What the philosophy of set theory has to do is to provide an illuminating explanation for the various cases of existence. For mathematicians concerned with foundational issues this surely is at some stage a must read, a unique blend of mathematical exposition mostly about the level of enderton, with a few glimpses beyond and extensive conceptual commentary. A critical introduction michael potter 2004 set theory and its philosophy. I didnt open this group, i just appropriated it after its first admin invited me and then left it. I discuss in detail the project of set theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. Free set theory books download ebooks online textbooks. Set theory, as a separate mathematical discipline, begins in the work of georg cantor. One might say that set theory was born in late 1873, when he made the amazing discovery that the linear continuum, that is, the real line, is not countable, meaning that its points cannot be counted using the natural numbers. Michael potter, set theory and its philosophy oup 2004 appendix c. It ought to displace quines set theory and its logic, for example.
We write \a\in a\ to indicate that the object \a\ is an. And while i am not certain, she seems to favor a pragmatic approach to set theory and possibly the rest of mathematics, which in my limited experience in philosophy of mathematics i have not found all that much of. He is also noted for work in the foundations of mathematics, including set theory and its philosophy 2004. Philosophy of set theory university of california, irvine.
Set theory and its philosophy paperback michael potter. Thanks to the hype around the upcoming fantastic b. Set theory and its philosophy by michael potter, 9780199270415, available at book depository with free delivery worldwide. Set theory and its philosophy this page intentionally left blank set theory and its philosophy a critical introduct. Potter does not merely anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. A first course is the best introduction to set theory in the english language. Although elementary set theory is wellknown and straightforward, the modern subject, axiomatic set theory, is both conceptually more di. Everyday low prices and free delivery on eligible orders. Set theory and its philosophy paperback michael potter oxford. By continuing to use our website, you are agreeing to our use of cookies.
Set theoretic pluralism is an increasingly influential position in the philosophy of set theory balaguer 1998, linksy and zalta 1995, hamkins 2012. Chapter 1 logic and set theory to criticize mathematics for its abstraction is to miss the point entirely. Its core is a slightly nonstandard development of axiomatic set theory, starting with the concept of a collection and working up through the axiom of choice and some simple cardinal arithmeticenough to understand the statement and significance of the continuum hypothesis, but not enough to appreciate the. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools. Thus, two sets are equal if and only if they have exactly the same elements. This note is an introduction to the zermelofraenkel set theory with choice zfc. A critical introduction clarendon press, 2004 360 pages 0191556432, 9780191556432 michael potter presents a comprehensive new philosophical introduction to set theory.
These readings will introduce you to the standard set theory zfc, and the iterative. Download it once and read it on your kindle device, pc, phones or tablets. Michael potter, set theory and its philosophy oup, 2004. What dark secrets have the harry potter movies been hiding. Set theory basic set theory stanford encyclopedia of. Set theory, philosophy of routledge encyclopedia of philosophy. In set theory and its philosophy, michael potter has given us a wonderful new book.
About the author michael potter is university lecturer in philosophy, and fellow of fitzwilliam college, at cambridge. Set theory, different systems of routledge encyclopedia of. I wrote it in the rm belief that set theory is good not just for set theorists, but for many mathematicians, and that the earlier a student sees the particular point of view that we call modern set theory, the better. Pdf set theory and its philosophy download full pdf. Harry potter and the set of all sets that do not contain themselves even magic cant get you out of staff meetings the set of all sets that do not contain themselves is the basis of russells paradox, which dealt a devastating blow to the projects of russell and frege in grounding all of mathematics in pure logic.
Among the other systems of set theory to have been proposed, the one that has received widespread attention is quines nf from the title of an article, new foundations for mathematical logic, which seeks to avoid paradox by means of a syntactic restriction but which has not been provided with an intuitive justification on the basis of. Click and collect from your local waterstones or get free uk delivery on orders over. Set theory and its philosophy faculty of philosophy. Harry potter and the set of all sets that do not contain. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. Readers who dont exactly fit the audience will learn an enormous amount from this book. The mathematical theory of sets is both a foundation in some sense for classical mathematics and a branch of mathematics in its own right. Michael potter is professor of logic at cambridge university, uk, and a life fellow of fitzwilliam college. A critical introduction michael potter auteur 1 download. Also listed, among others, are potter s st and its philosophy, and endertons a mathematical introduction to logic. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. A set is described by listing elements separated by commas, or by a characterizing property of its elements, within braces. This book presents a philosophical introduction to set theory.
Department of mathematics and statistics university of helsinki and institute for logic, language and computation university of amsterdam november 17, 2010 contents 1 introduction 1 2 elementary set theory 2 3 cardinal and ordinal numbers 3. Anyone wishing to work on the logical foundations of mathematics must. Sets are welldetermined collections that are completely characterized by their elements. 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 serious interest in mathematics. His studies in the history of analytic philosophy include reasons nearest kin 2000 and wittgensteins notes on logic 2009. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Anyone wishing to work on the logical foundations of. What makes the book unique is that it interweaves a careful presentation of the technical. Rowlings harry potter saga, captured in seven novels and eight films, has left an indelible mark on the. Andrews, st andrews, fife ky16 9al, scotland, 2department of philosophy, the ohio state university, univ we use cookies to enhance your experience on our website. I found that mary tiles might have ignore some of the necessary physics in her discussion of space and time.
Moreover, it is so clear and authoritative, and covers so much ground, that it deserves to be in the canon. Use features like bookmarks, note taking and highlighting while reading set theory and its philosophy. Nb note bene it is almost never necessary in a mathematical proof to remember that a function is literally a set of ordered pairs. An approach to the foundations of mathematics that is of relatively recent origin, scottpotter set theory is a collection of nested axiomatic set theories set out by the philosopher michael potter, building on earlier work by the mathematician dana scott and the philosopher george boolos. Buy set theory and its philosophy by michael potter from waterstones today. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. I offer a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. View set theory philosophy research papers on academia. The basic relation in set theory is that of elementhood, or membership. About the author michael potter is university lecturer in. Enderton, elsevier, 1997 handouts based on endertons book will be provided during the course.
Complex issues arise in set theory more than any other area of pure mathematics. A critical introduction this book presents a philosophical introduction to set theory. A critical introduction kindle edition by potter, michael. Would you like to proceed to the app store to download. Set theory and its philosophy by michael potter waterstones. It is designed for a onesemester course in set theory at the advanced undergraduate or beginning. Both its foundational role and its particular mathematical features the centrality of axiomatization and the prevalence of. There is considerable room for debate about how best to formulate set theoretic pluralism, and even about whether the view is coherent. Chow, a beginners guide to forcing, downloadable form the arxiv. Download now michael potter presents a comprehensive new philosophical introduction to set theory. Timothy bays in set theory and its philosophy, michael potter has. Set theory and its philosophy is a key text for philosophy, mathematical logic, and computer science. Set theory begins with a fundamental binary relation between an object o and a set a. Michael potter presents a comprehensive new philosophical introduction to set theory.