MANTEQ-PAZHUHI (LOGICAL STUDIES)
Year:2010 | Volume:1 | Issue:1|Papers Count:7

The present paper attempts to introduce vagueness and Sorites paradox. First, the observational adequacy of the issue and then its logical form are presented. Later on, the philosophical matters concerning the theoretical framework of vagueness and its philosophy are discussed. Finally, the present theories regarding vagueness are classified on the basis of various criteria and brief explanations are provided for each of them.

This paper presents an analysis to cogent conditional quantifier. There are various approaches to the analysis of conditional quantifier. Some researchers have called this pseudo-quantifier and other authors have interpreted it as being based on temporal logic; or modal logic. In this paper after investigating and criticizing these approaches, we analyze instances of the cogent conditional quantifier in natural language. Then we determined their formulation in modern logic. Also we have investigated the presuppositions in the ancient logic. The truth of that logic deduction is based on those presuppositions. In the current approach, it becomes clear that the cogent conditional quantifier can only be analyzed on the basis of relevant logic and modal logic. Also for truth of deductions, acceptance of two presuppositions "the possibility of the antecedent" and "the necessity of relevance of the antecedent and the consequence in the universals" is necessary.

In Organon, Aristotle treats predication exactly like affirmation. There exists no predication which is not affirmative. Negation in Organon is negation to the predication. When a quality is denied of an object, we are not faced with a kind of prediction. This paper attempts to prove that this Aristotelian view will lead to certain paradoxes which cannot be solved or answered through Aristotelian logic. However, finally, we prove that this Aristotelian notion is outright wrong and negative predication does not function like a deadlock in logic and it can be possible. Since, this article employs the method of Obversion and Aristotle defiantly rejects this method, to defend the methodology of this study, this Aristotelian view is analyzed and its falsity is displayed. In brief, the present article has the following claims:1) - Predication and affirmation are not the same and negative predication also exists.2) - Contrary to the views of almost all ancient logicians, Modified affirmative predicates are not really affirmative and they are negative.3) - Obversion, is a true and usable method for the goals of old logic.4) - Existential Import rule is true but incomplete, and its correct form can be as follows: "The attribution of a negative or affirmative judgment is subsidery to its proof." Therefore, any predication whether negative or affirmative cannot be operated on a non- existent entity and therefore negative Proposition with the Empty Subject are on the basis of their subjects false.

The principle of impossibility of contradiction categorically claims that every contradiction is impossible. In this study it is attempted to analyze concepts such as “Contradiction” and “No-contradiction” and the relations between these two concepts with man’s cognition and understanding. This study attempts to state that the above claims could at most mean that the present humans beings cannot justify “contradiction”. If this interpretation is valid, it might mean that the principle of the impossibility of “contradiction” cannot have valid proofs for itself. It is possible, therefore, to speak about the possibility of contradiction at least in paradoxical situations.

The necessities and requirements of the standard logic of phenomenology create some problems in the analysis of fictional propositions which are replete with imaginary identities and lack signifiers. However, the logical conditions of these propositions as the constituent parts of language, is very significant and it cannot be denied or ignored that in the ordinary language, fictional identities are referred to and their relevant propositions are both accepted and rejected. In this paper, the auther has attempted to employ the definite framework of the possible worlds, to find explanations for the manner of referring to these propositions and the value of their truth. A few logic-related issues of fictional texts are also treated in this study; the author, also presents a system for the logic of fictional propositions.

We know for logic two systems: the Ancient Logic and the Modern Logic, which are inconsistent in some points of view. In this paper, I want to see if Ancient Logic, versus Modern Logic, is really one logic, has one set of rules, and introduces one methodology. There are many disagreements on the number and the exact formulation of the valid rules of Ancient Predicate Logic. For instance, the various formulations of the Obversion and Contraposition (the congruent and the opposite) can be mentioned as evidence for the claim. Since Aristotle has not spoken of contraposition, it can be concluded that adding the two forms of contraposition to his logical rules provide us with two new logical systems, in which the formulations of the quantified propositions differ from that in Aristotle’s system. Also, since there have appeared different theories on Congruent Contraposition and the Obvertion between Muslim logicians, the number of the systems has reached the six. In this paper, introducing an exact definition for each of these systems, I present suitable formulations for the quantified propositions at the mentioned six systems.

In this article, I will at first explain the meaning-based theory of Davidson and the manner of its application in the identification of the criterion for the logical truth. To achieve this end I will refer to the Principles of lexical axioms and the principles of Phrasal axioms along with their applications in Davidson’s theory. In order to criticize Davidson's theory, Evans selects the extentional attributive adjectives and shows that through employing a certain Kind of interpretation, one can make a meaning based theory in which the extentional attributive adjectives can appear in the phrasal axioms; therefore these principles cannot identify the extention of logical constants. To answer Evans criticism; I will use the concept of the violence of the basic linguistic intuition which Davidson uses that in replying to Foster. To this end, I will show that in spite of their superficial differences the criticisms proposed by Foster and Evans have basic origins. In the conclusion part of this article, I refer to the impossibility of reducing the semantic features of language to its syntactic qualities.