In arguing for his humanist philosophy of mathematics, Hersh has some very good points to make, but he seems to spend much more time attacking the rival positions of formalism and Platonism. The history of mathematics also points in this direction.

Hersh doesn't seem to realize how arrogant this attitude is.

Platonism in mathematics is the most widely held view of modern mathematicians – or, so I believe. So far so good: it's an interesting proposal, and has much in its favor. In a subversive attack on traditional philosophies of mathematics, most … This book has four parts: In the first the author discusses his ideas about his philosophy of mathematics. Hersh calls this view of mathematics humanism. Reuben Hersh leads his reader at a comfortable pace through a well-structured argument. This is an interesting, important, ambitious, and infuriating book, one that deserves both attention and response from the mathematics community.

A Masterpiece on the Philosophy of Mathematics, Reviewed in the United States on December 26, 2019.

Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. Fulfillment by Amazon (FBA) is a service we offer sellers that lets them store their products in Amazon's fulfillment centers, and we directly pack, ship, and provide customer service for these products. In his preface Hersh recalls how he felt cheated by their explanation, and describes how this dissatisfaction ultimately became the motivation for writing “What is Mathematics, Really?” In search of a new philosophy of mathematics, Hersh explores what he calls the back of mathematics, a concept developed by the American sociologist Erving Goffman. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required. More a philosophy book than a mathematics book... though the author traces histories of several lines of mathematical thought, he assumes more knowledge than I came to the book with. Formalism is more solid than Hersh makes it seem, Platonism has been the position of serious philosophers who were not theists, and, after all, many philosophers do believe that God exists. What I think is missing from the book is a realization that the philosophy of mathematics is indeed philosophy, and not science, and that therefore it cannot ignore the overarching philosophical issues that relate to it. Mathematics (from Greek: μάθημα, máthēma, 'knowledge, study, learning') includes the study of such topics as quantity (number theory), structure (), space (), and change (mathematical analysis). After viewing product detail pages, look here to find an easy way to navigate back to pages you are interested in. Admittedly, he was a professional mathematician, while I’m a mere amateur mathematician and amateur philosopher. Against formalism, he follows and develops the criticisms of Imre Lakatos: he argues that no one actually writes formal proofs of anything, and that the view that mathematics is simply meaningless symbol-pushing is impossible to believe. However, I do not concur with the author’s philosophy of mathematics. The Platonists saw mathematics as almost an experimental science, studying objects that really exist (in some sense), though they clearly don't exist in a physical or material sense. Bring your club to Amazon Book Clubs, start a new book club and invite your friends to join, or find a club that’s right for you for free. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. He then adds "His attack on mathematicians is unique since St. Augustine," which is hard to understand, since in his section on St. Augustine Hersh explains that Augustine's "attack on mathematicians" is really nothing of the sort! There follows a short summary and some interesting and more technical notes. This shopping feature will continue to load items when the Enter key is pressed. 2. A look at the history of mathematics certainly seems to undermine a naive formalism (since "formal proof" is a relatively recent phenomenon). Top subscription boxes – right to your door, © 1996-2020,, Inc. or its affiliates. Virtually all philosophers treat mathematics as isolated, timeless, ahistorical, inhuman.


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