introduction to philosophy of math pdf

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Philosophy Of Mathematics

Author : Øystein Linnebo
ISBN : 9781400885244
Genre : Philosophy
File Size : 60. 94 MB
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A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholars Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Gödel, W. V. Quine, Paul Benacerraf, and Hartry H. Field. Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics.

Philosophy Of Mathematics

Author : David Bostock
ISBN : 9781405189927
Genre : Mathematics
File Size : 86. 56 MB
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Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author?s personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals

Introduction To Mathematical Philosophy

Author : Bertrand Russell
ISBN : 0415096049
Genre : Mathematics
File Size : 77. 53 MB
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Bertrand Russell is a leading mathematical philosopher of the 20th century. The author of The Principles of Mathematics and, with Alfred Whitehead, the massive Principia Mathematica, Russell brought together his formidable knowledge of the subject and his skills as a gifted communicator, to provide a classic introduction to the philosophy of mathematics. Introduction to Mathematical Philosophy sets out in a lucid and non-technical way the main ideas of Principia Mathematica. It is as inspiring and useful to the beginner now as it was when it was first published in 1919.

Philosophy Of Mathematics

Author : Paul Benacerraf
ISBN : 9781107268135
Genre : Science
File Size : 74. 70 MB
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The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

Outlines Of A Formalist Philosophy Of Mathematics

Author :
ISBN : 9780444533685
Genre : Electronic books
File Size : 57. 38 MB
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Essays On The Foundations Of Mathematics By Moritz Pasch

Author : Stephen Pollard
ISBN : 9048194164
Genre : Mathematics
File Size : 35. 63 MB
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Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert’s program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this technique yields an "empiricist" reconstruction of set theory; he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties; he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles; and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics.

Introduction To Mathematical Thinking

Author : Friedrich Waismann
ISBN : 9780486167428
Genre : Mathematics
File Size : 39. 63 MB
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Examinations of arithmetic, geometry, and theory of integers; rational and natural numbers; complete induction; limit and point of accumulation; remarkable curves; complex and hypercomplex numbers; more. Includes 27 figures. 1959 edition.

The Philosophy Of Mathematics Education Today

Author : Paul Ernest
ISBN : 9783319777603
Genre : Education
File Size : 75. 24 MB
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This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.

Frege

Author : Michael A. E. Dummett
ISBN : 0674319354
Genre : Philosophy
File Size : 87. 27 MB
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No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.

Author :
ISBN : 9789772937554
Genre : Philosophy
File Size : 88. 56 MB
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أجل إننا لسنا نوافق أفلاطون في كل نظرياته, وقد نشرناها على مسؤوليته، ولكننا معجبون وأكثر من معجبين, بنظام تفكيره, ورحابة صدره, وضبطه في الإحكام, وفيض بلاغته وبيانه. ونشاركه في غرض التأليف العام وهو((السعادة)) وفي الوسيلة الخاصة المؤدية إلى ذلك الغرض وهي ((الفضيلة)) ونافقه في أن الفضيلة تراد لذاتها ونتائجها. وفي أن الفرد دولة مصغرة والدولة جسـم كبير, وأن ما يسعد الدولة يسـعد الفرد، وأن الرجل الكـامل – المثـل الأعلى – هو الذي تحكم عقله في شهواته, وانقادت حماسته إلى حكمته, وعاش ومات في خدمة المجموع. body,div,table,thead,tbody,tfoot,tr,th,td,p { font-family:"Calibri"; font-size:x-small } a.comment-indicator:hover + comment { background:#ffd; position:absolute; display:block; border:1px solid black; padding:0.5em; } a.comment-indicator { background:red; display:inline-block; border:1px solid black; width:0.5em; height:0.5em; } comment { display:none; }

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