introduction to philosophy of math pdf

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Philosophy Of Mathematics

Author : Øystein Linnebo
ISBN : 9781400885244
Genre : Philosophy
File Size : 31. 68 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.

Principia Mathematica

Author : Alfred North Whitehead
ISBN : STANFORD:36105039675058
Genre : Logic, Symbolic and mathematical
File Size : 89. 76 MB
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Philosophie Der Mathematik Und Naturwissenschaft

Author : Herrmann Weyl
ISBN : 9783486849905
Genre : Mathematics
File Size : 81. 28 MB
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Hermann Weyls "Philosophie der Mathematik und Naturwissenschaft" erschien erstmals 1928 als Beitrag zu dem von A. Bäumler und M. Schröter herausgegebenen "Handbuch der Philosophie". Die amerikanische Ausgabe, auf der die deutsche Übersetzung von Gottlob Kirschmer beruht, erschien 1949 bei Princeton University Press. Das nunmehr bereits in der 8. Auflage vorliegende Werk ist längst auch in Deutschland zum Standardwerk geworden.

Introduction To Mathematical Philosophy

Author : Bertrand Russell
ISBN : 0415096049
Genre : Mathematics
File Size : 22. 72 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.

Beweise Und Widerlegungen

Author : Imre Lakatos
ISBN : 9783663001966
Genre : Mathematics
File Size : 70. 31 MB
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Outlines Of A Formalist Philosophy Of Mathematics

Author :
ISBN : 9780444533685
Genre : Electronic books
File Size : 38. 60 MB
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Introduction To Mathematical Thinking

Author : Friedrich Waismann
ISBN : 9780486167428
Genre : Mathematics
File Size : 36. 38 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.

Frege

Author : Michael A. E. Dummett
ISBN : 0674319354
Genre : Philosophy
File Size : 61. 83 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.

Essentials Of Mathematics

Author : Margie Hale
ISBN : 9780883857298
Genre : Mathematics
File Size : 78. 36 MB
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Textbook and self-study guide for students beginning to study mathematics requiring proof.

Essays On The Foundations Of Mathematics By Moritz Pasch

Author : Stephen Pollard
ISBN : 9048194164
Genre : Mathematics
File Size : 66. 25 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.

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