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"Mathematics Philosophy."
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Freedom in mathematics
This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani's popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political establishment. The authors explore three major directions in their dialogue: the highly complex relationship between mathematics and reality, the subject of many debates and opposing viewpoints; the freedom that the construction of mathematics has given humankind by enabling them to develop the natural sciences as well as mathematical research; and the responsibility with which the scientific community and governments should address the role of mathematics in research and education policies.
Book
Towards a Philosophy of Real Mathematics
In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
eBook
Plato's ghost
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions.
eBook
Second philosophy : a naturalistic method
Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. This book describes and practices a particularly austere form of naturalism called ‘Second Philosophy’. Without a definitive criterion for what counts as ‘science’ and what doesn't, Second Philosophy can't be specified directly — ‘trust only the methods of science!’ or some such thing — so the book proceeds instead by illustrating the behaviors of an idealized inquirer called here the ‘Second Philosopher’. This Second Philosopher begins from perceptual common sense and progresses from there to systematic observation, active experimentation, theory formation, and testing, working all the while to assess, correct, and improve methods along the way. ‘Second Philosophy’ is then the result of the Second Philosopher's investigations. This book delineates the Second Philosopher's approach by tracing reactions to various familiar sceptical and transcendental views (Descartes, Kant, Carnap, late Putnam, van Fraassen), comparing methods to those of other self-described naturalists (especially Quine), and examining a prominent contemporary debate (between disquotationalists and correspondence theorists in the theory of truth) to extract a properly second-philosophical line of thought. The book then undertakes to practice Second Philosophy in its reflections on the ground of logical truth, the methodology, ontology, and epistemology of mathematics, and the general prospects for metaphysics naturalized.
eBook
Mathematics and Information in the Philosophy of Michel Serres
This book introduces the reader to Serres’ unique manner of ‘doing philosophy’ that can be traced throughout his entire oeuvre: namely as a novel manner of bearing witness. It explores how Serres takes note of a range of epistemologically unsettling situations, which he understands as arising from the short-circuit of a proprietary notion of capital with a praxis of science that commits itself to a form of reasoning which privileges the most direct path (simple method) in order to expend minimal efforts while pursuing maximal efficiency. In Serres’ universal economy, value is considered as a function of rarity, not as a stock of resources. This book demonstrates how Michel Serres has developed an architectonics that is coefficient with nature. Mathematic and Information in the Philosophy of Michel Serres acquaints the reader with Serres’ monist manner of addressing the universality and the power of knowledge - that is at once also the anonymous and empty faculty of incandescent, inventive thought. The chapters of the book demarcate, problematize and contextualize some of the epistemologically unsettling situations Serres addresses, whilst also examining the particular manner in which he responds to and converses with these situations.
eBook
How mathematicians think
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics,How Mathematicians Thinkreveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results.
Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure.
The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, andHow Mathematicians Thinkprovides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a \"final\" scientific theory?
Ultimately,How Mathematicians Thinkshows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
eBook