In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice.

Author: Joel David Hamkins

Publisher: MIT Press

ISBN: 9780262362658

Category: Mathematics

Page: 352

View: 810

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical ...

Author: William Ewald

Publisher: Springer-Verlag

ISBN: 9783540694441

Category: Mathematics

Page: 1062

View: 634

The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.

In this collection of twenty-one lectures, Dr. Keyser has "endeavored to present in the language current among educated men and women some of the maturer fruits" of the study of "the nature of mathematics, upon its significance in thought, ...

In this collection of twenty-one lectures, Dr. Keyser has "endeavored to present in the language current among educated men and women some of the maturer fruits" of the study of "the nature of mathematics, upon its significance in thought, and upon its bearing on human life." These lectures are designed primarily for students of thought, but the author hopes that they "may not be ungrateful to a much wider circle of readers and scholars" among whom he instances "all readers who desire to acquire a fair understanding of such genuinely great mathematical ideas as are accessible to all educated laymen and to come into touch with the universal spirit of the science which Plato called divine." What mathematical training is necessary for a proper appreciation of these lectures? "So much knowledge of algebra, geometry and trigonometry as a capable student can acquire in one collegiate year." In propounding the question, "how much mathematical discipline is essential to the appropriate education of men and women as human beings?" The author clearly and forcibly states the "evident tokens and the cardinal constituents of that which in human beings is human," and which they possess in some recognizable measure: a sense for language, for expression in speech-the literary faculty; a sense for the past, for the value of experience-the historical faculty; a sense for the future, for prediction, for natural law-the scientific faculty; a sense for fellowship, cooperation and justice-the political faculty; a sense for the beautiful-the artistic faculty; a sense for logic, for vigorous thinking-the mathematical faculty; a sense for wisdom, for world harmony, for cosmic understanding -the philosophical faculty; and a sense for the mystery of divinity-the religious faculty. The aim of mathematics, says the author, is "to think vigorously whatever is vigorously thinkable, or whatever may become vigorously thinkable, in course of the upward striving and refining evolution of ideas." And thinking he defines as the "handling of ideas as ideas-the formation of concepts, the combination of concepts into higher and higher ones, discernment of the relations subsisting among them, embodiment of these relations in the forms of judgments or propositions, the ordering and use of these in the construction of doctrine regarding life and the world."

"From his return to Cambridge in 1929 to his death in 1951, Wittgenstein influenced philosophy almost exclusively through teaching and discussion.

Author: Ludwig Wittgenstein

Publisher: University of Chicago Press

ISBN: 9780226904269

Category: Mathematics

Page: 300

View: 732

"From his return to Cambridge in 1929 to his death in 1951, Wittgenstein influenced philosophy almost exclusively through teaching and discussion. These lecture notes indicate what he considered to be salient features of his thinking in this period of his life."--Publisher's description.

These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989.

Author: G. Corsi

Publisher: Springer Science & Business Media

ISBN: 9789401124966

Category: Philosophy

Page: 329

View: 779

Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general `malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.

"By looking at Frege's lectures on logic through the eyes of the young Carnap, this book casts new light on the history of logic and analytic philosophy.

Author: Gottlob Frege

Publisher: Open Court Publishing

ISBN: 0812695461

Category: Philosophy

Page: 170

View: 203

"By looking at Frege's lectures on logic through the eyes of the young Carnap, this book casts new light on the history of logic and analytic philosophy. As two introductory essays by Gottfried Gabriel and by Erich H. Reck and Steve Awodey explain, Carnap's notes allow us to better understand Frege's deep influence on Carnap and analytic philosophy, as well as the broader philosophical matrix from which both continental and analytic styles of thought emerged in the 20th century."--BOOK JACKET.

This book is a collection of papers presented at the conference New Trends in the History and Philosophy of Mathematics held at the University of Roskilde, Denmark, 6-8 August 1998.

Author: Tinne Hoff Kjeldsen

Publisher:

ISBN: UOM:39015061339001

Category: Technology & Engineering

Page: 161

View: 126

This book is a collection of papers presented at the conference New Trends in the History and Philosophy of Mathematics held at the University of Roskilde, Denmark, 6-8 August 1998. The purpose of the meeting was to present some of the new ideas on the study of mathematics, its character and the nature of its development. During the last decades work in history and philosophy of mathematics has led to several new original views on mathematics. Both new methods and angles of study have been introduced, and old views of, say, the nature of mathematical theories and proofs have been challenged. For instance, disciplines as etnohistorical studies of mathematics and the sociology of mathematics have resulted in several new insights, and classical historians of mathematics are also experimenting with new perspectives. In a similar way philosophy of mathematics has witnessed rather deep changes. Classical foundational studies have been challenged by new broader perspectives. The aim was to provide a forum within which historians of mathematics, philosophers, and mathematicians could exchange ideas and discuss different new approaches in the history and philosophy of mathematics. The book includes papers by Joan Richards, Henk J. M. Bos, Donald MacKenzie, Arthur Jaffe, Jody Azzouni and Paulus Gerdes. It also includes an extended introduction.

Author: Luitzen Egbertus Jan BrouwerPublish On: 2011-04-28

Brouwer's own powerful style is evident throughout the work.

Author: Luitzen Egbertus Jan Brouwer

Publisher: Cambridge University Press

ISBN: 0521177367

Category: Mathematics

Page: 122

View: 764

Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work.

In order to clarify what is meant by Wittgenstein ' s " new method " of philosophy
in connection with mathematical calculi as formulated in his manuscripts and lectures 1930 - 3 and later , we have to elucidate certain topics which are
relevant in ...

Kurt Gödel was the greatest logician of this century. This third volume of his collected works consists of previously unpublished material, both essays and lectures.

Author: Kurt Gödel

Publisher: Oxford University Press on Demand

ISBN: 0195072553

Category: Mathematics

Page: 532

View: 664

Kurt Gödel was the greatest logician of this century. This third volume of his collected works consists of previously unpublished material, both essays and lectures.

Lecture on Natural Philosophy . Books , 8C Remarks . The allotment of time and
the list of books must be considered as provisional , and subject to modification
as experience may dictate . Mathematics and Natural Philosophy , 8 hours per ...

This volume contains 11 lectures ranging over a variety of topics in the history of mathematics. The lectures, presented between 1970 and 1987, were delivered in a variety of venues and appeared only in less accessible publications.

Author: H. J. M. Bos

Publisher: American Mathematical Soc.

ISBN: 082189675X

Category: Mathematics

Page: 197

View: 860

" [These lectures] are about themes of the history of mathematics which for various reasons are dear to me. The early differential and integral calculus, Christiaan Huygens, and the concept of construction in seventeenth- and eighteenth-century mathematics are the three themes around which much of my research has concentrated and which continue to fascinate me by the insights they offer in the development of that special human activity called mathematics." ---from the Introduction. This volume contains 11 lectures ranging over a variety of topics in the history of mathematics. The lectures, presented between 1970 and 1987, were delivered in a variety of venues and appeared only in less accessible publications. Those who teach mathematics, as well as mathematics historians, will appreciate this insightful, wide ranging book. The History of Mathematics series is cojointly published with the London Mathematical Society

The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.

Author: A. Heyting

Publisher: Elsevier

ISBN: 9781483278155

Category: Mathematics

Page: 644

View: 330

L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.

The papers contained in this volume exhibit 12 outstanding examples of historians approaching their craft in distinct ways, yet consistent with Kenneth May's vision.

Author: Michael Kinyon

Publisher: Springer Science & Business Media

ISBN: 9780387282725

Category: Mathematics

Page: 358

View: 565

The Kenneth May Lectures have never before been published in book form Important contributions to the history of mathematics by well-known historians of science Should appeal to a wide audience due to its subject area and accessibility

... etc.; Mental Philosophy; Mathematics — Surveying; German; French; Spanish
or Italian (optional); Greek and Epman Mythology — Lectures; Constitutional
History; Zoology — Lectures; Mechanics. Second Term — Anglo-Saxon and
Early ...

Author: University of California (System). RegentsPublish On: 1875

... Composition - Literary Biography , Sketches , prose or verse , etc . ; Men . tal Philosophy ; Mathematics - Surveying ; German ; French ; Spanish or Italian (
optional ) ; Greek and Roman Mythology - Lectures ; Consti . tutional History ;
Zoology ...

Author: University of California (System). Regents

Philosophical Problems of Mathematics. By DR. BRUNo W. FREYTAG GEN.
LöRINGHoFF. Translated by Amethe Countess Won Zeppelin. New York: Philosophical Library, 1951. Pp. 88 with index. $2.75. Three lectures, “Philosophy
and ...