Routledge, 1952. — 253 p. The Development of Bertrand Russell’s Philosophy The Construction of Numbers, Descriptions, and Classes Numbers Descriptions Classes The Problem of The External World Hard vs. Soft Data Logical Atomism Physics and Perception The Construction of Material Objects and the Entities of Physics Material Objects as Classes of Appearances Material Objects as...
Изд-е 3-е. — Пер. со 2-го нем. изд-я, испр. и доп. — И. Яшунского. — М.: Либроком, 2009. — 120 с. — (Физико-математическое наследие: математика (философия математики)). Чем, собственно, занимается математика? Почему она долго являлась наименее популярной из всех наук, несмотря на то, что вся человеческая культура имеет подлинной своей основой математические науки? Каким образом...
Cambridge: Cambridge University Press, 2025. — 82 p. This Element looks at the very beginning of the philosophy of mathematics in Western thought. It covers the first reflections on attempts to untie mathematics from its practical usage in administration, commerce, and land-surveying and discusses the first ideas to see mathematical structures as constituents underlying the...
Palgrave Macmillan, 2024. — 397 p. This volume showcases some of the up-and-coming voices of an emerging field - the philosophy of set theory - which in recent years has gained prominence in the philosophy of mathematics. The chapters in this volume both present new topics and propose solutions to old problems. It contains a broad picture of the philosophy of set theory,...
Springer Cham, 2024. — 3269 p. — ISBN: 978-3031408458. The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of...
Cambridge University Press, 2024. — 86 p. Purity in Practice Einstein on Purity in Geometry Purity in Number Theory: Jacobi’s Four Squares Theorem Summing up the Case Studies Purity of Proof vs. Purity of Definition Looking Ahead A Brief History of Purity Types of Purity Geographical Purity Topical Purity Syntactic Purity Logical Purity Elemental Purity Values of Purity Purity...
Cambridge: Cambridge University Press, 2025. — 86 p. The aim of this Element is to provide an overview of abstractionism in the philosophy of mathematics. The authors distinguish between mathematical abstractionism, which interprets mathematical theories on the basis of abstraction principles, and philosophical abstractionism, which attributes a philosophical significance to...
Cambridge: Cambridge University Press, 2024. — 94 p. This Element lays the foundation, introduces a framework, and sketches the program for a systematic study of mathematical notations. It is written for everyone who is curious about the world of symbols that surrounds us, in particular researchers and students in philosophy, history, cognitive science, and mathematics...
AK Peters, 2003. — 350 p. This new approach to mathematics - the utilization of advanced computing technology in mathematical research - is often called experimental mathematics. The computer provides the mathematician with a "laboratory" in which she can perform experiments - analyzing examples, testing out new ideas, or searching for patterns. This book presents the rationale...
М.: Наука, 1975. — 152 с. Книга посвящена проблемам логики, семиотики, методологии науки. В ней говорится о структурных аспектах процесса познания в терминах математической логики и алгебры. Уточняется понятие модели и процедуры моделирования с помощью понятий изоморфизма, гомоморфизма и их обобщений. Рассматриваются возможности упрощения описываемой концептуальной схемы и...
A K Peters/CRC Press, 2025. — 180 p. — (AK Peters/CRC Recreational Mathematics Series). — ISBN: 978-1-003-28066-8. Mathematical Meditationsidentifies, explores, and celebrates those aspects of mathematics that are good for you and your overall wellbeing. It is necessary for everyone to have a little time to think every so often: to contemplate, meditate, and try to understand...
A K Peters/CRC Press, 2025. — 180 p. — (AK Peters/CRC Recreational Mathematics Series). — ISBN: 978-1-003-28066-8. Mathematical Meditationsidentifies, explores, and celebrates those aspects of mathematics that are good for you and your overall wellbeing. It is necessary for everyone to have a little time to think every so often: to contemplate, meditate, and try to understand...
A K Peters/CRC Press, 2025. — 180 p. — (AK Peters/CRC Recreational Mathematics Series). — ISBN: 978-1-003-28066-8. Mathematical Meditationsidentifies, explores, and celebrates those aspects of mathematics that are good for you and your overall wellbeing. It is necessary for everyone to have a little time to think every so often: to contemplate, meditate, and try to understand...
A K Peters/CRC Press, 2025. — 180 p. — (AK Peters/CRC Recreational Mathematics Series). — ISBN: 978-1-032-24906-3. Mathematical Meditationsidentifies, explores, and celebrates those aspects of mathematics that are good for you and your overall wellbeing. It is necessary for everyone to have a little time to think every so often: to contemplate, meditate, and try to understand...
Cambridge: Cambridge University Press, 2024. — 104 p. This Element discusses the philosophical roles of definitions in the attainment of mathematical knowledge. It first focuses on the role of definitions in foundational programs, and then examines their major varieties, both as regards their origins, their potential epistemic roles, and their formal constraints. It examines...
Springer, 2024. — 270 p. This book provides a philosophy of mathematics that resonates with critical mathematics education. It draws attention to the social complexities that characterise the period of Modernity including the extreme exploitation of manual workers and their families, brutal forms of colonisations, trading of slaves, and the formation of racist ideologies. It...
Cambridge: Cambridge University Press, 2024. — 80 p. This Element introduces a young field, the 'philosophy of mathematical practice'. We first offer a general characterisation of the approach to the philosophy of mathematics that takes mathematical practice seriously and contrast it with 'mathematical philosophy'. The latter is traced back to Bertrand Russell and the...
London: UCL, 2020. — 95 p. Typically, Wittgenstein is assumed to have been apathetic to the developments in computability theory through the 1930s. Wittgenstein’s disparaging remarks about Gödel’s incompleteness theorems, and mathematical logic in general, are well documented. It seems safe to assume the same would apply for Turing’s work. The chief aim of this thesis is to...
Oxford University Press, 1977. — 392 p. The book was planned and written as a single, sustained argument. But earlier versions of a few parts of it have appeared separately. The object of this book is both to establish the existence of the paradoxes, and also to describe a non-Pascalian concept of probability in terms of which one can analyse the structure of forensic proof...