Thinking about Mathematics: The Philosophy of Mathematics 1st Edition by Stewart Shapiro (PDF)

Description

This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy.

User’s Reviews

Editorial Reviews: About the Author Stewart Shapiro is Professor of Philosophy at Ohio State University at Newark and Professorial Fellow in the Department of Logic and Metaphysics at the University of St Andrews, Scotland.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a great book. It gives a comprehensive view of what math is really about, not about how to do math. It covers the fundamental issues as to the nature of mathematical entities and related problems all the way from ancient times to the present. It also engages some thorny problems concerning the discipline, all in fluent unobtrusive language that makes understanding easier than usual, without sacrificing depth or breath. I recommend it to anyone who, like myself, has struggled for a long time to grasp the significance, importance and limitations of math. As far as my needs are concerned, this is the best book on the subject that I have come across.

⭐Philosophy textbooks are a pretty mixed bag. Often the author has a position that they’re pushing, and fail to do justice to competing arguments. But Prof. Shapiro presents all the philosophical positions clearly and fairly.

⭐A good overview of the history of ideas and current positions within the philosophy of mathematics. Interesting to see what a struggle it has been to explain what something so seemingly intuitive as math actually is and the great efforts philosophers have made to answer these questions. Gets very dense and complicated as it goes on. The numerous Bill Clinton jokes have not aged well.

⭐Shapiro did not make the topic easy to understand. That’s impossible. It’s philosophy of math. But he made it as understandable to me, a reader with very little previous exposure to the subject, and did so concisely while presenting the fascinating arguments in all major veins of thought on the subject.

⭐The book contains few markings and the pages are in good condition. I don’t have any philosophical background but so far I have no difficulty reading it. Would recommend to anyone who’s curious about the subject.

⭐I am a reader with some basic background in logic and philosophy of language. Despite this background, I find Shapiro terribly difficult to read. For example, I read the section on Kant three times and am still not sure whether I understood anything. There must be simpler ways of explaining the material he presents.So this might be a great book for someone with a solid backgrounds in both philosophy and mathematics who wants to know more about questions at the crossroads of both fields. However, I absolutely do not recommend it as an introduction to these ideas.

⭐Language is confusing and convoluted. Students did not find the textbook helpful in explaining major concepts

⭐Skip this book, wordier than the typical book on philosophy.

⭐A pretty comprehensive overview of the philosophy of maths. The main thrust of the book is philosophical, and I feel it did a very good job of introducing a lot of different views on the subject. Although I am a maths student at university, I think the maths would be accessable to most people.

⭐It has some notes taken, which i find useful.

⭐Stewart Shapiro leistet mit diesem Werk eine gute Einführung in die Problematik der Philosophie der Mathematik. In diesem Werk umreißt er verständlich ( ein gewisses Grundwissen der Philosophie und oder aber der Mathematik vorausgesetzt) verschiedene philosophische Positionen bezüglich des Stellenwertes der Mathematik innerhalb der Philosophie und umgekehrt. Ich selbst behandele dieses Werk im Rahmen meines Masterstudiums der Philosophie.

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⭐fine

⭐現在の数学の哲学における第一線の研究者でもあるShapiroによる数学の哲学の教科書です。現代的視点（いわゆるベナセラフ(1973)以降）の視点から書かれていて、記述は明解、要旨も簡明。扱われているのは、一般的問題設定をサーベイしたあと、プラトン・アリストテレス・カント・ミルの「歴史的」な哲学者たち、それから論理主義・形式主義・直観主義という「御三家」。その後、数学の哲学における実在論と反実在論を巡る現代の人たちの見解がまとめられ、最後にShapiro自身の見解である構造主義で終わる。数学の哲学、あるいは論理学の哲学に興味のある人であれば入門書として初めに手に取るにいい好書です。ちなみに、論理式や数式はほとんど出てきません。なるべく出さないように苦労しています。いい本ですが、記述が淡泊で感動を呼ばないので星４つ。

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