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.
Conditional Kolmogorov complexity of a word $a$ given a word $b$ is the minimum length of a program that prints $a$ given $b$ as an input. We generalize this notion to quadruples of strings $a,b,c,d$: their joint conditional complexity $\K((a\to c)\land(b\to d))$ is defined as the minimum length of a program that given $a$ outputs $c$ and given $b$ outputs $d$. In this paper, we prove that the joint conditional complexity cannot be expressed in terms of usual conditional (and unconditional) Kolmogorov complexity. This result provides a negative answer to the following question, asked by A.Shen on a session of Kolmogorov seminar at Moscow State University in 1994: Is there a problem of information processing whose complexity is not expressible in terms of conditional (and unconditional) Kolmogorov complexity? We show that a similar result holds for classical Shannon entropy. We provide two proofs of both results, an effective one and a ``quasi-effective'' one. Finally we present a quasi-effective proof of a strong version of the following statement: there are two strings whose mutual information cannot be extracted. Previously, only a non-effective proof of that statement was known. The results concerning Kolmogorov complexity appeared, in a preliminary form, in the Proceedings of the 16th Annual IEEE Conference on Computational Complexity in 2001. [A. Muchnik and N. Vereshchagin. ``Logical operations and Kolmogorov complexity. II''. Proc. of 16th Annual IEEE Conference on Computational Complexity, Chicago, June 2001, pp. 256--265.]
The present manual is written on the basis of the course on inductive logic which is delivered in English to philosophy students of National Research University Higher School of Economics. The manual describes the main approaches to constructing inductive logic; it clarifies its key notions and rules, and it formulates its major problems. This introductory text can be useful for all readers who are interested in contemporary inductive logic.
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.