Mathematics Ideas and the Physical Real

Author: Albert Lautman
Publisher: A&C Black
ISBN: 9781441144331
Release Date: 2011-06-02
Genre: Philosophy

Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.

Essays on Deleuze

Author: Daniel W Smith
Publisher: Edinburgh University Press
ISBN: 9780748655373
Release Date: 2012-05-31
Genre: Philosophy

Brings together 18 key essays, plus two completely new essays, by one of the world's leading commentators on the work of the French philosopher Gilles Deleuze.

Badiou and Philosophy

Author: Sean Bowden
Publisher: Edinburgh University Press
ISBN: 9780748668335
Release Date: 2012-06-30
Genre: Philosophy

This collection of thirteen essays engages directly with the work of Alain Badiou, focusing specifically on the philosophical content of his work and the various connections he established with both his contemporaries and his philosophical heritage.

Literary Infinities

Author: Baylee Brits
Publisher: Bloomsbury Publishing USA
ISBN: 9781501331473
Release Date: 2017-11-16
Genre: Literary Criticism

Today, we have forgotten that mathematics was once aligned with the arts, rather than with the sciences. Literary Infinities analyses the connection between the late 19th-century revolution in the mathematics of the infinite and the literature of 20th-century modernism, opening up a novel path of influence and inquiry in modernist literature. Baylee Brits considers the role of numbers and the concept of the infinite in key modernists, including James Joyce, Italo Svevo, Jorge Luis Borges, Samuel Beckett and J.M. Coetzee. She begins by recuperating the difficult and rebellious German mathematician, Georg Cantor, for the broader artistic, cultural and philosophical project of modernism. Cantor revolutionized the mathematics of the infinite, creating reverberations across the numerical sciences, philosophy, religion and literary modernism. This 'modernist' infinity is shown to undergird and shape key innovations in narrative form, creating a bridge between the mathematical and the literary, presentation and representation, formalism and the tactile imagination.

Empiricism Logic and Mathematics

Author: Hans Hahn
Publisher: Springer Science & Business Media
ISBN: 9789400989825
Release Date: 2012-12-06
Genre: Science

The role Hans Hahn played in the Vienna Circle has not always been sufficiently appreciated. It was important in several ways. In the ftrst place, Hahn belonged to the trio of the original planners of the Circle. As students at the University of Vienna and throughout the fIrst decade of this century, he and his friends, Philipp Frank and Otto Neurath, met more or less regularly to discuss philosophical questions. When Hahn accepted his fIrSt professorial position, at the University of Czernowitz in the north east of the Austrian empire, and the paths of the three friends parted, they decided to continue such informal discussions at some future time - perhaps in a somewhat larger group and with the cooperation of a philosopher from the university. Various events delayed the execution of the project. Drafted into the Austrian army during the first world war" Hahn was wounded on the Italian front. Toward the end of the war he accepted an offer from the University of Bonn extended in recognition of his remarkable 1 mathematical achievements. He remained in Bonn until the spring of 1921 when he returm:d to Vienna and a chair of mathe matics at his alma mater. There, in 1922, the Mach-Boltzmann professorship for the philosophy of the inductive sciences became vacant by the death of Adolf Stohr; and Hahn saw a chance to realize his and his friends' old plan.


Author: Richard John Kosciejew
Publisher: Author House
ISBN: 9781496936356
Release Date: 2014-10-16
Genre: Philosophy

If the universe is a seamlessly interactive system that evolves to an assigning of some levelling plexuity, and that, the lawful regularities of this universe are emergent properties of this system; we can legibly assume that the cosmos, as a legitimate point of singularity, as an undivided totality in the contributions for making of its whole. In that, for evincing to the 'progressive principal order' of complementarity, as placed within the intertwining relations within its given parts. Minded that this collective and undivided whole exists in some sense within all contributions of its parts, then one can declare positively or firmly maintain that it operates in self-reflective fashion and is the evidence for all emergent plexuities. Since human consciousness evinces self-reflective awareness in the human brain and since this brain is equivalently matched to all physical phenomena, as this can be viewed as an emergent property in the possessive nature of totality, such that it can be found within the whole for existing by its reason of certainty. As, can be feasible as plausibly concluded, that locality presupposes the consciousness of the universe, as 'we' are conscious to its existing conventions within this prevalent response to approaching the expeditions into which of the past-present-future dimensions, allow to some marginal glimpse into the unthinkable.

Developing Mathematical Thinking

Author: Jonathan D. Katz
Publisher: Rowman & Littlefield
ISBN: 9781475810585
Release Date: 2014-07-07
Genre: Education

The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.

On True and False Ideas

Author: Antoine Arnauld
Publisher: Manchester University Press
ISBN: 0719032032
Release Date: 1990-01-01
Genre: Cognition

This is an English translation of Arnauld's philosophical reply to Malebranche's Search After Truth. It forms the core of one of the most important philosophical controversies of the 17th century, and one which was to have an impact on 18th-century philosophy, especially in Britain. The translation is accompanied by an introductory essay which looks at the history of the problem of perceptual cognition up until the dispute between Arnauld and Malebranche. The subsequent exchanges between the two are discussed in an appendix.

Mathematics and the Physical World

Author: Morris Kline
Publisher: Courier Corporation
ISBN: 9780486136318
Release Date: 2012-03-15
Genre: Mathematics

Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

The Non Local Universe

Author: Robert Nadeau
Publisher: Oxford University Press
ISBN: 9780198030416
Release Date: 2001-05-31
Genre: Science

Classical physics states that physical reality is local--a point in space cannot influence another point beyond a relatively short distance. However, In 1997, experiments were conducted in which light particles (photons) originated under certain conditions and traveled in opposite directions to detectors located about seven miles apart. The amazing results indicated that the photons "interacted" or "communicated" with one another instantly or "in no time." Since a distance of seven miles is quite vast in quantum physics, this led physicists to an extraordinary conclusion--even if experiments could somehow be conducted in which the distance between the detectors was half-way across the known universe, the results would indicate that interaction or communication between the photons would be instantaneous. What was revealed in these little-known experiments in 1997 is that physical reality is non-local--a discovery that Robert Nadeau and Menas Kafatos view as "the most momentous in the history of science." In The Non-Local Universe, Nadeau and Kafatos offer a revolutionary look at the breathtaking implications of non-locality. They argue that since every particle in the universe has been "entangled" with other particles like the two photons in the 1997 experiments, physical reality on the most basic level is an undivided wholeness. In addition to demonstrating that physical processes are vastly interdependent and interactive, they also show that more complex systems in both physics and biology display emergent properties and/or behaviors that cannot be explained in the terms of the sum of parts. One of the most startling implications of non-locality in human terms, claim the authors, is that there is no longer any basis for believing in the stark division between mind and world that has preoccupied much of western thought since the seventeenth century. And they also make a convincing case that human consciousness can now be viewed as emergent from and seamlessly connected with the entire cosmos. In pursuing this groundbreaking argument, the authors not only provide a fascinating history of developments that led to the discovery of non-locality and the sometimes heated debate between the great scientists responsible for these discoveries. They also argue that advances in scientific knowledge have further eroded the boundaries between physics and biology, and that recent studies on the evolution of the human brain suggest that the logical foundations of mathematics and ordinary language are much more similar than we previously imagined. What this new knowledge reveals, the authors conclude, is that the connection between mind and nature is far more intimate than we previously dared to imagine. What they offer is a revolutionary look at the implications of non-locality, implications that reach deep into that most intimate aspect of humanity--consciousness.

God Very Probably

Author: Robert H. Nelson
Publisher: Wipf and Stock Publishers
ISBN: 9781498223768
Release Date: 2015-11-11
Genre: Religion

In recent years, a number of works have appeared with important implications for the age-old question of the existence of a god. These writings, many of which are not by theologians, strengthen the rational case for the existence of a god, even as this god may not be exactly the Christian God of history. This book brings together for the first time such recent diverse contributions from fields such as physics, the philosophy of human consciousness, evolutionary biology, mathematics, the history of religion, and theology. Based on such new materials as well as older ones from the twentieth century, it develops five rational arguments that point strongly to the (very probable) existence of a god. They do not make use of the scientific method, which is inapplicable to the question of a god. Rather, they are in an older tradition of rational argument dating back at least to the ancient Greeks. For those who are already believers, the book will offer additional rational reasons that may strengthen their belief. Those who do not believe in the existence of a god at present will encounter new rational arguments that may cause them to reconsider their opinion.

Teaching Mathematics in the Block

Author: Susan Nicodemus Gilkey
Publisher: Eye On Education
ISBN: 188300151X
Release Date: 1998-01-01
Genre: Education

Provides detailed instructional strategies, sample lesson plans, and sample assessments so that mathematics teachers can make the best use of the additional time.