Logical Studies

Abstract This research examines the relation between logic and ethics and tries to investigate logically the corresponding dilemmas. Standard Deontic Logic which is initially appeared for studying ethical propositions cannot offer a suitable and accurate solution for conflict between duties. Therefore some new deontic logics are made to represent this situation formally. For example Defeasible Deontic Logic and specially Reiter's Default Logic has a new approach to these moral dilemmas and offers an acceptable explanation of them.
 
 

Abstract In this article, a new definition of two concepts, i.e. Conceivability and Imaginability, is presented. First, the desiderata of a definition of Conceivability are given and by choosing two presuppositions, a theory about Conceivability is suggested. In this step, two strategies for the distinction between the process of Conceiving and Imagining is introduced and after scrutiny about these two strategies, positive definitions of the concepts Conceivability and Imaginability are presented. Second, by perusing the restrictions of Conceivability and by mentioning wide and narrow approaches, a negative definition of these concepts is given. Then, these two definitions are epitomized into one definition. After all, the article is ended by evaluating the capability of our theory about satisfying the desiderata.
 
 

Abstract In his 1987 paper, Jordan Howard Sobel showed that Gödel’s ontological argument faces modal collapse and, therefore, it is not sound. C. Anthony Anderson, in his 1990 paper, proposed an amended version of the argument in which modal collapse is blocked. In his parody, Graham Oppy, however, cast a serious doubt on the soundness of Anderson’s version. Alexander Pruss, however, in his 2009 paper, endeavored to block this parody by proposing some new Gödelian ontological arguments. In this paper, I will be trying to inquire into Gödel’s ontological argument, Sobel’s objections, Anderson’s emendations, Oppy’s parody, and Pruss’ ontological arguments.

Abstract The first who discussed separately the conversion of the verity and actuality propositions  was Fakhr Al-Din Al-Razi, but Afzal Al-Din Al-Khunaji criticized most of the logical rules introduced by Al-Razi on the conversions of those propositions and many criticisms of Al-Khunaji have been accepted by the later logicians. I have discussed the conversion of the actuality propositions in another paper and showed that in two cases, Al-Razi was wrong and Al-Khunaji was right; but on the other cases, their controversies is rooted in different interpretations of the terms involved. In this paper, I'll show that similar fallacies and similar differences in interpretations have occurred; thus, Al-Razi insisted that in verity propositions, the affirmative modal propositions (but the two possible) were not self-converted and the negative perpetual ones had not conversions. In these cases, Modern Modal Logic supports Al-Khunaji's judgments.  In the other cases, I'll show that Al-Razi have been taking the modal verity propositions with two modal operators and Al-Khunaji with one; and this is the secret behind the controversies on the conversion.
 
 
 

Abstract From the very beginning up to now the concept of existence has been one of the most controversial ones among the philosophers. Such discussions can be divided into two main parts. The first one refers to the ontological aspects of existence for which one is involved with two schools namely Possibilism and Actualism anyone of which tries to talk of the scope and limit of things within their own metaphysical principles. The second part includes the issues about existence as a predicate. For these discussions and because we want to consider existence as a first or a second order predicate, we can either talk about the possible existence or its counterpart i.e., the necessary existence of the things. The necessary existence is one of the formula which, in the simplest quantified modal logic of S5 and just like those formula such as BF and CBF, is provable and valid. Although talking of the validity of necessary existence things needs to provide a second degree concept of existence but discussing the validity of Barcan formula needs an existential commitment to the possible things which the possibilists believe are not among the existent things. Following Linsky and Zalta and for defending BF and NE formula, Timotty Williamson has excluded the validity issue of Barcan formula from the first part and he has transferred it to the second part. Thus using the modal properties he provides a new definition of possible things through which one can defend the validity of Barcan formula as well as the necessary existence of things without having any existential commitment to the possibilia. Afterwards, Williamson provides the conditions for talking of the logical existence for things by providing a second-order concept of existence in unrestricted quantification theory and in this way one can have a better understanding of necessary existence.
 

Abstract Two things which equal the same thing also equal one another. This well-known sentence had widely been accepted from the period of ancient Greeks and perhaps earlier as an evident axiom. By the introduction of Logic into the Islamic field,
Ibn Sina and most of other Muslim logicians after him tried to affirm this chapter following the lead of Aristotelian syllogism or some other methods. However, it seems that their efforts haven’t been as fulfilled and have received criticism. Arguments for the above syllogism and other similar ones are also continued among the contemporaries. Nevertheless, it gives the impression that lack of enough attention to the contents of the premises of such syllogisms has led to the disappointment of any efforts in demonstrating them. Through the usage of the chapter of four-fold relations, in the analysis of these premises, the equality syllogism would easily be proved provided that the terms used in these syllogistics are universal. Furthermore, through the amalgamation of the chapters of syllogism and the four-fold relations a variety of other syllogisms corresponding to other relations other than equality would emerge all of which would be proved if we employ the previous method and within the traditional logic.