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Author: Alma Steingart
Publisher: University of Chicago Press
ISBN: 0226824195
Category : Mathematics
Languages : en
Pages : 300
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Book Description
The first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century. Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In recovering the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought. The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics. For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization. Axiomatics focuses on American mathematicians during a transformative time, following a series of controversies among mathematicians about the nature of mathematics as a field of study and as a body of knowledge. The ensuing debates offer a window onto the postwar development of mathematics band Cold War epistemology writ large. As Steingart’s history ably demonstrates, mathematics is the social activity in which styles of truth—here, abstraction—become synonymous with ways of knowing.
Author: Alma Steingart
Publisher: University of Chicago Press
ISBN: 0226824195
Category : Mathematics
Languages : en
Pages : 300
Get Book Here
Book Description
The first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century. Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In recovering the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought. The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics. For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization. Axiomatics focuses on American mathematicians during a transformative time, following a series of controversies among mathematicians about the nature of mathematics as a field of study and as a body of knowledge. The ensuing debates offer a window onto the postwar development of mathematics band Cold War epistemology writ large. As Steingart’s history ably demonstrates, mathematics is the social activity in which styles of truth—here, abstraction—become synonymous with ways of knowing.
Author: Jaakko Hintikka
Publisher: Springer Science & Business Media
ISBN: 9400990456
Category : Science
Languages : en
Pages : 359
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Book Description
Proceedings of the 1978 Pisa, Italy, September 4-8, 1978 Conference on the History and Philosophy of Science
Author: Robert Blanché
Publisher:
ISBN:
Category : Axioms
Languages : en
Pages : 84
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Book Description
Author: John Robb Carnes
Publisher:
ISBN:
Category : Axiomatic set theory
Languages : en
Pages : 156
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Book Description
Author: William Thomson
Publisher: Springer Nature
ISBN: 3031293983
Category :
Languages : en
Pages : 314
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Book Description
Author: M. Bunge
Publisher: Springer Science & Business Media
ISBN: 9401025223
Category : Science
Languages : en
Pages : 259
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Book Description
This book deals with some of the current issues in the philosophy, methodology and foundations of physics. Some such problems are: - Do mathematical formalisms interpret themselves or is it necessary to adjoin them interpretation assumptions, and if so how are these as sumptions to be framed? - What are physical theories about: physical systems or laboratory operations or both or neither? - How are the basic concepts of a theory to be introduced: by ref erence to measurements or by explicit definition or axiomatically? - What is the use ofaxiomatics in physics? - How are the various physical theories inter-related: like Chinese boxes or in more complex ways? - What is the role of analogy in the construction and in the inter pretation of physical theories? In particular, are classical analogues like those of particle and wave indispensable in quantum theories? - What is the role of the apparatus in quantum phenomena and what is the place of measurement theory in quantum mechanics? - How does a theory face experiment: single-handed or with the help of further theories? These and several other questions of the kind are met with by the research physicist, the physics teacher and the physics student in their everyday work. If dodged they will recur. And a wrong answer to them may obscure the understanding of what has been achieved and may even hamper further advancement. Philosophy, methodology and foundations, like rose bushes, are enjoyable when cultivated but become ugly and thorny when neglected.
Author: Antonio Piccolomini d'Aragona
Publisher: Springer Nature
ISBN: 3031514068
Category :
Languages : en
Pages : 421
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Book Description
Author: Ahmet Cevik
Publisher: CRC Press
ISBN: 1000468801
Category : Mathematics
Languages : en
Pages : 353
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Book Description
The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France
Author: Peter Hallward
Publisher: A&C Black
ISBN: 1847144470
Category : Philosophy
Languages : en
Pages : 286
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Book Description
Slavoj Š ZiŠzek is not alone in thinking that Alain Badiou's recent work is "the event of contemporary philosophy." Think Again, the first publication of its kind, goes a long way towards justifying his assessment. Badiou is nothing if not polemical and the most suitable way to approach his philosophy is precisely through the controversies it creates. This book, which opens with an introduction aimed at readers new to Badiou's work, presents a range of essays which explore Badiou's most contentious claims in the fields of ontology, politics, ethics and aesthetics. Alain Badiou has devised perhaps the only truly inventive philosophy of the subject since Sartre. Almost alone among his peers, Badiou's work promises a genuine renewal of philosophy, a subject he sees as conditioned by innovation in spheres ranging from radical politics to artistic experimentation to mathematical formalization. Slavoj Š ZiŠzek is not alone in thinking that Alain Badiou's recent work is "the event of contemporary philosophy." Think Again, the first publication of its kind, goes a long way towards justifying his assessment. Badiou is nothing if not polemical and the most suitable way to approach his philosophy is precisely through the controversies it creates. This book, which opens with an introduction aimed at readers new to Badiou's work, presents a range of essays which explore Badiou's most contentious claims in the fields of ontology, politics, ethics and aesthetics.
Author: Jaakko Hintikka
Publisher: Springer Science & Business Media
ISBN: 1402020414
Category : Philosophy
Languages : en
Pages : 244
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Book Description
Aristotle thought of his logic and methodology as applications of the Socratic questioning method. In particular, logic was originally a study of answers necessitated by earlier answers. For Aristotle, thought-experiments were real experiments in the sense that by realizing forms in one's mind, one can read off their properties and interrelations. Treating forms as independent entities, knowable one by one, committed Aristotle to his mode of syllogistic explanation. He did not think of existence, predication and identity as separate senses of estin. Aristotle thus serves as an example of a thinker who did not rely on the distinction between the allegedly different Fregean senses, thereby shedding new light on our own conceptual presuppositions. This collection comprises several striking interpretations that Jaakko Hintikka has put forward over the years, constituting a challenge not only to Aristotelian scholars and historians of ideas, but to everyone interested in logic, epistemology or metaphysics and in their history.
