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Author | : Tomasz Placek |
Publisher | : Springer Science & Business Media |
Total Pages | : 229 |
Release | : 2013-03-09 |
Genre | : Science |
ISBN | : 9401593159 |
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In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being. Brouwer attacked the main currents of the philosophy of mathematics: the formalists and the Platonists. In tum, both these schools began viewing intuitionism as the most harmful party among all known philosophies of mathematics. That was the origin of the now-90-year-old debate over intuitionism. As both sides have appealed in their arguments to philosophical propositions, the discussions have attracted the attention of philosophers as well. One might ask here what role a philosopher can play in controversies over mathematical intuitionism. Can he reasonably enter into disputes among mathematicians? I believe that these disputes call for intervention by a philo sopher. The three best-known arguments for intuitionism, those of Brouwer, Heyting and Dummett, are based on ontological and epistemological claims, or appeal to theses that properly belong to a theory of meaning. Those lines of argument should be investigated in order to find what their assumptions are, whether intuitionistic consequences really follow from those assumptions, and finally, whether the premises are sound and not absurd. The intention of this book is thus to consider seriously the arguments of mathematicians, even if philosophy was not their main field of interest. There is little sense in disputing whether what mathematicians said about the objectivity and reality of mathematical facts belongs to philosophy, or not.
Author | : Carl J. Posy |
Publisher | : Cambridge University Press |
Total Pages | : 116 |
Release | : 2020-11-12 |
Genre | : Science |
ISBN | : 1108593259 |
Download Mathematical Intuitionism Book in PDF, ePub and Kindle
L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth.
Author | : R.L. Tieszen |
Publisher | : Springer Science & Business Media |
Total Pages | : 223 |
Release | : 2012-12-06 |
Genre | : Philosophy |
ISBN | : 9400922930 |
Download Mathematical Intuition Book in PDF, ePub and Kindle
"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.
Author | : Markus Sebastiaan Paul Rogier van Atten |
Publisher | : Cengage Learning |
Total Pages | : 108 |
Release | : 2004 |
Genre | : Education |
ISBN | : |
Download On Brouwer Book in PDF, ePub and Kindle
This book offers a concise, yet comprehensive, introduction to this philosopher's most important ideas.
Author | : Arend Heyting |
Publisher | : Elsevier |
Total Pages | : 159 |
Release | : 1966 |
Genre | : Electronic books |
ISBN | : 0444534067 |
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Author | : Carl J. Posy |
Publisher | : Cambridge University Press |
Total Pages | : 75 |
Release | : 2020-11-12 |
Genre | : Science |
ISBN | : 9781108723022 |
Download Mathematical Intuitionism Book in PDF, ePub and Kindle
L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism - from elementary number theory through to Brouwer's uniform continuity theorem - and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth.
Author | : Mark van Atten |
Publisher | : Springer Science & Business Media |
Total Pages | : 432 |
Release | : 2008-11-09 |
Genre | : Science |
ISBN | : 3764386533 |
Download One Hundred Years of Intuitionism (1907-2007) Book in PDF, ePub and Kindle
Intuitionism is one of the main foundations for mathematics proposed in the twentieth century and its views on logic have also notably become important with the development of theoretical computer science. This book reviews and completes the historical account of intuitionism. It also presents recent philosophical work on intuitionism and gives examples of new technical advances and applications. It brings together 21 contributions from today's leading authors on intuitionism.
Author | : Stewart Shapiro |
Publisher | : Oxford University Press |
Total Pages | : 850 |
Release | : 2005-02-10 |
Genre | : Mathematics |
ISBN | : 0198033990 |
Download The Oxford Handbook of Philosophy of Mathematics and Logic Book in PDF, ePub and Kindle
Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
Author | : Nick Haverkamp |
Publisher | : |
Total Pages | : 0 |
Release | : 2015 |
Genre | : Mathematics |
ISBN | : 9783465139065 |
Download Intuitionism Vs. Classicism Book in PDF, ePub and Kindle
In the early twentieth century, the Dutch mathematician L.E.J. Brouwer launched a powerful attack on the prevailing mathematical methods and theories. He developed a new kind of constructive mathematics, called intuitionism, which seems to allow for a rigorous refutation of widely accepted mathematical assumptions including fundamental principles of classical logic. Following an intense mathematical debate esp. in the 1920s, Brouwer's revolutionary criticism became a central philosophical concern in the 1970s, when Michael Dummett tried to substantiate it with meaning-theoretic considerations.
Author | : Bharath Sriraman |
Publisher | : Springer Nature |
Total Pages | : 3221 |
Release | : |
Genre | : |
ISBN | : 3031408462 |
Download Handbook of the History and Philosophy of Mathematical Practice Book in PDF, ePub and Kindle