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| hartry h field: Science without Numbers Hartry Field, 2016-10-13 Science Without Numbers caused a stir in philosophy on its original publication in 1980, with its bold nominalist approach to the ontology of mathematics and science. Hartry Field argues that we can explain the utility of mathematics without assuming it true. Part of the argument is that good mathematics has a special feature (conservativeness) that allows it to be applied to nominalistic claims (roughly, those neutral to the existence of mathematical entities) in a way that generates nominalistic consequences more easily without generating any new ones. Field goes on to argue that we can axiomatize physical theories using nominalistic claims only, and that in fact this has advantages over the usual axiomatizations that are independent of nominalism. There has been much debate about the book since it first appeared. It is now reissued in a revised contains a substantial new preface giving the author's current views on the original book and the issues that were raised in the subsequent discussion of it. |
| hartry h field: Saving Truth From Paradox Hartry Field, 2008-03-06 Saving Truth from Paradox is an ambitious investigation into paradoxes of truth and related issues, with occasional forays into notions such as vagueness, the nature of validity, and the Gödel incompleteness theorems. Hartry Field presents a new approach to the paradoxes and provides a systematic and detailed account of the main competing approaches. Part One examines Tarski's, Kripke’s, and Lukasiewicz’s theories of truth, and discusses validity and soundness, and vagueness. Part Two considers a wide range of attempts to resolve the paradoxes within classical logic. In Part Three Field turns to non-classical theories of truth that that restrict excluded middle. He shows that there are theories of this sort in which the conditionals obey many of the classical laws, and that all the semantic paradoxes (not just the simplest ones) can be handled consistently with the naive theory of truth. In Part Four, these theories are extended to the property-theoretic paradoxes and to various other paradoxes, and some issues about the understanding of the notion of validity are addressed. Extended paradoxes, involving the notion of determinate truth, are treated very thoroughly, and a number of different arguments that the theories lead to revenge problems are addressed. Finally, Part Five deals with dialetheic approaches to the paradoxes: approaches which, instead of restricting excluded middle, accept certain contradictions but alter classical logic so as to keep them confined to a relatively remote part of the language. Advocates of dialetheic theories have argued them to be better than theories that restrict excluded middle, for instance over issues related to the incompleteness theorems and in avoiding revenge problems. Field argues that dialetheists’ claims on behalf of their theories are quite unfounded, and indeed that on some of these issues all current versions of dialetheism do substantially worse than the best theories that restrict excluded middle. |
| hartry h field: Truth and the Absence of Fact Hartry Field, 2001-03-01 Hartry Field presents a selection of thirteen essays on a set of related topics at the foundations of philosophy; one essay is previously unpublished, and eight are accompanied by substantial new postscripts.Five of the essays are primarily about truth, meaning, and propositional attitudes, five are primarily about semantic indeterminacy and other kinds of 'factual defectiveness' in our discourse, and three are primarily about issues concerning objectivity, especially in mathematics and in epistemology. The essays on truth, meaning, and the attitudes show a development from a form of correspondence theory of truth and meaning to a more deflationist perspective.The next set of papers argue that a place must be made in semantics for the idea that there are questions about which there is no fact of the matter, and address the difficulties involved in making sense of this, both within a correspondence theory of truth and meaning, and within a deflationary theory. Two papers argue that there are questions in mathematics about which there is no fact of the mattter, and draw out implications of this for the nature of mathematics. And the final paper arguesfor a view of epistemology in which it is not a purely fact-stating enterprise.This influential work by a key figure in contemporary philosophy will reward the attention of any philosopher interested in language, epistemology, or mathematics. |
| hartry h field: Realism, Mathematics, and Modality Hartry H. Field, 1991-01-01 |
| hartry h field: Philosophy of Mathematics Øystein Linnebo, 2017-05-30 A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholars Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Gödel, W. V. Quine, Paul Benacerraf, and Hartry H. Field. Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics. |
| hartry h field: Mathematics and Reality Mary Leng, 2010-04-22 Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized. |
| hartry h field: A Companion to the Philosophy of Language Bob Hale, Crispin Wright, Alexander Miller, 2017-02-15 “Providing up-to-date, in-depth coverage of the central question, and written and edited by some of the foremost practitioners in the field, this timely new edition will no doubt be a go-to reference for anyone with a serious interest in the philosophy of language.” Kathrin Glüer-Pagin, Stockholm University Now published in two volumes, the second edition of the best-selling Companion to the Philosophy of Language provides a complete survey of contemporary philosophy of language. The Companion has been greatly extended and now includes a monumental 17 new essays – with topics chosen by the editors, who curated suggestions from current contributors – and almost all of the 25 original chapters have been updated to take account of recent developments in the field. In addition to providing a synoptic view of the key issues, figures, concepts, and debates, each essay introduces new and original contributions to ongoing debates, as well as addressing a number of new areas of interest, including two-dimensional semantics, modality and epistemic modals, and semantic relationism. The extended “state-of-the-art” chapter format allows the authors, all of whom are internationally eminent scholars in the field, to incorporate original research to a far greater degree than competitor volumes. Unrivaled in scope, this volume represents the best contemporary critical thinking relating to the philosophy of language. |
| hartry h field: Defending the Axioms Penelope Maddy, 2011-01-27 Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate. |
| hartry h field: The Things We Mean Stephen Schiffer, 2003-09-04 Stephen Schiffer presents a groundbreaking account of meaning and belief, and shows how it can illuminate a range of crucial problems regarding language, mind, knowledge, and ontology. He introduces the new doctrine of 'pleonastic propositions' to explain what the things we mean and believe are. He discusses the relation between semantic and psychological facts, on the one hand, and physical facts, on the other; vagueness and indeterminacy; moral truth; conditionals; and the role of propositional content in information acquisition and explanation. This radical new treatment of meaning will command the attention of everyone who works on fundamental questions about language, and will attract much interest from other areas of philosophy. |
| hartry h field: Wittgenstein's Metaphilosophy Paul Horwich, 2012-12-13 Paul Horwich presents a bold new interpretation of Wittgenstein's later work. He argues that it is Wittgenstein's radically anti-theoretical metaphilosophy - and not his identification of the meaning of a word with its use - that underpins his discussions of specific issues concerning language, the mind, mathematics, knowledge, art, and religion. |
| hartry h field: An Introduction to the Philosophy of Mathematics Mark Colyvan, 2012-06-14 A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic. |
| hartry h field: The Reason's Proper Study Bob Hale, Crispin Wright, 2003 Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the most powerful presentation yet of a neo-Fregean program. |
| hartry h field: A Structural Account of Mathematics Charles S. Chihara, 2004 Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings.A Structural Account of Mathematics will be required reading for anyone working in this field. |
| hartry h field: A Companion to the Philosophy of Science W. H. Newton-Smith, 2001-10-08 Unmatched in the quality of its world-renowned contributors, this companion serves as both a course text and a reference book across the broad spectrum of issues of concern to the philosophy of science. |
| hartry h field: The Wave Function Alyssa Ney, David Z Albert, 2013-04-08 This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? Does quantum mechanics support the existence of any other fundamental entities, e.g. particles? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics? What is the relationship between the fundamental ontology of quantum mechanics and ordinary, macroscopic objects like tables, chairs, and persons? This collection includes a comprehensive introduction with a history of quantum mechanics and the debate over its metaphysical interpretation focusing especially on the main realist alternatives. |
| hartry h field: Mental Representation Stephen P. Stich, Ted A. Warfield, 1994-07-19 This volume is a collection of new and previously published essays focusing on one of the most exciting and actively discussed topics in contemporary philosophy: naturalistic theories of mental content. The volume brings together important papers written by some of the most distinguished theorists working in the field today. Authors contributing to the volume include Jerry Fodor, Rugh Millikan, Fred Dretske, Ned Block, Robert Cummins, and Daniel Dennett. |
| hartry h field: A Subject With No Object John P. Burgess, Gideon Rosen, 1997-01-16 Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. A Subject With No Object cuts through a host of technicalities that have obscured previous discussions of these projects, and presents clear, concise accounts, with minimal prerequisites, of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. |
| hartry h field: A Companion to Atheism and Philosophy Graham Oppy, 2019-05-06 PROSE 2020 Single Volume Reference Finalist! Philosophers throughout history have debated the existence of gods, but it is only in recent years that the absence of such a belief has become a significant topic of philosophical analysis, in particular for philosophers of religion. Although it is difficult to trace the historical contours of atheism as the lack of belief in a higher power, the reasoned, reflective, and thoughtful rejection of theism has become commonplace in many modern intellectual circles, including academic philosophy where disciplinary data indicates that a large majority of philosophers self-identify as atheists. As the first book of its kind to bring together a collection of writing on the philosophical aspects of atheism both historical and contemporary, the Companion to Atheism and Philosophy stages an explicit, constructive, and comprehensive conversation between philosophy and atheism to examine the ways in which atheist thought intersects with ideas and positions from a variety of philosophical and theological sub-disciplines. The Companion begins by addressing the foundational questions and lingering controversies which underpin philosophical thought about atheism, exploring the implications of major developments in the history of philosophy for the modern atheistic worldview. Divided into eight distinct sections, essays consider a range of thinkers who were widely believed to have been atheists—including David Hume, Mary Wollstonecraft, Karl Marx, and Elizabeth Cady Stanton—and survey different kinds of objections to theism and atheism, including logical, evidential, normative, and prudential. Later chapters trace the relationship between atheism and metaphysics, epistemology, ethics, and political philosophy oriented around topics such as pragmatism, postmodernism, freedom, education, violence, and happiness. Deftly curated and thoughtfully composed, A Companion to Atheism and Philosophy is the most ambitious and authoritative account of philosophical thinking on atheism available, and is a first-rate resource for academics, professionals, and students of philosophy, religious studies, and theology. |
| hartry h field: The Cambridge Companion to Popper Jeremy Shearmur, Geoffrey Stokes, 2016-06-27 This is one of the most comprehensive collections of critical essays to be published on the philosophy of Karl Popper. |
| hartry h field: Ontological Economy Dale Gottlieb, 1980 Shows that when Qyuine's criterion of ontological commitment is modified to allow for the legitimacy of substitutional quantification, two consequences follow: (i) fundamental questions of ontology cease to be settled by mere appeal to logical form and truth, and (ii) a powerful method for reducing ontological commitments becomes available. |
| hartry h field: The Indispensability of Mathematics Mark Colyvan, 2001 Annotation. The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with manyinfluential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges. |
| hartry h field: Knowing Right From Wrong Kieran Setiya, 2012-11-29 Can we have objective knowledge of right and wrong, of how we should live and what there is reason to do? Can it be anything but luck when our beliefs are true? Kieran Setiya confronts these questions in their most compelling and articulate forms, and argues that if there is objective ethical knowledge, human nature is its source. |
| hartry h field: Ontology and Objectivity Thomas Hofweber, 1999 |
| hartry h field: How is Quantum Field Theory Possible? Sunny Y. Auyang, 1995 How can we know the microscopic world without a measurement theory? What are the general conditions of the world that make possible such knowledge? What are the presuppositions of physical theories? This book includes an analysis of quantum field theory, and quantum mechanics and interacting systems are addressed in a unified framework. |
| hartry h field: Truth Alexis G. Burgess, John P. Burgess, 2011-02-28 This is a concise introduction to current philosophical debates about truth. Combining philosophical and technical material, the book is organized around, but not limited to, the view known as deflationism. In clear language, Burgess and Burgess cover a wide range of issues, including the nature of truth, the status of truth-value gaps, the relationship between truth and meaning, relativism and pluralism about truth, and semantic paradoxes from Alfred Tarski to Saul Kripke and beyond. The book provides a rich picture of contemporary philosophical theorizing about truth, one that will be essential reading for philosophy students as well as philosophers specializing in other areas. |
| hartry h field: Bohmian Mechanics and Quantum Theory: An Appraisal J.T. Cushing, Arthur Fine, S. Goldstein, 2013-04-17 We are often told that quantum phenomena demand radical revisions of our scientific world view and that no physical theory describing well defined objects, such as particles described by their positions, evolving in a well defined way, let alone deterministically, can account for such phenomena. The great majority of physicists continue to subscribe to this view, despite the fact that just such a deterministic theory, accounting for all of the phe nomena of nonrelativistic quantum mechanics, was proposed by David Bohm more than four decades ago and has arguably been around almost since the inception of quantum mechanics itself. Our purpose in asking colleagues to write the essays for this volume has not been to produce a Festschrift in honor of David Bohm (worthy an undertaking as that would have been) or to gather together a collection of papers simply stating uncritically Bohm's views on quantum mechanics. The central theme around which the essays in this volume are arranged is David Bohm's version of quantum mechanics. It has by now become fairly standard practice to refer to his theory as Bohmian mechanics and to the larger conceptual framework within which this is located as the causal quantum theory program. While it is true that one can have reservations about the appropriateness of these specific labels, both do elicit distinc tive images characteristic of the key concepts of these approaches and such terminology does serve effectively to contrast this class of theories with more standard formulations of quantum theory. |
| hartry h field: Truth Paul Horwich, 1998-12-03 What is truth? Paul Horwich gives the definitive exposition of a notable philosophical theory, `minimalism'. This is the controversial theory that the nature of truth is entirely captured in the trivial fact that each proposition specifies its own condition for being true, and that truth is therefore, despite the philosophical struggles to which it has given rise, an entirely mundane and unpuzzling concept. Horwich makes a powerful case for the minimalist view, and gives a careful systematic explanation of its implications for a cluster of important philosophical issues on which questions about truth have impinged. The first edition of Truth, published in 1990, established itself both as the best account of minimalism and as an excellent introduction to the debate for students. For this new edition Paul Horwich has refined and developed his treatment of the subject in the light of subsequent discussions, while preserving the distinctive format which made the book so successful. It appears simultaneously with his new book Meaning, a companion work which sets out the broader philosophical context for the theory of truth: an account of meaning which seeks to accommodate the diversity of valuable insights that have been gained in the twentieth century within a common-sense view of meaning as deriving from use. The two books together present a compelling view of the relations between language, thought, and reality. Horwich's demystification of meaning and truth will be essential reading for all philosophers of language. Praise for the first edition: 'subtle, penetrating and ingenious . . . everyone interested in philosophy is in his debt' Michael Dummett, University of Oxford 'lucid and compact . . . a forthright presentation of an interesting thesis' Donald Davidson, University of California, Berkeley 'This is an excellent book and deserves to be widely read and used as a text. It states its thesis clearly and argues for it briskly: a style that seems well calculated to start discussions . . . It seems like an admirable starting-point for several weeks' worth of discussions in a philosophy of language course at upper-division undergraduate level.' Australasian Journal of Philosophy 'clearly written and well-structured' British Journal for the Philosophy of Science 'clear, informed and provocative ... I thoroughly recommend the book to everyone in the philosophy of language, philosophy of science, and metaphysics' Michael Devitt, Mind and Language |
| hartry h field: Truth in Mathematics Harold G. Dales, Gianluigi Oliveri, 1998 The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. The great advances in mathematics and philosophy in the twentieth centuryand in particular the proof of Gödel's theorem and the development of the notion of independence in mathematicshave led to new viewpoints on this question in our era. This book is the result of the interaction of a number of outstanding mathematicians and philosophersincluding Yurii Manin, Vaughan Jones, and Per Martin-Löfand their discussions of this problem. It provides an overview of the forefront of current thinking, and is a valuable introduction and reference for researchers in the area. |
| hartry h field: Panentheism and Panpsychism Godehard Brüntrup, Benedikt Paul Göcke, Ludwig Jaskolla, 2020 Panpsychism has become a highly attractive position in the philosophy of mind. On panpsychism, both the physical and the mental are inseparable and fundamental features of reality. Panentheism has also become immensely popular in the philo-sophy of religion. Panentheism strives for a higher reconciliation of an atheistic pantheism, on which the universe itself is causa sui, and the ontological dualism of necessarily existing, eternal creator and contingent, fi nite creation. Historically and systematically, panpsychism and panentheism often went together as essential parts of an all-embracing metaphysical theory of Being. The present collection of essays analyses the relation between panpsychism and panentheism and provides critical reflections on the significance of panpsychistic and panentheistic thinking for recent debates in philosophy and theology. |
| hartry h field: Logic, Epistemology, and the Unity of Science Shahid Rahman, John Symons, Dov M. Gabbay, jean paul van bendegem, 2009-03-15 The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality. |
| hartry h field: Philosophical Logic John MacFarlane, 2020-11-29 Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'—and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter |
| hartry h field: Revenge of the Liar JC Beall, 2007-12-13 The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says (only) that it is false. How, then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another. JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics. |
| hartry h field: The Philosophy of Mathematical Practice Paolo Mancosu, 2008-06-19 Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics. |
| hartry h field: The Philosophy of Mathematics Today Matthias Schirn, 2003 Representing the state of the art in the field of the philosophy of mathematics, this collection of 20 essays deals with fundamental issues, ranging from the nature of mathematical knowledge to sets and natural 'number'. |
| hartry h field: Mathematics as a Science of Patterns Michael D. Resnik, 1997-07-31 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. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics—the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology. |
| hartry h field: Abstract Objects José L. Falguera, Concha Martínez-Vidal, 2020-05-08 This volume examines the question “Do abstract objects exist?”, presenting new work from contributing authors across different branches of philosophy. The introduction overviews philosophical debate which considers: what objects qualify as abstract, what do we mean by the word exist” and indeed, what evidence should count in favor or against the thesis that abstract objects exist. Through subsequent chapters readers will discover the ubiquity of abstract objects as each philosophical field is considered. Given the ubiquitous use of expressions that purportedly refer to abstract objects, we think that it is relevant to attend to the controversy between those who want to advocate the existence of abstract objects and those who stand against them. Contributions to this volume depict positions and debates that directly or indirectly involve taking one position or other about abstract objects of different kinds and categories. The volume provides a variety of samples of how positions for or against abstract objects can be used in different areas of philosophy in relation to different matters. |
| hartry h field: Science Without Numbers Hartry H. Field, 2016 'Science Without Numbers' caused a stir when it was originally published in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for 20 years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate. |
| hartry h field: Truth, Objects, Infinity Fabrice Pataut, 2017-01-27 This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a workshop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of “Mathematical Truth” due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status of numbers: Frege’s logicism, fictionalism, structuralism, and Bourbaki’s theory of structures are called up for an appraisal of Benacerraf’s negative conclusions of “What Numbers Could Not Be.” The third is devoted to supertasks and bears witness to the unique standing of Benacerraf’s first publication: “Tasks, Super-Tasks, and Modern Eleatics” in debates on Zeno’s paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics. Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the mid 1970’s. A complete chronological bibliography of Benacerraf’s work to 2016 is provided.Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio León-Sánchez and Ana C. León-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro. |
| hartry h field: World Enough and Space-Time John Earman, 1992-03-01 Newton's Principia introduced conceptions of space and time that launched one of themost famous and sustained debates in the history of physics, a controversy that involves fundamentalconcerns in the foundations of physics, metaphysics, and scientific epistemology.This bookintroduces and clarifies the historical and philosophical development of the clash between Newton'sabsolute conception of space and Leibniz's relational one. It separates the issues and provides newperspectives on absolute relational accounts of motion and relational-substantival accounts of theontology of space time.Earman's sustained treatment and imaginative insights raise to a new levelthe debate on these important issues at the boundary of philosophy and physics. He surveys thehistory of the controversy from Newton to Einstein develops the mathematics and physics needed topose the issues in sharp form and provides a persuasive assessment of the philosophical problemsinvolved.Most importantly, Earman revitalizes the connection of the debate to contemporary science.He shows, for example, how concerns raised by Leibniz form the core of ongoing debate on thefoundations of general theory of relativity, moving the discussion into a new and vital arena andintroducing arguments that will be discussed for years to come.John Earman is Professor of Historyand Philosophy of Science at the University of Pittsburgh. A Bradford Book |
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World Class Horse Racing In South Florida | Pegasus World Cup
Located in Hallandale Beach, The Pegasus World Cup is South Florida's premiere horse racing experience live from Gulfstream Park Racing and Casino.
Pegasus World Cup Invitational Stakes - Wikipedia
The Pegasus World Cup Invitational Stakes is an American Thoroughbred horse race whose first running was on January 28, 2017 at Gulfstream Park in Hallandale Beach, Florida. [1][2] It is run …
How to watch 2025 Pegasus World Cup: Schedule, post time, …
Jan 24, 2025 · The 2025 Pegasus World Cup takes place this Saturday, January 25 at Gulfstream Park in Hallandale Beach, Florida, marking the first major horse racing event of the year. Live …
Pegasus World Cup race results, winners and past history
Discover Pegasus World Cup race results, winners, and past history on this comprehensive horse racing page.
Everything you need to know about the Pegasus World Cup 2025
Jan 14, 2025 · Located in Hallandale Beach, Florida, between Miami and Fort Lauderdale, Gulfstream Park will host the World Cup on Saturday, January 25, 2025. The highlight of the day, …
Pegasus World Cup 2025 - Daily Racing Form
Jan 25, 2025 · HALLANDALE BEACH, Fla. – White Abarrio completed serious preparations for the $3 million Pegasus World Cup Invitational on Thursday morning, breezing an easy half-mile in …
Pegasus World Cup 2025 predictions, horses, odds, field, lineup ...
Jan 25, 2025 · Todd Pletcher has two 2025 Pegasus World Cup horses running on Saturday at Gulfstream Park, Crupi (15-1) and Locked, the 5-2 favorite in the latest 2025 Pegasus World Cup …
Pegasus World Cup - YouTube
Experience the 10 Year Anniversary of the Pegasus World Cup. January 2026. https://www.pegasusworldcup.com Re-live the 2025 Pegasus World Cup at Gulfstream Park in …
What You Need to Know Before You Go to 2025 Pegasus World Cup
Jan 20, 2025 · The Pegasus World Cup, boasting a purse of $3 million, is expected to draw a large, competitive field and serves as the crown jewel on a card that will include a total of seven graded …
Pegasus World Cup 2026 - Runners, Odds, Tips & Bets
Nicknamed “Florida’s Greatest Horse Race,” the Pegasus World Cup is a Grade I Thoroughbred flat race run over 1⅛ miles (about 1,810 meters) on Gulfstream Park’s left-handed dirt track.
