MANTEQ-PAZHUHI (LOGICAL STUDIES)
Year:2011 | Volume:2 | Issue:1 (3)|Papers Count:7

The current paper is an attempt to analyze the Avicennian Cogent conditional quantifier based on Second-order Logic. Contemporary researchers have provided various formalizations of Avicennian conditionals to the Modern Logic language. A major difference between these formalizations is the analysis of conditional quantifier. In the most recent studies, Khajeh Nasir al-Din Toosi views about conditional quantifier, is used for analysis. His analysis of conditional quantifier can be formalized by Second order Logic language. Therefore, some analyses are proposed to show using the Second order Logic, the Avicennian cogent conditional finally could be formalized by Relevant Logic and Modal Logic. In this paper, it is shown this analysis is true assuming a temporal consequent and antecedent. Because of this assumption, the analysis has some difficulties. In order to solve this issue, we based the analysis on the assumption of temporal consequent and antecedent then analyzed the cogent conditional using Second order Logic, Temporal Logic, Relevant Logic, and Modal Logic. The resulting formalization is a combination of Relevant Logic, Temporal Logic and Modal Logic.

In this paper I expose and evaluate supervaluationist theory of vagueness. Specially, I concentrate on the standard version of it. This criticism is twofold: first, this theory cannot model all intuitions about vague predicates and though it select a proper subset of these intuitions, its preference is not justified; second, its psychological solution of sorties paradoxes either is not satisfactory or is ad hoc. I will conclude that, at least, standard version of supervaluationism does not handle vagueness related problems.

The Liar is a self-referential sentence which says that it is false. In this article, we will first show that the main two traditional and well-known solutions of this paradox cannot survive a serious scrutiny. Then, we will use two important premises to introduce a new solution for the problem. The first premise is that “propositions” (rather than sentences) are truth-bearers (even though we sometimes assign truth value to sentences, when we do that, we are well aware that we are not talking accurately; but this kind of inaccuracy is allowed only as far as it doesn’t cause serious problems such as paradoxes). After adding this premise to the discourse, the Liar sentence will be rephrased in a more accurate way as a sentence which says that the proposition it expresses is false. The second premise is the theory of structured propositions according to which propositions are ordered sets (that is to say a proposition is of the ontological genre of sets). Then, using the regularity principle in set theory, we will show that no set can be a member of itself and since a proposition is a set, it can’t include itself as a member and can’t express its own falsehood. In this way, we prove that no such proposition exists and the Liar sentence is without content and meaningless. Taking propositions as truth bearers and using the theory of structured propositions lead to an acceptable solution for the Liar paradox which in its turn can be taken as an advantage of those theories about truth bearers and the nature of propositions.

Hintikkain analysis of the semantics of epistemic logic, according to respond to the problem of logical omniscience, used Impossible Worlds. It was the first appearance of the term Impossible World. Graham Priest also appeals to Impossible Worlds in analysis of intentional contexts. After an exposition of different approaches to Impossible Worlds and their applications, we will analyze Priest’s responses to the problem of logical omniscience and three other problems concerning epistemic logic. The semantic which he invented for intentional contexts is widely based on Impossible Worlds. During our inquiry we will also meet different aspects of these non-normal worlds.

In his Isagoge, Porphyry provides circular definitions for genus and species; and to justify this point, following Aristotle, he attaches emphasis to correlation between the two concepts and that the definitions for two correlative concepts should be circular. Ibn Sina, however, interprets Aristotelian point in another way; and, in some places in his works, he rejects Porphyry's definitions strongly. Jonathan Barthes, who is one of the most eminent editors (experts) of the ancient philosophy, provides a report and assessment other than those of Ibn Sina. The present essay concerns a comparative study of Ibn Sina and Bartes' ideas and represents similarities and dissimilarities between ideas of the two commentators in this special field.

Faqihs and Osulians have dealt with some kinds of universality which are 1. “Distributive”, “separative” or “inclusive universality”, 2. “aggregative”, “collective” or “cumulative universality”, and 3. “alternative universality”. They found many uses and examples for the kinds. In this paper, I want to formalize in Modern Logic some of the uses and the examples and to show complexities and intricacies thereof. For this, I employ the combination of quantifiers with negations, conditionals and quantifiers. Then I show that this method, despite its elegance and potentiality, when the rules of Modern Logic are applied to it, gives astonishing, sometimes inadmissible, results and collapse aggregative universality and alternative universality into distributive universality. So, this paper aims to show that the kinds of universality have intricacies and complexities which seek more investigation on their unknown and dark angles.

Lewis Carroll in “What the Tortoise Said to Achilles?” questioning one the most important basis of logic and by narrating a fanciful dialog asks why we should move from premises to the conclusion. Is logic itself enough to justify the use of logic or we need something beyond logic to do that.In this article two main approaches have been considered. First, logical approach which Bertrand Russell is its most important member and second, social-internalism approach which Peter Winch advocates. These two main philosophers have referred several times to Carroll’s article. According to Russell, analyzing logic is suffice to explain why consequent will infer from premises, and on the other hand, Winch and his followers think every inference has a root in historic understanding of life and if this understanding fails, logic will falls apart too. I will make some objections to both of these.At the end, I propose that the solution is to return to formal logic. If formal logic understood well, there won’t be any need to seek for logic to teach us how to use logic. Valid formal inferences are what logic consists of and if someone violates these inferences, he is out of the boundaries of logic.