Mathematical Structuralism

Mathematical Structuralism
Title Mathematical Structuralism PDF eBook
Author Geoffrey Hellman
Publisher Cambridge University Press
Pages 167
Release 2018-11-29
Genre Science
ISBN 110863074X

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The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.

The Prehistory of Mathematical Structuralism

The Prehistory of Mathematical Structuralism
Title The Prehistory of Mathematical Structuralism PDF eBook
Author Erich H. Reck
Publisher Oxford University Press
Pages 469
Release 2020
Genre Mathematics
ISBN 0190641223

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This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.

Conceptions of Set and the Foundations of Mathematics

Conceptions of Set and the Foundations of Mathematics
Title Conceptions of Set and the Foundations of Mathematics PDF eBook
Author Luca Incurvati
Publisher Cambridge University Press
Pages 255
Release 2020-01-23
Genre History
ISBN 1108497829

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Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Phenomenology and Mathematics

Phenomenology and Mathematics
Title Phenomenology and Mathematics PDF eBook
Author Mirja Hartimo
Publisher Springer Science & Business Media
Pages 244
Release 2010-03-11
Genre Philosophy
ISBN 9048137292

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During Edmund Husserl’s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl’s writings can be fruitfully compared and contrasted with both 19th century figures (Boole, Schröder, Weierstrass) as well as the 20th century characters (Heyting, Zermelo, Gödel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl’s phenomenology offers also a systematically rich but little researched area of investigation. This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics. It gathers the contributions of the main scholars of this emerging field into one publication for the first time. Combining both historical and systematic studies from various angles, the volume charts answers to the question "What kind of philosophy of mathematics is phenomenology?"

Structures Mères: Semantics, Mathematics, and Cognitive Science

Structures Mères: Semantics, Mathematics, and Cognitive Science
Title Structures Mères: Semantics, Mathematics, and Cognitive Science PDF eBook
Author Alberto Peruzzi
Publisher Springer Nature
Pages 191
Release 2020-09-14
Genre Philosophy
ISBN 3030518213

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This book reports on cutting-edge concepts related to Bourbaki’s notion of structures mères. It merges perspectives from logic, philosophy, linguistics and cognitive science, suggesting how they can be combined with Bourbaki’s mathematical structuralism in order to solve foundational, ontological and epistemological problems using a novel category-theoretic approach. By offering a comprehensive account of Bourbaki’s structuralism and answers to several important questions that have arisen in connection with it, the book provides readers with a unique source of information and inspiration for future research on this topic.

Constructibility and Mathematical Existence

Constructibility and Mathematical Existence
Title Constructibility and Mathematical Existence PDF eBook
Author Charles S. Chihara
Publisher Clarendon Press
Pages 298
Release 1990-04-12
Genre Mathematics
ISBN 0191520004

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This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach in an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.

The Metaphysics and Mathematics of Arbitrary Objects

The Metaphysics and Mathematics of Arbitrary Objects
Title The Metaphysics and Mathematics of Arbitrary Objects PDF eBook
Author Leon Horsten
Publisher Cambridge University Press
Pages 251
Release 2019-06-13
Genre History
ISBN 110703941X

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Develops and defends a new metaphysical and logical theory of arbitrary objects that will reinvigorate the philosophy of mathematics.