Quantum Mechanics is the revolutionary theory that changes the structure of human thinking. From Einstein up to now, however, with its enormous successes in the world, there are many scientists that opposed it and denyed it as a complete theory. One of the ways to question the completeness of this theory is to use Gö del’ s incompleteness theorems. Kurt Gö del, in his Ph. D. studied and just after working on the Hilbert’ s completeness and consistency program in the formal systems, proved two important theorems which are known as the Gö del’ s incompleteness theorems. These theorems deny Hilbert’ s programs and the completeness of the formal system. Generalizing these theorems to the quantum theory is an over decades challenge in the foundations of physics. In this Paper, we explain the problem and we will discuss and critrize the possible usage of the Gö del’ s incompleteness theorems on the quantum mechanics.

One of the most important applications of Gödel's completeness theorems is based on their roles the arguments of impossibility of formalization of human mathematical mind in capture of an algorithm or a finite formal system. Two main arguments have been proposed in this way of reasoning. In both of these arguments, it has been claimed that: the fact according to which human being can understand the truth of the unprovable Godelian sentence, shows the superiority of human being’s ability in mathematical reasoning to all machines’. But there are some important debates on both arguments. After explaining these two arguments, we will investigate the extensive contentions and challenges between mechanists and anti-mechanists. By explaining and analyzing Godel's incompleteness theorems and their connection to human arithmetical knowledge, we will show that there is no plausible argument, based on Gödel's incompleteness theorems, which can show the superiority of human being’s ability in mathematical reasoning to the machines’.

In this essay, after short explanation, the effects of Godel’s first and second incompleteness theorems on philosophy of mathematics and philosophy of mind and against materialism and positivism is examined. The effect of Godel’s theorems on philosophy of mathematics has examined in three fields of logicism, formalism and nature of proof. In the area of philosophy of mind , the effect of Godel’s theorems on antimechanist proofs is pointed out.

Since 1970, when Gödel tried to provide a new articulation of the so called ontological argument, many considerable discussions has been emerged due to assessment of his argument's validity and soundness. For example, Sobel tries to show some defects of Gödel's argument. Petr Hájek, the eminent logician and mathematician, tries to save this argument from Sobel's critiques by some small amendments. According to him, if we articulate this argument in S5 system of modal logic with a few changes, we can have a safe argument. Besides, Hájek believes that this argument is of little interest from theological perspective. In this article, after a survey of Hájek’s work, we shall try to put this later claim under scrutiny and show the theological relevance of the argument. Finally, we show that despite the fact that Hájek and many other logicians consider Gödel's argument just as a "formal model" of an ancient argument, this argument seems a bona fide and justified argument for God’s existence.

In the area of fuzzy logic, expansions of these logics by Δ operator have been intensively studied; the interest of Δ operator is due to the fact that it presents a fuzzy behavior, the associated systems were studied in propositional and first-order level. On the other hand, the possibility operators that define Ł ukasiewicz-Moisil algebras have been studied over different classes of algebras; these operators are known as Moisil’ s operators in the literature. One of these operators coincides with Δ , showing there are other operators with fuzzy behavior. In this paper, we present the study of Moisil’ s operators over an extension of a fuzzy logic; namely, n-valued Gö del logic, thus opening the possibility to explore more fuzzy operators.

There are two general methods for interpreting and analyzing khārijī and ḥaqīqī propositions: first, by analyzing them within a unified logic; second, by assigning separate logics to khārijī and ḥaqīqī propositions. So far, most interpretations and analyses of khārijī and ḥaqīqī propositions have been carried out using the first method within either traditional logic or a branch of modern logic, while the second method has rarely been used for this purpose. In this article, we aim to use the second method and demonstrate that the appropriate logic for ḥaqīqī propositions is classical predicate logic, while for khārijī propositions, it is predicate-free logic. We show that non-classical predicate-free logic restricts the rules of introduction and elimination of the quantifiers on the existence of khārijī objects, making it the most suitable logic for khārijī propositions. In contrast, classical predicate logic, which does not restrict the quantifiers on the external existence of objects, is more suitable for ḥaqīqī propositions. Additionally, we illustrate that by incorporating modal logic and temporal logic into classical and free predicate logics, the principles and rules of ḥaqīqī and khārijī propositions become more distinguishable, resulting in more distinct logics. In particular, we demonstrate that the Barcan Formula, the Buridan Formula, and the converse Barcan Formula hold true for ḥaqīqī propositions and are proven in classical modal and temporal logics, while they are false for khārijī propositions and remain unprovable in free modal and temporal logic.

Various definitions can be found in the western philosophy regarding analytic propositions (or judgment"). Some of the most important definitions belong to Leibniz, Hume, Kant, Ayer, Mill, Frege, and Quine. According to their scope, such definitions can be classified into three sets: the most particular, particular, and the most general ones. In order to find the correct definition, we have to look for the one which tits best the goals and the foundations of the division of propositions into analytic and synthetic. Having determined the goals and the foundations of these western philosophers, the article shows that their definitions neither satisfy their goals, nor are congruous with their fundamental principles. One of the crucial ends of such a division is dividing facts into intellectual vs. real facts, and differentiating between primary and derived intellectual facts. This goal is the same for predicatory and conditional propositions on the one hand, and for affirmative and negative ones on the other, and for true and false propositions on the third. But all the above-mentioned definitions (among other deficiencies) stay short of encompassing all these propositions. The author suggests an alternative definition, more particular than the most general definition, and still more general that the particular one, compensating for faults of the previous definitions.

In his various works, Ibn Sina has referred to different meanings of "All J is B", which his followers have called "ḥaqīqī" and "khārijī" propositions. Ibn Sina's examples for "khārijī proposition" are sometimes only related to the present time, sometimes related to past and present times, and his followers have extended these meanings to all three tenses: past, present, and future. To distinguish these three meanings, which have arranged from specific to general, I call them "specific," "intermediate," and "general" khārijī propositions. In this article, I show that for each meaning of khārijī proposition, its relation to a more general meaning of khārijī is similar to its relation to ḥaqīqī propositions, in that mixed khārijī-khārijī syllogisms (mixed of two kinds of khārijīs) have exactly the same rules as mixed khārijī-ḥaqīqī syllogisms.