The expression “the invisible hand of the market” (from the Adam Smith’s “Wealth of Nations”) sometimes acquires in modern ecomomical and everyday journalism the most unexpected overtones, like “why “the invisible hand of the market» totally disregard writer”? In the area of the scientific economic thinking “the «invisible hand” is interpreted as the objective market mechanism which coordinates the decisions of buyers and sellers. The attempts to analyze the epistemological status of “the invisible hand” are quite rare, especially in the (...) modality of the formation of the Economics as a science. Meanwhile, as it is shown in the article, there is reason to see here the first fundamental step to the origination of the scientific research program of the economic science in the strict sense. The author assumes that phenomena like “the invisible hand of the market” is comparable to what Thomas Kuhn designates as “the metaphysical parts of paradigms”, i. e. basic ontological models, which define peculiar scientific vision of the reality under research. The main difficulty for the scientific rationality in the attempts of generating scientific knowledge about society, was to represent the corresponding processes of human activity in the form of objective reality, which is required by the basic ideological attitude of the science as such. (shrink)

Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this (...) book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999. (shrink)

Cut reductions are defined for a Kripke-style formulation of modal logic in terms of indexed systems of sequents. A detailed proof of the normalization (cutelimination) theorem is given. The proof is uniform for the propositional modal systems with all combinations of reflexivity, symmetry and transitivity for the accessibility relation. Some new transformations of derivations (compared to standard sequent formulations) are needed, and some additional properties are to be checked. The display formulations [1] of the systems considered can be presented as (...) encodings of Kripke-style formulations. (shrink)

Ackermann proved termination for a special order of reductions in Hilbert's epsilon substitution method for the first order arithmetic. We establish termination for arbitrary order of reductions.

We introduce a basic intuitionistic conditional logic \(\textsf{IntCK}\) that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that \(\textsf{IntCK}\) stands in a very natural relation to other similar logics, like the basic classical conditional logic \(\textsf{CK}\) and the basic intuitionistic modal logic \(\textsf{IK}\). As for the basic intuitionistic conditional logic \(\textsf{ICK}\) proposed in Weiss (_Journal of Philosophical Logic_, _48_, 447–469, 2019 ), \(\textsf{IntCK}\) (...) extends its language with a diamond-like conditional modality \(\Diamond \hspace{-4.0pt}\rightarrow \), but its ( \(\Diamond \hspace{-4.0pt}\rightarrow \) )-free fragment is also a proper extension of \(\textsf{ICK}\). We briefly discuss the resulting gap between the two candidate systems of basic intuitionistic conditional logic and the possible pros and cons of both candidates. (shrink)

The epsilon substitution method was proposed by D. Hilbert as a tool for consistency proofs. A version for first order predicate logic had been described and proved to terminate in the monograph “Grundlagen der Mathematik”. As far as the author knows, there have been no attempts to extend this approach to the second order case. We discuss possible directions for and obstacles to such extensions.

We present a survey of proof theory in the USSR beginning with the paper by Kolmogorov [1925] and ending (mostly) in 1969; the last two sections deal with work done by A. A. Markov and N. A. Shanin in the early seventies, providing a kind of effective interpretation of negative arithmetic formulas. The material is arranged in chronological order and subdivided according to topics of investigation. The exposition is more detailed when the work is little known in the West or (...) the original presentation can be improved using notions or results which appeared later. This includes such topics as Novikov's cut-elimination method (regular formulas) and Maslov's inverse method for the predicate logic. (shrink)

We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing. Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods.

Freud's legacy deriving from his work The project for a scientific psychology (1895) could give a new impetus to the dialogue between psychoanalysis and neurosciences. A rapproachment phase is warrented. Based on the work of psychoanalysts who are themselves neuroscientists (such as Mauro Mancia, Martha Koukkou and Harold Shevrin) or have a long term dialogue with neuroscientists (Arnold Modell), three points of epistemological congruence are described: dualism is no longer a satisfactory solutioncautions for the centrality of interpretation (hermeneutics)the self-criticism of (...) neuroscientists. (shrink)

This article will formulate an explanatory model in which all the specifics of the controversy between Rome and Constantinople in the schism of 1054 will be considered in theological and ecclesiastical-political terms. Thus, both the complexity of the historical context and the diversity of the motives of its protagonists will be taken into account. In a first step, the current state of research on the events of 1054 will be presented, before confronting it with open questions in a second step. (...) They are derived partly from the historical context, partly from the ambivalent information conveyed by Latin and Greek sources. The latter entails several source-critical problems, but thereby offers a chance to pose new questions to „old“ sources. Based on these open questions, the sources will be re-read and re-interpreted in terms of determining the course of events in 1054 and the motives of the protagonists of the 1054 schism. (shrink)

This paper presents a formulation and completeness proof of the resolution-type calculi for the first order fragment of Girard's linear logic by a general method which provides the general scheme of transforming a cutfree Gentzen-type system into a resolution type system, preserving the structure of derivations. This is a direct extension of the method introduced by Maslov for classical predicate logic. Ideas of the author and Zamov are used to avoid skolomization. Completeness of strategies is first established for the Gentzen-type (...) system, and then transferred to resolution. The propositional resolution system was implemented by T. Tammet. (shrink)

We formulate epsilon substitution method for elementary analysisEA (second order arithmetic with comprehension for arithmetical formulas with predicate parameters). Two proofs of its termination are presented. One uses embedding into ramified system of level one and cutelimination for this system. The second proof uses non-effective continuity argument.

Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to k-asimulations for some k, and then that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to asimulations. Finally, it is proved that a first-order formula is equivalent to a (...) standard translation of an intuitionistic propositional formula over the class of intuitionistic Kripke models iff it is invariant with respect to asimulations between intuitionistic models. (shrink)

A Short Introduction to Modal Logic presents both semantic and syntactic features of the subject and illustrates them by detailed analyses of the three best-known modal systems S5, S4 and T. The book concentrates on the logical aspects of ...

In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that (...) relate the various notions of proving to each other and to notions of justified knowledge, implicit knowledge, and possibility. We also point out and comment upon certain principles our semantics fails to validate. (shrink)

Our thinking is still the captive of the dichotomy “national/ international.” The reaction to nationalism takes the form of an abstract internationalism, and reaction to internationalism leads to the rebirth of nationalism. However, this dichotomy was only true (and that relatively) in 19th century Europe, or at the latest, at the beginning of the twentieth century, when subnational cultures seemed on the way to disappearing, and everything European was considered “universal” (two hypotheses that the facts prove to be untrue). As (...) H. Frey observes, “Today, the decline or decadence of the West is part of the contemporary view of the world, like the electron or the dinosaur.” The linear outline of progress, with Europe at the head, did not withstand the test of the First World War. The year 1918 marked the beginning of the end of Europeanism. Since then, we have begun to speak of “areas of civilization” (Splengler), “civilizations” (Toynbee), “cultural coalitions” (Lévi-Strauss). The existence of “areas of civilization” (regions) is commonly admitted today; it has entered journalistic language and even the structure of regional commissions and agencies of the United Nations (Europe, Near East, Southern Asia, South-east Asia, and the Far East). New communities have inserted themselves between nations and humanity. What do they represent? Are they something unique, or are they divided into a certain number of types in opposition to each other because of some characteristic? And in what way have they modified our view of universal history? (shrink)

The article examines the main meanings of the concept of “social philosophy” and reveals three such meanings. First, social philosophy presents the views of a particular thinker on society and its nature. Second, social philosophy is the study of the most general laws of development of nature and society. Third, social philosophy is a value- worldview analysis of the most urgent and complex problems of social development, including philosophical criticism of the prevailing ideas in this society and the search for (...) constructive value alternatives. The author adheres to the third approach to understanding the meaning of social philosophy and gives two examples of socio-philosophical work: 1) analysis of the problem of labor in Russia in the context of the dominance of the theory of ‘catching up’ modernization; 2) analysis of the problem of democracy in the context of prevailing ideas about the inevitability of political authoritarianism as the main path of development of Russian civilization. (shrink)

The article analyzes the features of three main models of the welfare state: German, Northern European, and Anglo-Saxon. The author turns to the analysis of these models, first, because the problem of the welfare state in the world is again coming to the fore, and secondly, because social development in the most developed countries, in the author’s opinion, in the future will be largely determined by the values and behavioral models that are embedded in the three main versions of the (...) social state in Europe. From the author’s point of view, the key features of the European social model, which combines these three versions, are respect for rights and human dignity, the ideas of equality and solidarity, the ideas of social and political compromise, and the choice of an evolutionary path of development. According to the author, these features are the main difference between the European model and what characterizes the political culture of Russia with its maximalism and tendency to extremes. The author believes that the social experience of Europe is something that needs to be addressed today in Russian conditions and that can be extremely valuable for us. At the same time, as shown in the article, the welfare state in Europe has important country features. The German model is characterized by an emphasis on maintaining the socio-economic status of the individual – this is a conservative model. The Northern European model is based on the principles of universal equality and universalism – it is a social-democratic model. And the Anglo-Saxon model, based on the low role of the state, on the great importance of civil society, is a liberal model. Nevertheless, despite significant differences, as shown in the article, all these models are characterized by the desire to implement compromise principles, to find a “Golden mean,” which makes them highly effective. (shrink)

Ideas of previous constructions are combined into a short proof of topological completeness of modal logic S4 first for rational numbers and after that for real numbers in the interval.

In Part I of this paper we presented a Hilbert-style system $\Sigma _D$ axiomatizing stit logic of justification announcements interpreted over models with discrete time structure. In this part, we prove three frame definability results for $\Sigma _D$ using three different definitions of a frame plus another version of completeness result.

We consider the propositional logic equipped withChellas stitoperators for a finite set of individual agents plus the historical necessity modality. We settle the question of whether such a logic enjoys restricted interpolation property, which requires the existence of an interpolant only in cases where the consequence contains no Chellas stit operators occurring in the premise. We show that if action operators count as logical symbols, then such a logic has restricted interpolation property iff the number of agents does not exceed (...) three. On the other hand, if action operators are considered to be nonlogical symbols, then the restricted interpolation fails for any number of agents exceeding one. It follows that unrestricted Craig interpolation also fails for almost all versions of stit logic. (shrink)

We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing, 259–279, 2018).

A simple cut elimination proof for arithmetic with the epsilon symbol is used to establish the termination of a modified epsilon substitution process. This opens a possibility of extension to much stronger systems.

The completeness of the modal logic S4 for all topological spaces as well as for the real line , the n-dimensional Euclidean space and the segment etc. was proved by McKinsey and Tarski in 1944. Several simplified proofs contain gaps. A new proof presented here combines the ideas published later by G. Mints and M. Aiello, J. van Benthem, G. Bezhanishvili with a further simplification. The proof strategy is to embed a finite rooted Kripke structure for S4 into a subspace (...) of the Cantor space which in turn encodes . This provides an open and continuous map from onto the topological space corresponding to . The completeness follows as S4 is complete with respect to the class of all finite rooted Kripke structures. (shrink)

In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant domains [13]. More precisely, we show that there is a valid implication $\phi \rightarrow \psi $ with no interpolant. Importantly, this result does not contradict the unfortunately named ‘Craig interpolation’ theorem established by Rauszer in [24] since that article is about the property more correctly named ‘deductive interpolation’ (see (...) Galatos, Jipsen, Kowalski and Ono’s use of this term in [5]) for global consequence. Given that the deduction theorem fails for bi-intuitionistic logic with global consequence, the two formulations of the property are not equivalent. (shrink)