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Author: Geoffrey Hellman
Publisher: Cambridge University Press
ISBN: 110863074X
Category : Science
Languages : en
Pages : 167
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Book Description
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.
Author: Geoffrey Hellman
Publisher: Cambridge University Press
ISBN: 110863074X
Category : Science
Languages : en
Pages : 167
Get Book Here
Book Description
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.
Author: Erich H. Reck
Publisher: Oxford University Press
ISBN: 0190641223
Category : Mathematics
Languages : en
Pages : 469
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Book Description
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.
Author: Alisa Bokulich
Publisher: Springer Science & Business Media
ISBN: 9048195977
Category : Science
Languages : en
Pages : 194
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Book Description
Recently there has been a revival of interest in structuralist approaches to science. Taking their lead from scientific structuralists such as Henri Poincaré, Ernst Cassirer, and Bertrand Russell, some contemporary philosophers and scientists have argued that the most fruitful approach to solving many problems in the philosophy of science lies in focusing on the structural features of our scientific theories. Much of the work in scientific structuralism to date has been focused on the problem of scientific realism, where it has been argued that even in cases of radical theory change the most important structural features of predecessor theories are preserved. These structural realists argue that what our most successful theories get right about the world is these abstract structural features, rather than any particular ontological claims. More recently, philosophers of science have adopted structuralist approaches to many other issues in the philosophy of science, such as scientific explanation and intertheory relations. The nine articles collected in this volume, written by the leading researchers in scientific structuralism, represent some of the most important directions of research in this field. This book will be of particular interest to those philosophers, scientists, and mathematicians who are interested in the foundations of science.
Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255
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Book Description
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author: Mirja Hartimo
Publisher: Springer Science & Business Media
ISBN: 9048137292
Category : Philosophy
Languages : en
Pages : 244
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Book Description
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?"
Author: Charles S. Chihara
Publisher: Clarendon Press
ISBN: 0191520004
Category : Mathematics
Languages : en
Pages : 298
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Book Description
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.
Author: Leon Horsten
Publisher: Cambridge University Press
ISBN: 110703941X
Category : History
Languages : en
Pages : 251
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Book Description
Develops and defends a new metaphysical and logical theory of arbitrary objects that will reinvigorate the philosophy of mathematics.
Author: Oxford University Press
Publisher: Oxford University Press, USA
ISBN: 0199808937
Category : Philosophy
Languages : en
Pages : 27
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Book Description
This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.
Author: Timothy Garrick Murphy
Publisher:
ISBN:
Category :
Languages : en
Pages : 246
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Book Description
Author: Robert Hanna
Publisher: OUP Oxford
ISBN: 0191025593
Category : Philosophy
Languages : en
Pages : 490
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Book Description
In Cognition, Content, and the A Priori, Robert Hanna works out a unified contemporary Kantian theory of rational human cognition and knowledge. Along the way, he provides accounts of (i) intentionality and its contents, including non-conceptual content and conceptual content, (ii) sense perception and perceptual knowledge, including perceptual self-knowledge, (iii) the analytic-synthetic distinction, (iv) the nature of logic, and (v) a priori truth and knowledge in mathematics, logic, and philosophy. This book is specifically intended to reach out to two very different audiences: contemporary analytic philosophers of mind and knowledge on the one hand, and contemporary Kantian philosophers or Kant-scholars on the other. At the same time, it is also riding the crest of a wave of exciting and even revolutionary emerging new trends and new work in the philosophy of mind and epistemology, with a special concentration on the philosophy of perception. What is revolutionary in this new wave are its strong emphases on action, on cognitive phenomenology, on disjunctivist direct realism, on embodiment, and on sense perception as a primitive and proto-rational capacity for cognizing the world. Cognition, Content, and the A Priori makes a fundamental contribution to this philosophical revolution by giving it a specifically contemporary Kantian twist, and by pushing these new lines of investigation radically further.
