A Mathematical Prelude to the Philosophy of Mathematics

Author: Stephen Pollard

Publisher: Springer

ISBN: 3319058169

Category: Science

Page: 202

View: 4080

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.
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Philosophical Introduction to Set Theory

Author: Stephen Pollard

Publisher: Courier Dover Publications

ISBN: 0486805824

Category: Mathematics

Page: 192

View: 3536

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
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The Joy of x

Die Schönheit der Mathematik

Author: Steven Strogatz

Publisher: Kein & Aber AG

ISBN: 3036992693

Category: Mathematics

Page: 352

View: 7910

Mathematik durchdringt den ganzen Kosmos. Das weiß jeder, doch nur die wenigsten verstehen die Zusammenhänge wirklich. Steven Strogatz nimmt uns bei der Hand und spaziert mit uns durch diese Welt der Weisheit, Klarheit und Eleganz. Als Reiseleiter geht er neue, erfrischende Wege, deutet auf Besonderheiten, schildert Hintergründe und erklärt die unsichtbaren Mechanismen. Wir erfahren unter anderem von dem Wunder des Zählens, der genialen Einfachheit der Algebra, dem ewigen Erbe Newtons, dem Tango mit Quadraten, der Zweisamkeit von Primzahlen und der Macht des Unendlichen. Mit all seiner Begeisterung, seinem Scharfblick und seinem leichtem Ton hat Steven Strogatz ein herrliches Buch für alle geschrieben, die ihr Verständnis von Mathematik auf eine neue Art vertiefen möchten.
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Theorems, Corollaries, Lemmas, and Methods of Proof

Author: Richard J. Rossi

Publisher: John Wiley & Sons

ISBN: 1118030575

Category: Mathematics

Page: 318

View: 7428

A hands-on introduction to the tools needed for rigorous andtheoretical mathematical reasoning Successfully addressing the frustration many students experience asthey make the transition from computational mathematics to advancedcalculus and algebraic structures, Theorems, Corollaries, Lemmas,and Methods of Proof equips students with the tools needed tosucceed while providing a firm foundation in the axiomaticstructure of modern mathematics. This essential book: * Clearly explains the relationship between definitions,conjectures, theorems, corollaries, lemmas, and proofs * Reinforces the foundations of calculus and algebra * Explores how to use both a direct and indirect proof to prove atheorem * Presents the basic properties of real numbers * Discusses how to use mathematical induction to prove atheorem * Identifies the different types of theorems * Explains how to write a clear and understandable proof * Covers the basic structure of modern mathematics and the keycomponents of modern mathematics A complete chapter is dedicated to the different methods of proofsuch as forward direct proofs, proof by contrapositive, proof bycontradiction, mathematical induction, and existence proofs. Inaddition, the author has supplied many clear and detailedalgorithms that outline these proofs. Theorems, Corollaries, Lemmas, and Methods of Proof uniquelyintroduces scratch work as an indispensable part of the proofprocess, encouraging students to use scratch work and creativethinking as the first steps in their attempt to prove a theorem.Once their scratch work successfully demonstrates the truth of thetheorem, the proof can be written in a clear and concise fashion.The basic structure of modern mathematics is discussed, and each ofthe key components of modern mathematics is defined. Numerousexercises are included in each chapter, covering a wide range oftopics with varied levels of difficulty. Intended as a main text for mathematics courses such as Methods ofProof, Transitions to Advanced Mathematics, and Foundations ofMathematics, the book may also be used as a supplementary textbookin junior- and senior-level courses on advanced calculus, realanalysis, and modern algebra.
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Usefullness of Mathematical Learning

Usefulness Mathematical Learning

Author: Isaac Barrow

Publisher: Routledge

ISBN: 1317845536

Category: Education

Page: 500

View: 1073

First published in 1970. Routledge is an imprint of Taylor & Francis, an informa company.
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Strands of System

The Philosophy of Charles Peirce

Author: Douglas R. Anderson,Charles Sanders Peirce

Publisher: Purdue University Press

ISBN: 9781557530585

Category: Philosophy

Page: 204

View: 2264

The American thinker Charles Sanders Peirce, best known as the founder of pragmatism, has been influential not only in the pragmatic tradition but more recently in the philosophy of science and the study of semiotics, or sign theory. Strands of System provides an accessible overview of Peirce's systematic philosophy for those who are beginning to explore his thinking and its import for more recent trends in philosophy.
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Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences

Author: Ivor Grattan-Guinness

Publisher: Routledge

ISBN: 1134957491

Category: Reference

Page: 1840

View: 3668

* Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century * 176 articles contributed by authors of 18 nationalities * Chronological table of main events in the development of mathematics * Fully integrated index of people, events and topics * Annotated bibliographies of both classic and contemporary sources * Unique coverage of Ancient and non-Western traditions of mathematics
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The Cambridge Companion to Galileo

Author: Peter Machamer

Publisher: Cambridge University Press

ISBN: 1139825666

Category: Philosophy

Page: N.A

View: 447

Not only a hero of the scientific revolution, but after his conflict with the church, a hero of science, Galileo is today rivalled in the popular imagination only by Newton and Einstein. But what did Galileo actually do, and what are the sources of the popular image we have of him? This 1998 collection of specially-commissioned essays is unparalleled in the depth of its coverage of all facets of Galileo's work. A particular feature of the volume is the treatment of Galileo's relationship with the church. It will be of interest to philosophers, historians of science, cultural historians and those in religious studies.
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Thomas Kuhn's 'Linguistic Turn' and the Legacy of Logical Empiricism

Incommensurability, Rationality and the Search for Truth

Author: Dr Stefano Gattei

Publisher: Ashgate Publishing, Ltd.

ISBN: 1409485854

Category: Philosophy

Page: 292

View: 1872

Presenting a critical history of the philosophy of science in the twentieth century, focusing on the transition from logical positivism in its first half to the "new philosophy of science" in its second, Stefano Gattei examines the influence of several key figures, but the main focus of the book are Thomas Kuhn and Karl Popper. Kuhn as the central figure of the new philosophy of science, and Popper as a key philosopher of the time who stands outside both traditions. Gattei makes two important claims about the development of the philosophy of science in the twentieth century; that Kuhn is much closer to positivism than many have supposed, failing to solve the crisis of neopostivism, and that Popper, in responding to the deeper crisis of foundationalism that spans the whole of the Western philosophical tradition, ultimately shows what is untenable in Kuhn's view. Gattei has written a very detailed and fine grained, yet accessible discussion making exceptionally interesting use of archive materials.
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Prelude to Mathematics

Author: W. W. Sawyer

Publisher: Courier Corporation

ISBN: 0486152774

Category: Mathematics

Page: 224

View: 2844

This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition.
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The Life and Work of George Boole

A Prelude to the Digital Age

Author: Des MacHale

Publisher: N.A

ISBN: 9781782050049

Category: Biography & Autobiography

Page: 342

View: 1947

First edition published in 1985 as: George Boole: his life and work. Dublin: Boole Press, 1985.
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Essays on the Foundations of Mathematics by Moritz Pasch

Author: Stephen Pollard

Publisher: Springer Science & Business Media

ISBN: 9789048194162

Category: Mathematics

Page: 248

View: 3336

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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A Treatise of Legal Philosophy and General Jurisprudence

Vol. 9: A History of the Philosophy of Law in the Civil Law World, 1600-1900; Vol. 10: The Philosophers' Philosophy of Law from the Seventeenth Century to Our Days.

Author: Damiano Canale,Paolo Grossi,Hasso Hofmann,Patrick Riley

Publisher: Springer Science & Business Media

ISBN: 9048129648

Category: Philosophy

Page: 740

View: 4236

TO VOLUMES 9 AND 10 OF THE TREATISE I am happy to present here the third batch of volumes for the Treatise project: This is the batch consisting of Volumes 9 and 10, namely, A History of the P- losophy of Law in the Civil Law World, 1600–1900, edited by Damiano Canale, Paolo Grossi, and Hasso Hofmann, and The Philosophers’ Philosophy of Law from the Seventeenth Century to Our Days, by Patrick Riley. Three v- umes will follow: Two are devoted to the philosophy of law in the 20th c- tury, and the third one will be the index for the entire Treatise, which will 1 therefore ultimately comprise thirteen volumes. This Volume 9 runs parallel to Volume 8, A History of the Philosophy of Law in the Common Law World, 1600–1900, by Michael Lobban, published in 2007. Volume 10, for its part, takes up where Volume 6 left off: which appeared under the title A History of the Philosophy of Law from the Ancient Greeks to the Scholastics (edited by Fred Miller Jr. in association with Carrie-Ann Biondi, likewise published in 2007), and which is mainly a history of the p- losophers’ philosophy of law (let us refer to this philosophy as A).
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Probability Theory

Philosophy, Recent History and Relations to Science

Author: Vincent F. Hendricks,Stig Andur Pedersen,Klaus Frovin Jørgensen

Publisher: Springer Science & Business Media

ISBN: 9780792369523

Category: Mathematics

Page: 183

View: 1494

A collection of papers presented at the conference on Probability Theory - Philosophy, Recent History and Relations to Science, University of Roskilde, Denmark, September 16-18, 1998. Since the measure theoretical definition of probability was proposed by Kolmogorov, probability theory has developed into a mature mathematical theory. It is today a fruitful field of mathematics that has important applications in philosophy, science, engineering, and many other areas. The measure theoretical definition of probability and its axioms, however, are not without their problems; some of them even puzzled Kolmogorov. This book sheds light on some recent discussions of the problems in probability theory and their history, analysing their philosophical and mathematical significance, and the role pf mathematical probability theory in other sciences.
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Prelude to Philosophy

An Introduction for Christians

Author: Mark W. Foreman

Publisher: InterVarsity Press

ISBN: 0830896600

Category: Religion

Page: 208

View: 1627

"The unexamined life is not worth living," according to Socrates, but pursuing the examined life strikes many as daunting, unappealing and even unnecessary. Is philosophy important? Why do I need philosophy if I have the Bible? Aren't philosophers simply engaged in meaningless disputes that are irrelevant to everyday life? Mark Foreman addresses these and other questions in this "prelude" to the subject. Unlike a full introduction to philosophy, this book is a preliminary discussion that dispels misunderstandings and explains the rationale for engaging in philosophical reasoning. In the first half of the book, Foreman defines the task of philosophy, compares it to other disciplines and demonstrates its practical value to Christians interested in developing a more thoughtful faith. The second half introduces the reader to logic and argumentation, the essential tools of a philosopher. Concise and straightforward, Prelude to Philosophy is a guide for those looking to embark on the "examined life."
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The Philosophy of Husserl

Author: Burt Hopkins

Publisher: Routledge

ISBN: 131749444X

Category: Philosophy

Page: 290

View: 9334

As the founder of phenomenology, Edmund Husserl has been hugely influential in the development of contemporary continental philosophy. In The Philosophy of Husserl, Burt Hopkins shows that the unity of Husserl’s philosophical enterprise is found in the investigation of the origins of cognition, being, meaning, and ultimately philosophy itself. Hopkins challenges the prevailing view that Husserl’s late turn to history is inconsistent with his earlier attempts to establish phenomenology as a pure science and also the view of Heidegger and Derrida, that the limits of transcendental phenomenology are historically driven by ancient Greek philosophy. Part 1 presents Plato’s written and unwritten theories of eidê and Aristotle’s criticism of both. Part 2 traces Husserl’s early investigations into the formation of mathematical and logical concepts and charts the critical necessity that leads from descriptive psychology to transcendentally pure phenomenology. Part 3 investigates the movement of Husserl’s phenomenology of transcendental consciousness to that of monadological intersubjectivity. Part 4 presents the final stage of the development of Husserl’s thought, which situates monadological intersubjectivity within the context of the historical a priori constitutive of all meaning. Part 5 exposes the unwarranted historical presuppositions that guide Heidegger’s fundamental ontological and Derrida’s deconstructive criticisms of Husserl’s transcendental phenomenology. The Philosophy of Husserl will be required reading for all students of phenomenology.
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Protocols, Truth and Convention

Author: Thomas Oberdan

Publisher: Rodopi

ISBN: 9789051835380

Category: Philosophy

Page: 147

View: 5626

The continuing philosophical interest in the famous 'Protocol Sentence Debate' in the Vienna Circle of Logical Positivists is, to a large measure, due to the focus on the epistemological issues in the dispute, and the neglect of differences among the leading players in their philosophical views of logic and language. In Protocols, Truth and Convention, the current understanding of the debate is advanced by developing the contemporaneous views of logic and language held by the principal disputants. Rudolf Carnap and Moritz Schlick. It is argued - largely on the basis of unpublished manuscripts and correspondence - that, despite apparent differences in their respective conceptions of language, there are nonetheless striking similarities, particularly with respect to the conventionality of language. Nonetheless, one key issue - concerning the syntacticism inherent in Carnap's early Thirties' philosophy - separates the two viewpoints in the clash over protocols. Finally, it is argued that Carnap's syntacticism is untenable, a conclusion that Carnap himself finally reached in the closing exchanges of the protocol sentence controversy.
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Philosophy of Mathematics

5 Questions

Author: Vincent F. Hendricks,Hannes Leitgeb

Publisher: Automatic Press Publishing

ISBN: 9788799101351

Category: Mathematics

Page: 342

View: 8474

Philosophy of Mathematics: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in this field. We hear their views aim, scope, use, the future direction and how their work fits in these respects.
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