Logical Studies

Abstract It is obvious that things are subject to change in our world. For example, the nib of a pencil may be broken; however, the pencil is the same pencil as before, with the only change that its nib is now broken. However, the problem is not so simple. During the history of metaphysics, there have been those- such as Parmenides, Melissus, Zenon, McTaggart, Geach, Russell- who rejected change and motion in such a customary sense. On the other hand, philosophers’ mainstream has tried to represent views and sound arguments for the existence of motion and change, for instance, Aristotelian-Avicennian approach is one of the most important of them. The peripatetic account relies on the distinction of essence and accidence and develops its theory of motion. In this paper we try to show that both positive and negative approaches mentioned above are defeated; their defeat is not due to the weakness of their arguments but is rooted in the wrong logic selected for the base of their metaphysics. This paper is an endeavor to show the advantage of paraconsistent logic relative to classical logic in explaining the problem of change.

Abstract The present article is one of the first written in the Western world on the relationship between logic and ontology (or metaphysics in general). Bocheński shows that Gottlob Frege, the father of mathematical logic, by placing truth instead of inference as the subject matter of logic, brought logic very close to ontology and metaphysics, to the point that some of Frege's followers, such as Heinrich Scholz, considered logic and ontology to be one and the same. On the other hand, of course, a group such as Ernest Nagel remained faithful to tradition and considered logic and ontology to be completely distinct from each other. In explaining this historical controversy on the relationship between logic and ontology, Bocheński points out that the roots of this controversy are in Aristotle's two books on syllogisms and polemics (originally titled Prior Analytics and Topics). In Prior Analytics, Aristotle expresses his logical results (i.e., the moods of syllogism) in the form of truths and laws, while in Topics, he had proposed logical results in the form of rules of debate and of dialogue between two opponents (the questioner and the answerer). Bocheński claims that the logical tradition after Aristotle, from the Stoics to before modern logic, all saw logic in the form of Aristotele’s Topics, i.e. as rules of debate and dialogue, unlike mathematical logicians such as Leibniz, George Boole, and Frege, who saw logic in the form of Aristotele’s Prior Analytics, i.e. as axioms and laws.

Abstract Mirza Qomi's explanation about practical reason is important in three ways: (1) He is considered one of the most serious critics of Aristotelian logic and the way of reasoning in this logic, and he has followed a different path from the defenders of this logic. (2) The logic governing Mirza Qomi's thought is considered a psychological logic. and (3) by presenting a different explanation of the nature of reason, he considers imitation as a type of reason and opens the chapter of reference to imitation in practical matters.
It is shown that Mirzai Qomi considers every persuasive thing as a reason. By deviating from formalism in Aristotelian logic, Mirza believes in the multiplicity of forms in argument and believes that the manner of the mujtahid's reasoning determines the form of the argument a posteriori; Therefore, as a priori, no form can be accepted as the form of argument. According to Mirza, there is no logical certainty and logical certainty is also a kind of psychological certainty. If absolute certainty is a psychological matter, three requirements arise: (1) The distinction between specific suspicion and general suspicion disappears and all suspicions become equally valid. Therefore, (2) there is no difference in the validity of suspicions from which source they come? and (3) persuasive imitation has no difference from the epistemological point of view with psychological certainty, and rather it is considered a partial imitation of certainty; Therefore (4) we can use imitation in practical matters.

Abstract Foundationalism is an epistemological theory of truth in which knowledge acquires its validity from self-evident propositions, but these basic propositions, due to their conceptual clarity, are not treated as to their significance. One important, yet unanswered question is, what is the criteria for being self-evident? In this article, various definitions and conditions will be presented and then we will deal with five criteria, all of which have been mentioned in philosophical and logical literature: the first one offers immediate(presential) knowledge as a guarantee for the truth value of self-evident, the second considers self-evident as if they are incorporated in our nature, the third idea find a connection to a divine being as a solution, and finally the fourth theory is a compound one, it distinguishes between conceptual clarity and truth-value and for each one suggests an independent solution, for conceptual clarity it points out to the self-sufficiency of these propositions i.e. they do not need any external middle term to relate the subject to the predicate, and for truth value, it suggests intuition as evidence and then practical argument assists our intuition to guarantee the truth value of self-evident propositions, the last theory seems to offer a more plausible explanation than others

Abstract In this article, we discuss absolutely unprovable propositions from the point of view of Brouwerian intuitionism. According to Brouwer’s definition, a proposition is absolutely unprovable if the creative mind as an ideal mathematician has a proof that both the proposition itself and its negation are unprovable from a constructive point of view. Brouwer has shown that the existence of such propositions is impossible. In his book on Brouwer and Intuitionism, Mark van Atten has described and elaborated Brouwer’s short proof on this matter. The Persian translator of this book has reconstructed and explained this proof in two different ways. In this paper, we present a more appropriate reconstruction of Brouwer’s proof. In the meantime, we will deal with Gödel’s work in generalizing Brouwer’s result from propositional logic to first-order predicate logic. In addition, we will point out that such formalizations of intuitionistic ideas in the formal language of logic cannot do justice to Brouwer’s ideas.

Abstract Naïve truth, T(x), is a predicate that applies to all of the sentences of the language and also for every sentence A of the language, T(˹A˺)↔A holds. Tarski for avoiding the liar paradox and trivializing of the language (theory) forced to withdraw from defining the naïve notion of truth and he defined truth of every language in a metalanguage. Proponents of paraconsistency claim that by accepting paraconsistent logics we can retain the naïve truth predicate. A logic would be called paraconsistent if contradiction does not entail everything. But there is another paradox, the Curry paradox, which is related to conditionals and without using EFQ can trivialize naïve theories of truth. In this paper I will argue that although if we add arithmetic and naïve truth predicate to paraconsistent logics we would have a non-trivial theory, but for low deductive power, losing some prospected properties of naïve truth predicate and leaking of inconsistency to pure arithmetic parts, these logics will be unjustifiable.

Abstract The explanation of the meaning of logical connectives in this paper is under epistemological and semantic topics and has a philosophical-logical approach. Also, the field of philosophy of language and the relationship between grammar and logic is one of the other areas that have been addressed. After establishing of classical logic, new logical systems appeared in the field with the aim of generalizing or modifying classical logic. The invalidity of some theorems of classical logic in these new reformed systems, which were called non-classical logic, created serious challenges and questions about the nature of logic. Quine is among those who, by proposing the theory of meaning-variance thesis, took a completely different position towards deviant logics. He judged between logics from an epistemological point of view and relying on natural language. His thesis was quite clear. "A change in logic is a change in the subject and actually a change in the meaning of logical connectives". Quine's thesis is generally accepted, but it also has critics. In the next step, the criticisms against Quine are described and evaluated. Meanwhile, the focus is on Putnam's criticism and his interpretation of the meaning of logical connectives. Also, Morten's criticisms from the perspective of the philosophy of language to Quine's thesis of meaning-variance have been described and evaluated. At the end, it is concluded that changing different logics does not always mean changing the subject and accepting the change of subject can not necessarily change the meaning of logical connectives.

Abstract Alfred Tarski is one of the principal founders of logical semantics. He founded representational approach in 30s and this approach is dominant in the logical semantics nowadays. But if we return to Tarski’s 20s works it seems in first glance there is no semantical approach in his 20s works. Current commentary of Tarski’s the 20s works is that he regarded logic with syntactical and proof theoretic approach in this periods. But one of Tarski’s commentators, Douglas Patterson, has showed in details that in Tarski’s the 20s works is seen a kind of semantical approach which can regard it as expressive approach. Tarski called this approach intuitionistic formalism, following his teacher Stanisław Leśniewski. In this article we are intend to address, according to Patterson’s interpretation, what is Tarski’s the expressive approach. we will attempt to establish two claims: (a) intuitionistic formalism, according to Tarski, is an approach about function of language not an articulated semantical theory in which the central concepts of expressive approach are defined and analyzed; (b) intuitionistic formalism has no conflict with representational approach about language and the former is present in background of Tarski’s works, even several years after establishment of representational approach by him.

Abstract Contextualism is the main opponent of minimalism. The debate between these two semantical approaches, stem in an old fashion dispute to determine the border between semantics and pragmatics. Contextualists claim that the sentences in the natural language are not truth-evaluable before being enriched pragmatically. In contrast, in minimalists’ viewpoint, there is a minimal semantic content that provides the truth-evaluable meaning of sentences in a way that context of utterance has limited effects on it. This contrast is based on the way and extent to which context affects semantic content. In this paper, after introducing these two approaches, the main arguments of contextualists against minimalist are discussed, then we show that minimalistic semantics like Kaplan's LD with objective interpretation of context cannot present any proper model even for sentences containing first-person reference, and on the basis of a subjective interpretation of context, the indexical/non-indexical distinction is not clear and other expressions of natural languages can be indexical, in a broad sense.

Abstract In article of “social factors in mathematical and logical knowledge” The Author shows that social factors are determinant in logical and mathematical knowledge as differences of mathematicians, variety of contradiction in Reductio ad absurdum, deconstruction in infinite values, Wittgenstein`s analysis of Sum, change of the concept of evidence in history, Begging the question of proof of axioms, Begging the question of justification of logical rules by the value tables, Prior`s argument against formalists, absence of preference for psychological explanations against sociological ones, paradoxes of material implication, To appeal to intuition rather than reasoning, the critique of circular reasoning, conventionality of logical rules, harvest paradox …
In analysis of this evidences, first, I determined minimalistic evidences as the principle of contradiction, modus ponens, reductio ad absurdum. Second, I analyzed the cases as Infinite values, Wittgenstein`s point of view, value tables, Prior`s argument, convention,
Lack of necessity in obviousness of concepts in the obvious propositions, uncertain conceptions… At last I showed that social factors are not considered essential in logical and mathematical knowledge.

Abstract Sentential connectives in classical propositional logic, according to their definition, are truth function. Contemporary philosophers of logic and language propose two main theories regarding truth functionality of counterparts of the sentential connectives in natural language. Some (including Strawson 1952; Mitchel 2008; Young 1972; Read 1995) have argued that counterparts of the sentential connectives in natural language are not truth function; on the other hand, others (including Grice 1975; Clark 1971; Jackson 1979) propose arguments for their truth functionality. Grice's (1975) defense of truth functionality of conditionals ("if…then…") in natural language which is formulated on the basis of the ideas of assertability and implicature has had a central role in the literature of recent decades. The main goal of this paper is to consider and criticize Grice's defense of truth functionality of conditionals in natural language.

Abstract Cobreros et al. (2012) developed a theory of vagueness in order to model tolerance principles coherently, in the sense that not everything falls under a vague predicate and no sorites paradox is valid. It is argued in this paper that their characterization of tolerance principles does not match with the standard conception of tolerance in the literature. In addition, their theory validates a stronger version of tolerance which suffers from clear counter examples. Furthermore, their theory validates tolerance just in a weak sense. That assimilates their theory with dominant theories of vagueness, those which accommodate tolerance principles not as true.

Abstract One of the most basic doctrines in the predicate logic is that existence can never be a predicate; rather, it is the particular quantifier. Here I''ll try to explore the views of the founders of Fregean logic on the structure of the proposition, and why it does not take existence as a predicate. Then I''ll state their explanation and solution for existential propositions. Finally, I''ll investigate the shortcomings of their analysis. Many analytical philosophers, including Moore, Kneale, Wisdon, Ayer, etc, who have denied ''existence'' as a predicate, have done so as part of their refutation of the ontological argument for the God''s existence. However, here I''ll deal only with Frege, Russell, and Quine. The other philosophers'' stance can more or less be found in one of these three.

Abstract The "Strong Programme" in the sociology of scientific knowledge is known by Edinburgh school and the relativistic approach of this school. According to their attitude all things accounted as "knowledge", have causes that make them acceptable in the society; no matter they are right or wrong. And the sociologists have to find these causes. This program, despite weaker programs that exclude scientific knowledge, is based on the idea that social factors have a role in the formation of empirical scientific knowledge, and even mathematics and logic -- types of essential knowledge. In this article we are trying to introduce and explain Edinburgh school's thought on logic and mathematics. So, first of all we will introduce the intellectual foundations of this school, and then we will try to explain briefly its main approaches with respect to sociological aspects in mathematics and knowledge. Then we will focus on the most important and outstanding case studies and their appraisal. Finally we will bring forward some points about their theoretical approaches and present some conclusions that seem to be drawn from this discussion.