As an historical map of the philmath terrain, this book is essential. Frege and the philosophy of mathematics book, 1980. Philosophy of language, the first of two volumes devoted to a survey and discussion of freges philosophy, considered as roughly divisible between the philosophy of language and philosophy of mathematics. In calling mathematics a science he implies that it has a factual subjectmatter and that mathematical knowledge is on a par with other scientific knowledge. When i was young, most teachers of philosophy in british and american universities were hegelians, so that, until i read hegel, i supposed there must be some truth to his system. On the basis of the law of excluded middle, classical mathematics is committed to the existence of statements which are true.
Jan 04, 2012 there is no doubt that michael dummett made a stunning contribution to philosophy and was for many years britains leading philosopher, as well as one of our leading humanitarian activists. No one has figured more prominently in the study of the german philosopher gottlob frege than michael dummett. Wittgenstein and the turning point in the philosophy of mathematics. This was the anthology of important essays when it came out, and remained so for a lot of years. His research focuses on the history of analytic philosophy, especially frege, russell, and the early wittgenstein. Books on the philosophy of mathematics and logic mathematics. It aims to understand the nature and methods of mathematics, and finding out the place of mathematics in peoples lives. Cohen set theory and the continuum hypothesis, alfred tarski undecidable theories, gary chartrand introductory graph theory, hermann weyl the concept of a riemann surface, shlomo sternberg dynamical systems. The philosophy of mathematics is the branch of philosophy charged with trying to understand this queen.
Dummett and wittgensteins philosophy of mathematics. International handbook of research in history, philosophy and. Good books on philosophy of mathematics stack exchange. However, formatting rules can vary widely between applications and fields of interest or study. Probably the people who are not fans of intuitionism think of dummett as an expert on frege. The first is a straightforward question of interpretation. The preponderating inclination, however, to deal with the similar as the equal an illogical inclination, for there is no thing equal in itself first created the whole basis of logic. I think there are probably some good introduction to classical philosophy of math that im not aware of, but what i find most interesting are modern treatments of philosophy of math. The oxford handbook of philosophy of mathematics and logic stewart shapiro editor, professor of philosophy, ohio state university abstract. Philosophy of mathematics is a 1991 book about the philosopher gottlob frege by the british philosopher michael dummett. Philosophy of mathematics mathematical association of.
Elements of intuitionism michael dummett, professor of. This book provides comprehensive and accessible coverage of the disciplines of philosophy of mathematics and philosophy of logic. Contents of the book preface a plea for a critical transformative philosophy of mathematics education, luis radford pages 110. Philosophy of mathematics and mathematical practice in the seventeenth century fraser, craig, notre dame journal of formal logic, 1999. There is no doubt that michael dummett made a stunning contribution to philosophy and was for many years britains leading philosopher, as well as one of our leading humanitarian activists. Discover delightful childrens books with prime book box, a subscription that delivers new books every 1, 2, or 3 months new customers receive 15% off your. This collection of essays addresses three main developments in recent work on freges philosophy of mathematics. Logic, mathematics, philosophy, vintage enthusiasms. Mathematics as a science of patterns is the definitive exposition of a system of ideas about the nature of mathematics which michael resnik has been elaborating for a. Excerpt this book was written for two groups of people, philosophically informed mathematicians with a serious interest in the philosophy of their subject, and philosophers with a. Browse the amazon editors picks for the best books of 2019, featuring our favorite. In that sense the paper was a good read, but a good read is not enough to make a good philosophical paper.
I met and talked with him on a number of occasions, largely about his seminal works on frege, logicism and the philosophy of mathematics in general. Michael dummett this is a wonderful book that challenges the reader to examine that relationships between philosophy and mathematics. The final factor in the transformation of the philosophy of mathematics is the rise of modern logic. Philosophy of mathematics michael dummett download. His own contributions to philosophy have been bound up with his interpretations of the earlier philosophers frege and wittgenstein. Philosophy of mathematical practice oxford scholarship. David eugene smith, a source book in mathematics karpinski, l. Contents of the book preface a plea for a critical transformative philosophy of mathematics education, luis radford pages 110 introduction to the field the philosophy of. This book coauthored with william ewald of the university of pennsylvania, will be c. This new approach is innovative in at least two ways. His philosophy of mathematics contains deep insights and remains a useful and necessary point. This book provides a unified presentation of this new wave of work in philosophy of mathematics. He received his phd from the university of pittsburgh in 1986.
We investigate the limits of mathematics, the subject matter of mathematics, the relationship between mathematics and the rest of science, the logic of mathe. Gottlob frege 18481925 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 twentiethcentury angloamerican philosophy. Michael otte bielefeld university, bielefeld faculty of. This is the second volume in a corrected paperback edition.
We investigate the limits of mathematics, the subject matter of mathematics, the relationship between. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts. Philosophy of mathematics michael dummett, professor. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Lakoff and nunezs book called where mathematics comes from. I was cured, however, by discovering that everything he said on the philosophy of mathematics was plain nonsense. It was just so in order that the conception of substance should originate, this being indispensable to logic. I am not an expert in either discipline, and my answer would probably annoy both mathematician. How are works distinguished from waste and, incidentally, archives. Philosophy of language 1973, it is dummetts chief contribution to frege scholarship.
Dummetts 1973 book on frege helped to make freges thought central to modern philosophy. Mathematics as a science of patterns is the definitive exposition of a system of ideas about the nature of mathematics which michael resnik has been elaborating for a number of years. Philosophy of mathematics, branch of philosophy that is concerned with two major questions. Library of philosophy series in which introduction to mathematical philosophy was originally published. Readers are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism. Philosophy mathematics without apologies, by michael harris. Of all the technical areas in which we publish, dover is most recognized for our magnificent mathematics list. Philosophy of mathematics stanford encyclopedia of philosophy. This was when weyl thought predicativity would put mathematics on a more secure basis. How the embodied mind brings mathematics into being uses modern cognitive science to discuss.
Michael otte bielefeld university, bielefeld faculty. Michael detlefsen 20 october 1948 21 october 2019 was a mcmahonhank professor of philosophy at the university of notre dame. Logic, the philosophy of mathematics, the interpretation of freges philosophy. Stillwell, shelley, notre dame journal of formal logic, 1989. This excellent book can be recommended to the student of mathematics or philosophy wishing to get a comprehensive and reliable introduction to modern intuitionism. Some people would see this as a little narrow, but intuitionism is important both in its own right, and as a philosophy opposed by others. Good books on philosophy of mathematics math stack exchange. International handbook of research in history, philosophy. Philosophy of mathematics mathematical association of america. While i may not agree with all of it, it is definately worthy of the read. This book expounds a system of ideas about the nature of mathematics which michael resnik has been elaborating for a number of years. Philosophy of mathematics stanford encyclopedia of. Set theory and its philosophy is a key text for philosophy, mathematical logic, and computer science.
Freges philosophy of mathematics william demopoulos. Bosanquet, norman malcolm, rush rhees, and yorick smythies. Philosophy of language is a sustained, systematic analysis of freges thought, omitting only the issues in philosophy of mathematics. Philosophy of mathematics has been highly influential. In this work dummett discusses, section by section, freges masterpiece the foundations of arithmetic and freges treatment of real numbers in the second volume. If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. Michael potters set theory and its philosophy oup 2004 is exactly. In this work dummett discusses, section by section, freges masterpiece the foundations of arithmetic and freges treatment of. 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. What are some good books on the philosophy of mathematics. The papers contained in this book, and dummetts replies, will, it is hoped, not.
He wrote in the preface of this 1973 book, this book is the first volume of two about frege. Michael frank hallett philosophy mcgill university. This is a wonderful book that challenges the reader to examine that relationships between philosophy and mathematics. Mathematics and philosophy edited by bonnie gold and roger a. Michael dummett, wittgensteins philosophy of mathematics. The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics.
Frege 18481925 was a logician, mathematician, and philosopher whose work had enormous impact on bertrand russell and later on the young ludwig wittgenstein, making him one of the central influences on twentiethcentury angloamerican philosophy. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Sir michael dummett he was knighted in 1991 is one of the most influential of living philosophers. A musthave book, if youre a student of the philosophy of mathematics. Wittgensteins lectures on the foundations of mathematics, cambridge, 1939. We are the home of such worldclass theorists as paul j. The paper does not connect to the current debates on value ethics in mathematics at all. Shapiros book, the philosophy of mathematics today, for a good reliable. The oxford handbook of philosophy of mathematics and logic. Michael potter is a fellow of fitzwilliam college, cambridge, and university lecturer in philosophy, having previously been lecturer in mathematics.
In a nutshell, the philosophy of mathematics deals with the special problems that arise from our possession of mathematical knowledge. The mathematics are extremely clearly presented, its an easy book to learn from. But anyone familiar with this area will be aware of the need for new approaches that will pay closer attention to mathematical practice. His areas of special interest were logic, history of mathematics, philosophy of mathematics and epistemology. Kant, philosophy of science, history of twentieth century philosophy, including the interaction between philosophy and the exact sciences from kant through the logical empiricists, prospects for postkuhnian philosophy of science in light of these developments, and the relationship between analytic and continental traditions in the early twentieth century. Therefore it is a branch of epistemology, the study of how we know things, just as philosophy of science and philosophy of perception are. Contemporary philosophy of mathematics offers us an embarrassment of riches. Philosophy of mathematics new edition by dummett, michael isbn. Developed by frege, cantor and others in the late nineteenth century, modern logic pervades contemporary mathematics, philosophy and computer science, and has had an immeasurable effect on the philosophy of mathematics. Mathematics, computer science and logic a never ending story. Over the past 30 years, michael dummett, sometime professor of logic at oxford, has argued for intuitionism by attacking freges semantic arguments for realism. Those who, relying on the distinction between mathematical philosophy and the philosophy of mathematics, think that this book is out of place in the present library, may be referred to what the author himself says on this head in the preface.
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