Set theory and its philosophy this page intentionally left blank set theory and its philosophy a critical introduct. Set theory and its philosophy is a key text for philosophy, mathematical logic, and computer science. Set theory is a branch of mathematics that investigates sets and their properties. Rowling was adamant that the seventh book was the last. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. 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. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. The proposed model is designed to help a decisi onmaker more. 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.
The boy who lived m r and mrs dursley, of number four, privet drive, were proud to say that they were perfectly normal, thank you very much. After harry potter and the deathly hallows was published in july 2007, author j. Potter, michael 2004, set theory and its philosophy, oxford university press, isbn 9780199269730. The introduction to zermelos paper makes it clear that set theory is regarded as a fundamental theory. For example, the set containing only the empty set is a nonempty pure set. A theory of havruta learning 4 human partners, and meaningmaking efforts involving three partners two people and the text kent, 2006. Set theory, as a separate mathematical discipline, begins in the work of georg cantor.
It discusses in detail the project of settheoretic reduction. Wittgensteins tractatus history and interpretation edited by peter sullivan and michael potter mind association occasional series. A set is pure if all of its members are sets, all members of its members are sets, and so on. I believe potter is trying to capture as much as he can of freges original view of sets as logical objects, although he doesnt say this. A presentation of set theory intended for beginning graduate students. Zermelos axiomatization of set theory stanford encyclopedia. This book presents a philosophical introduction to set theory. Each succeeding level is then obtained by forming the power set of the preceding one. In this book, michael potter improves on scotts axiomatization in order to provide a highly motivated presentation of set theory as a description of the cumulative hierarchy. The book offers an account of cardinal and ordinal arithmetic, and the various axiom candidates. What the philosophy of set theory has to do is to provide an illuminating explanation for the various cases of existence. There is a precedent for this treatment of set theory potter 1990.
Michael potter presents a comprehensive new philosophical introduction to set theory. Philosophy of set theory school of social sciences. It is a rewarding read even for those who dont intend to follow all the technical details. Set theory begins with a fundamental binary relation between an object o and a set a. Michael potter, set theory and its philosophy oup, 2004. Now almost wholly supplanted by set theory and its philosophy which was originally conceived as a second edition of it. The book is a collection of essays on harry potter by philosophers analyzing different aspects of the story. A set is described by listing elements separated by commas, or by a characterizing property of its elements, within braces. 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. The essays are loosely grouped together on overhead topics and many of the essays lead into the following one thematically, creating a relatively cohesive experience. Set theory is that branch of mathematics whose task is to investigate mathematically the fundamental notions number, order, and function, taking them in their pristine, simple form, and to develop thereby the logical foundations of all of arithmetic and. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. The mathematical theory of sets is both a foundation in some sense for classical mathematics and a branch of mathematics in its own right. His studies in the history of analytic philosophy include reasons nearest kin 2000 and wittgensteins notes on logic 2009.
Set theory and its philosophy faculty of philosophy. It discusses in detail the project of settheoretic reduction, which aims to interpret the rest of mathematics in. The basic concepts of set theory are fairly easy to understand and appear to be selfevident. Jeanpierre marquis, from a geometrical point of view.
A critical introduction by michael potter, oup 2004. This theory reflects a set of six core practices in three dynamic pairs. Click and collect from your local waterstones or get free uk delivery on orders over. Buy set theory and its philosophy by michael potter from waterstones today. The book contains exercises in most chapters, in line with its super cial character of being an elementary set theory text, but no representation as. Set theory, philosophy of routledge encyclopedia of. The book contains exercises in most chapters, in line with its super cial character of being an elementary set theory text, but no representation as to pedagogical soundness is made. The ultimate harry potter and philosophy was an enjoyable read. 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. Set theory is important for philosophy of mathematics and metaphysics. This book is dedicated to prabir roy, louis mcauley, jonathan. 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 potter 1990, 2004 clarified and simplified the approach of scott 1974, and showed how the. Michael potter is professor of logic at cambridge university, uk, and a life fellow of fitzwilliam college. Enderton, elsevier, 1997 handouts based on endertons book will be provided during the course.
In my next study of many more havruta interactions, i developed a theory of havruta in one context. In set theory and its philosophy, michael potter has given us a wonderful new book. Both its foundational role and its particular mathematical features the centrality of. By continuing to use our website, you are agreeing to our use of cookies. Review of michael potter, set theory and its philosophy. Rowlings harry potter saga, captured in seven novels and eight films, has left an indelible mark on the. Both its foundational role and its particular mathematical features the centrality of axiomatization and the prevalence of. A history and philosophy of category theory, birkhauser 2007. We have no control over the nature, content and availability of those sites. 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. From a more philosophical perspective, potters book is noteworthy for its extensive discussion of the conceptual motivations behind our set. Through this website you are able to link to other websites which are not under the control of filepursuit.
Harry potter and the set of all sets that do not contain. He discusses in detail the project of set theoretic reduction, which aims to interpret. Potters book provides a great introduction to set theory and its philosophy. Archangels of magick wordly wise 3000 book 6 lesson 8 answer key pokemon detective pikachu war on gold and the financial endgame the practice of magical evocation pdf data communications and computer networks protocolo emdr chem 3 lab 10 chem 3 envision florida algebra 1 answers envision florida algebra 1 initiation into hermetics pdf emdr portugal electrical panel heights. It is roughly parallel in structure to halmoss classic naive set theory, though more topics have been added. Anyone wishing to work on the logical foundations of mathematics must. 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. Handouts based on endertons book will be provided during the course. 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. Set theory, philosophy of routledge encyclopedia of philosophy. But there are evidently other ways of extending the theory so as. Set theory and its philosophy paperback michael potter. Archangels of magick wordly wise 3000 book 6 lesson 8 answer key pokemon detective pikachu war on gold and the financial endgame the practice of magical evocation pdf data communications and computer networks protocolo emdr chem 3 lab 10 chem 3 envision florida algebra 1 answers envision florida algebra 1 initiation into hermetics pdf emdr portugal electrical. Potter does not merely anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart.
Set theory is a very general but still entirely exact theory of objects called sets. Review of david corfield, towards a philosophy of real mathematics. Introduction in this paper my main goal is to elaborate on some ideas from a talk which i gave at the workshop on \set theory and the philosophy of mathematics held at the university of pennsylvania in october 2010. Innovative principally because of its use of a simplified and significantly weaker version of dana scotts very intuitive axiom system for set theory.
The theory of levels developed in chapter 3 was wholly neutral as to how many levels there are in the hierarchy, since it was based solely on the axiom scheme of separation. 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. This book is dedicated to prabir roy, louis mcauley. Pdf set theory and its philosophy download full pdf.
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. 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. This set is often taken by mathematicians to be empty, thus restricting attention to what are known as pure sets, although this runs the danger of cutting set theory off from its intended application. They were the last people youd expect to be involved in anything strange or mysterious, because they just didnt hold with such nonsense. Zu allows flocks of doves and packs of wolves to be sets. Set theory and its philosophy by michael potter waterstones. A critical introduction by michael potter, oup 2004 lecture 1. Chapter 4 added the assumptions the axioms of creation and infinity which can be thought of as saying that the hierarchy extends to a certain height. Weyl philosophy of mathematics and natural science. Ryllnardzewski, czeslaw 1952, the role of the axiom of induction in elementary arithmetic pdf, fundamenta mathematicae, 39.
1263 1172 621 698 892 906 1491 438 931 605 916 1169 1292 63 1420 688 868 1520 514 1176 658 1244 223 112 180 324 1260 740 203 49 346 1339 564 823 162 779 1449 31 1119