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Monographs

 

 

Dragalina-Chernaya E. G. Informal Notes on Logical Form. SPb.: Aleteiya, 2015.

 

The monograph presents  traces the evolution of philosophical ideas about the logical form from Antiquity to the present day. Different versions of logical hylomorphism are systematized on the basis of the dichotomy of substantial and dynamic models of formality.

 The book is intended for specialists in the field of logic and philosophy of language, as well as for everyone who is interested in the history and the present state of philosophical logic, formal philosophy and their present state.

V. Vasyukov, E. Dragalina-Chernaya, V. Dolgorukov. Logica Ludicra: aspects of game-theoretic semantics and pragmatics. Saint-Petersburg. Aleteya, 2014.

 


The monograph is concerned with various aspects of game-theoretic semantics and pragmatics: the use of game-theoretic tools for the construction of semantics of nonclassical logics, revealing of historical and philosophical background, justification of the relevancy of game-theoretic methods for the analysis of the pragmatic architecture of natural language.

 The book is intended for specialists in the field of philosophical logic, philosophy of language, linguistic pragmatics, as well as for everyone who is interested in the current research work in the field of formal philosophy.

Dragalina-Chernaya E. G. Ontologies for Abelard and Eloise. Moscow, HSE, 2012.

 


The monograph is devoted to the ontology of standard and deviant quantification. The paper compares heuristic possibilities and ontological commitments of two paradigms in interpretation of quantifiers: as second-order predicates and as choice function from their origins(G. Frege and C. S. Pierce) to the current interpretations (abstract logic and IF-logic). The novelty of the research is in philosophical evaluation of recent technical results dedicated to the expressive and deductive potential of logic with non-standard quantification. The monograph includes approbation of the developed methods in the logical analysis of language, as well as in the logical-ontological explication of the classical philosophical problems caused by the predicative interpretation of existence.

 

Rodin A. V. Axiomatic Method and Category Theory. Dordrecht: Springer, 2014.

 

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics.

Makeeva L.B. Language, ontology and realism. Moscow, HSE, 2011.

 

The book is devoted to revealing of the specific character of realism in analytic philosophy of the twentieth century. The problem of realism is investigated in the context of the ontological approach based on the analysis of the structure of the language which we use to talk about reality. The book shows the evolution of ideas of leading analytical philosophers (B. Russell, L. Wittgenstein, R. Carnap, W. V. O. Quine, P. F. Strawson, D. Davidson, etc.) on the connection between language and reality. Additionally the views of M. Dummett and H. Putnam on the nature of analytical realism are analyzed and compared.

Geurts Bart. Quantity Implicatures. Cambridge: Cambridge University Press, 2010.

 

In recent years, quantity implicatures - a type of pragmatic inference — have been widely debated in linguistics, philosophy, and psychology, and have been subject to an enormous variety of analyses, ranging from lexical, syntactic, semantic, and pragmatic, to various hybrid accounts. In this first book-length discussion of the topic, Bart Geurts presents a theory of quantity implicatures that is resolutely pragmatic, arguing that the orthodox Gricean approach to conversational implicature is capable of accounting for all the standard cases of quantity implicature, and more. He shows how the theory deals with free-choice inferences as merely a garden variety of quantity implicatures, and gives an in-depth treatment of so-called 'embedded implicatures'. Moreover, as well as offering a comprehensive theory of quantity implicatures, he also takes into account experimental data and processing issues. Original and pioneering, and avoiding technical terminology, this insightful study will be invaluable to linguists, philosophers, and experimental psychologists alike.

V. Vasyukov. Formal Ontology. M.: Institute of Philosophy, RAS, 2006.

 

The book is devoted to formal ontology-an interdisciplinary field of research that emerged at the intersection of logic and ontology in the early XX century. The author of the monograph provides a chronology of research on formal ontology, considers examines the typology of formal ontology systems. The book thoroughly investigates  the problems of constructing formal languages for formal ontology, in particular the problem of ontological obligations of logical languages. Also the book provides an overview of formal ontology systems for artificial intelligence. A special chapter is devoted to the philosophical problems of the relationship between logic and formal ontology. A conception of global and local ontology isput forward and justified.

 The author implements various approaches and constructs systems of ontologics, which allow coordination of ontological obligations of developed formal languages and ontology of subject areas. The constructed systems form the theory of these subject areas.

 

 

Pietarinen Ahti-Veikko. Signs of Logic: Peircean Themes on the Philosophy of Language, Games, and Communication. Dordrecht: Springer, 2006.

 

Charles Sanders Peirce (1839-1914), the principal subject of this book, was one of the most profound and prolific thinkers and scientists to have come out of the United States. His pragmatic logic and scientific methodology largely represent the application of interactive and intercommunicative triadic processes, best viewed as strategic and dialogic conceptualisations of logical aspects of thought, reasoning and action. These viewpoints also involve pragmatic issues in communicating linguistic signs, and are unified in his diagrammatic logic of existential graphs. The various game-theoretic approaches to the semantics and pragmatics of signs and language, to the theory of communication, and to the evolutionary emergence of signs, provide a contemporary toolkit, the relevance of which Peirce envisioned to a wondrous extent.

 This work sheds considerable new light on these and other aspects of Peirce’s philosophy and his pragmatic theory of meaning. Many of his most significant writings in this context reflect his later thinking, covering roughly the last 15-20 years of his life, and they are still unpublished. Drawing comprehensively from his unpublished manuscripts, the book offers a fresh and rich picture of this remarkable man’s original involvement with logical aspects of thought in action.

V. Vasyukov. Quantum Logics. M.: PER SE, 2005.

 

The book is devoted to quantum logic -an interdisciplinary scientific field, which is an object of interest for physicists, mathematicians, logicians and philosophers. Quantum logics is addressed from the point of view of logical calculus and logical technique. The main attention is paid to syntactic reconstruction of quantum logic systems and construction of various abstract semantics for the obtained systems. Philosophical questions arising in the process of constructing quantum logic systems, for example, the nature of time in the quantum world, are considered and solved through the prism of non-classical methods of modern logic. At the same time, the book briefly describes the history of quantum logic and provides an overview of current research trends in this area. The last three chapters, devoted to the author's so-called quantum logic of the observed, designed to bridge the gap between the used in most quantum research formalisms and mathematical apparatus of modern quantum theory.

V. Vasyukov. Categorical Logics. M.: ANO Institute of Logics, 2005.

 
The monograph is devoted to the study of categorical deductive systems.  The categorical deductive systems is a kind of logical calculus, which includes formulas, codes of proof, converted by certain rules of inference, and operations on them. These deductive systems turn into categories if we define a system of certain identities for proofs, i.e. a category is a deductive system with inference entries and rules for their identification. The monograph regards categorical logic from the point of view of non-classical logic and its needs (in particular, the theory of proofs). Considerable attention is paid to the systematic construction of calculus of categorical logic and theoretical-categorical semantics for systems of non-classical logic, designed to replace the set-theoretic and algebraic semantics of these systems.

The book is of interest to logicians, philosophers and mathematicians and can be used in the study of theoretical and metatheoretic issues of modern logic.

Rodin A. V. Euclid’s Mathematics in Context of Plato’s and Aristotle’s Philosophy, Moscow, Nauka, 2003.

 

This book suggests a new reading of Euclidean “The Elements” on the basis of the understanding of mathematics, which is reconstructed from the classical ancient philosophical texts of Plato and Aristotle. This approach allows a new interpretation of the classic work of Euclid; also it gives a better understanding for the goals of the great mathematician of antiquity and helps to clarify elucidate difficult places of the text.

V. Vasyukov. Formal Phenomenology.  M.: Nauka, 1999.

 

The book is devoted to the construction of phenomenologically oriented formal languages that allow interpretation of rational aspects of the philosophical teachings of such prominent philosophers of the twentieth century, as Franz Brentano, Edmund Husserl, Alexius Meinong, Kazimierz Twardowski, Roman Ingarden, Jean-Paul Sartre. The book contains extensive material which illustrates the basic framework of formal phenomenology, which can be qualified as a new independent direction of logical and philosophical thought. This is a new field of scientific knowledge which is emerging from the convergence of several philosophical disciplines – ontology, logic, phenomenology.


 

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