shall see, his explanation at categorical propositions is inconsistent with his discussion at conditionals; and his analogy between the two realms is more confusing than explaining! Despite this, in this paper, I’ ll show that by using some branches in Modern Logic, such as second-order logic, modal logic and temporal logic, many of the ambiguities and the objections can be replied. Also, I’ ll glance at the reflection of the discussion in some of Ibn-Sina’ s great followers: Fakhr Al-Din Al-Razi, Afdal Al-Din Al-Khunaji, Athir Al-Din Al-Abhari, Khaje Nasir Al-Tusi, Shams Al-Din Al-Samaqandi and Qutb Al-Din Al-Razi. I shall show haw far they are from Ibn-Sina. Besides, it will be clear that their distinctions between contingent conditional and particular cogent conditional are very weak and, indeed, cannot help any way to understand the distinction.

In recent decades, formalization in mathematical structures has been developed in different areas with logical nature. These mathematical structures besides providing more precise and sufficient languages than natural ones, would be a base for constructing assistant software in these areas. One of these logic-nature areas is "osool'e fegh" which is the logic governing jurisprudential inferences in Islamic approaches. Hence, a mathematical logic for "osool'e fegh" would provide a useful device for both 'analyzing and comparison of jurisprudential inferences' and, 'designing assistant software'. In this paper we introduce our mathematical logic approach to "osool' e fegh". We search a determining logic for "ossl'e fegh" in the formal logic context, as it is in fact the "logic of Fegh". After a survey on different meanings of "vajeb" and its properties, which is the basic deontic concept in "osool' e fegh" literature, we construct a formal language for "logic of Fegh" according to dynamic logic and formalize some jurisprudential rules in this language.

The debate of Abu Sa'id Syrafi Nahwi and Abu Bashar Mata is one of the key nodes of Islamic civilization. This debate was the focus of the two main streams that arose from the Abbasid ideological reform. One-way Translation Movement and its implications and other way ideological and theological and jurisprudential systems, generated in Age of Editing. Apart from serious issues regarding the position of logic and the relation between logic and language and syntax, this debate drives the tension caused by the collision of the two above-mentioned flows. In this paper, with the historical and genealogical descriptions of the Translation Movement and the Age of Editing, we go to discursive analysis of the debate, and explain this ideological tension. It seems that the results of this debate have also had a wide range of implications for Islamic thought, and have had sustained changes in both the ideological and philosophical trends. After debate, the ideological stream left out the former enemy with logic and attracted logic for use. The philosophical flow was also diverted from logics and went to the foundations that Farabi and Avicenna called peripatetic school.