Soyons Logiques / Let Us Be Logical
“Let's be Logical” is a double invitation. Although logic often refers to a disposition of mind that we all share, this disposition might be confused once its theoretical sources are questioned. The present volume offers thirteen articles that address various aspects of the discipline of logic and its methods, notably formalism, the theory of opposition, mathematical truth, and history of logic. This volume has been prepared with the pedagogical concern of making it accessible to a wide audience of logic and philosophy readers.
The aim of the present paper is twofold. On the basis of Frege's "Sense and Denotation", to compare two competing theories of meaning, namely: a one-sorted semantics à la Frege, where every sign symbolizes uniformly; a two-sorted semantics à la Kripke, where a distinction can be made between two modes of functioning among these entities. Then to depict Hintikka's epistemic logic as an internalization of sense, that is, a calculus by means of the operations leading to Frege's theory of meaning.
In this early paper C. Wright Mills tries to ground the possibility for the study of thinking (including logical) from the perspective of sociology of knowledge. Following G.H. Mead, he shows that thinking is a social process because every thinker converses with his or her audience using the norms of rationality and logicality common to his or her culture. Language serves as a mediator between thinking and social patterns. Proposing to consider the meaning of language as the common social behavior evoked by it, Mills finds a way to combine three levels of analysis: psychological, social and cultural.
The article is devoted to considering the problem of possible worlds in Leibniz. The author shows that the idea of possible worlds is basic in Leibniz’s theory of «the best of all possible worlds» where it is postulated in the metaphysical justification of the divine creation as a free act and in the solution of the theological problem concerning the existence of evil. Also, Leibniz connects this idea with logic which he interprets as a science about all possible worlds. Leibniz's dichotomy between «truths of reason» and «truths of fact» is investigated in the context of necessity and contingency. Logical and moral reasons for God's choice of the best of possible worlds are examined in detail in both early and mature works by Leibniz.
Recently some elaborations were made concerning the game theoretic semantic of Lℵ0 and its extension. In the paper this kind of semantics is developed for Dishkant’s quantum modal logic LQ which is also, in fact, the speciﬁc extension of Lℵ0 . As a starting point some game theoretic interpretation for the S L system (extending both Lukasiewicz logic Lℵ0 and modal logic S5) was exploited which has been proposed in 2006 by C.Ferm˝uller and R.Kosik . They, in turn, based on ideas already introduced by Robin Giles in the 1970th to obtain a characterization of Lℵ0 in terms of a Lorenzen style dialogue game combined with bets on the results of binary experiments that may show dispersion.
The present volume is devoted to the 'Open Rusian-Finish Colloquium on Logic' (ORFIC), held at the Saint-Petersburg State University, on June 14-16, 2012. Among the participants there were such prominent Finish logicians as Jaakko Hintikka, Ilkka Niiniluoto ang Gabriel Sandu. The volume covers the most interesting results recently obtained in different areas of research in logic.
This volume is of interest to everyone, concerned in modern logic.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.