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The paper examines questions which are essential for philosophical interpretation of the notion 'philosophical logic' (PhL): How is PhL possible and relevant?What is PhL called? For what scientific and practical reasons did the term 'PhL' become popular? The common usage of the term 'PhL' and the common objections against it. Is PhL a kind of logic? What are the relations between PhL, logic and philosophy? We consider four meaningful interpretations of the term 'PhL': PhL as a collection of logical systems in connection with philosophy; 'PhL' as logic in (of) philosophy; 'PhL' as a philosophy of logic, the latter is the main goal of the second part of this paper. The development of logic is evaluated in respect to the popular conceptions of philosophy of science (Kuhn's concept of scientific revolutions and Lacatos' concept of proliferation connected to the problem of monism and pluralism in logic). We also survey two different revolutions in modern logic: a transition from traditional to classical logic and a transition from classical to non-classical logic. The reason for both revolutions was that the development of practical applications of logic has gone ahead in relation to logical theory. We propose the idea of 'logical neofundamentalism', concerning the problem of the universality of logic and classifications of logical systems.
EN
In this paper we consider perspectives of application of coinductive and corecursive methods of non-well-founded mathematics to philosophical logic. So, it is shown that the problem of analysis can be solved by using greatest fixed points. Means of well-founded mathematics are enough only for an explication of the trivial analysis. We claim that the nontrivial analysis should be explicated by means of non-well-funded mathematics. Further, we build a non-well-founded propositional logic with syntax and semantics whose objects are defined by coinduction as streams. We also survey perspectives of relationship between non-well-founded logics and unconventional computing.
EN
Since Antiquity, logic has always enjoyed a status of something crucially important, because it shows us how to reason, if we are to reason correctly. Yet the twentieth century fostered an unprecedented boost in logical studies and delivered a wealth of results, most of which are not only understandable by non-specialists, but their very connection with the original agenda of logic is far from clear. In this paper, the author surveys how the achievements of modern logic are construed by non-specialists and subject their construal to critical scrutiny. He argues that logic cannot be taken as a theory of the limits of our world and that its prima facie most plausible construal as a theory of reasoning is too unclear to be taken at face value. He argues that the viable construal of logic takes it to be explicative of the constitutive (rather than strategic) rules of reasoning, not of the rules that tell us how to reason, but rather of rules that make up the tools with which (or in terms of which) we reason.
EN
The article has been inspired by Quine's investigations of the status of the second order logic. Following his mentor, the author adopts an ontological interpretation of the second order logic as a logic that is a general theory of individuals, classes and relations. Here the dependence ends, however, as the author undertakes to defend a new, specific status of a theory of such kind, different from the status that was assigned to it by Quine in the usual interpretation of his arguments.
EN
This paper focuses on two interrelated issues about the prospects for research projects in experimental philosophical logic. The first issue is about the role that logic plays in such projects; the second involves the role that experimental results from the cognitive sciences play in them. I argue that some notion of logic plays a crucial role in these research projects, and, in turn, the results of these projects might inform substantive debates in the philosophy of logic.
EN
In this paper, we survey the development of philosophical logic in Russia within the framework of worldwide tendencies. Philosophical logic is an extremely wide area of logical studies, requiring philosophical judgement of the basic concepts, used in modern logic, and the outcomes obtained by means of mathematical logic. However, we need to remark that the term 'philosophical logic' is uncertain and has no uniform use. Even if philosophical logic is represented as a special scientific discipline, it is not possible to define its subject, limits of application, and methods. Therefore we consider the background of different directions in philosophical logic and its connection with philosophy of logic, foundations of logic, and computerization of logic.
EN
Deductivism is explained and defended. The thesis holds that logic generally, both formal and informal, is primarily concerned with the normative distinction between good and bad reasoning, and interprets good reasoning as minimally deductively valid inference. If deductivism is true, then it follows that all fallacies of reasoning, including the so-called informal or rhetorical fallacies, are deductively invalid. Deductivism as an ideology nevertheless cuts across the distinction between formal and informal logic. To defend deductivism against potential counterexamples, it is necessary to show that common fallacies are reconstructible as deductively invalid inferences. The present essay undertakes the groundwork of such a defense by arguing that even inductive argumentation, including inductive fallacies, along with circular reasoning, can be interpreted deductively. A large selection of other informal fallacies are also reconstructed as explicit deductive invalidities following a pattern that can be used to bring other fallacies under the deductivist umbrella.
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