• Philosophy

Truth and the Absence of Fact


Author: Hartry Field
Publisher: Oxford University Press on Demand
ISBN: 0199241716
Category: Philosophy
Page: 401
View: 7402
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a selection of thirteen essays on a set of related topics at the foundations of philosophy; one essay is previously unpublished, and eight are accompanied by substantial new postscripts.Five of the essays are primarily about truth, meaning, and propositional attitudes, five are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.

    • Philosophy

Science without Numbers


Author: Hartry Field
Publisher: Oxford University Press
ISBN: 0191083771
Category: Philosophy
Page: 176
View: 8231
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.

    • Philosophy

Saving Truth From Paradox


Author: Hartry Field
Publisher: Oxford University Press
ISBN: 0199230757
Category: Philosophy
Page: 406
View: 655
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.

    • Mathematics

Philosophy of Logic


Author: N.A
Publisher: Elsevier
ISBN: 9780080466637
Category: Mathematics
Page: 1218
View: 1139
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter

    • Philosophy

An Historical Introduction to the Philosophy of Mathematics: A Reader


Author: Russell Marcus,Mark McEvoy
Publisher: Bloomsbury Publishing
ISBN: 1472529480
Category: Philosophy
Page: 896
View: 6284
A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.

    • Philosophy

Philosophy of Mathematics


Author: N.A
Publisher: Elsevier
ISBN: 9780080930589
Category: Philosophy
Page: 733
View: 5111
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

    • Science

Mathematical Thought and its Objects


Author: Charles Parsons
Publisher: Cambridge University Press
ISBN: 9781139467278
Category: Science
Page: N.A
View: 8073
Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.

    • Mathematics

Identity and Modality


Author: Fraser MacBride
Publisher: Oxford University Press
ISBN: 0199285748
Category: Mathematics
Page: 268
View: 392
The papers in this volume address fundamental, and interrelated, philosophical issues concerning modality and identity, issues that have not only been pivotal to the development of analytic philosophy in the twentieth century, but remain a key focus of metaphysical debate in the twenty-first. How are we to understand the concepts of necessity and possibility? Is chance a basic ingredient of reality? How are we to make sense of claims about personal identity? Do numbers requiredistinctive identity criteria? Does the capacity to identify an object presuppose an ability to bring it under a sortal concept?Rather than presenting a single, partisan perspective, Identity and Modality enriches our understanding of identity and modality by bringing together papers written by leading researchers working in metaphysics, the philosophy of mind, the philosophy of science, and the philosophy of mathematics. The resulting variety of perspectives correspondingly reflects both the breadth and depth of contemporary theorizing about identity and modality, each paper addressing a particular issue andadvancing our knowledge of the area.This volume will provide essential reading for graduate students in the subject and professional philosophers.

    • Philosophy

Realism and Anti-Realism


Author: Stuart Brock,Edwin Mares
Publisher: Routledge
ISBN: 1317494261
Category: Philosophy
Page: 224
View: 9013
There are a bewildering variety of ways the terms "realism" and "anti-realism" have been used in philosophy and furthermore the different uses of these terms are only loosely connected with one another. Rather than give a piecemeal map of this very diverse landscape, the authors focus on what they see as the core concept: realism about a particular domain is the view that there are facts or entities distinctive of that domain, and their existence and nature is in some important sense objective and mind-independent. The authors carefully set out and explain the different realist and anti-realist positions and arguments that occur in five key domains: science, ethics, mathematics, modality and fictional objects. For each area the authors examine the various styles of argument in support of and against realism and anti-realism, show how these different positions and arguments arise in very different domains, evaluate their success within these fields, and draw general conclusions about these assorted strategies. Error theory, fictionalism, non-cognitivism, relativism and response-dependence are taken as the most important positions in opposition to the realist and these are explored in depth. Suitable for advanced level undergraduates, the book offers readers a clear introduction to a subject central to much contemporary work in metaphysics, epistemology and philosophy of language.

    • Language Arts & Disciplines

Modality and Tense

Philosophical Papers
Author: Kit Fine
Publisher: Oxford University Press
ISBN: 0199278709
Category: Language Arts & Disciplines
Page: 387
View: 4125
In this book, Kit Fine draws together a series of essays, three of them previously unpublished, on possibility, necessity, and tense.

    • Philosophy

Husserl Or Frege?

Meaning, Objectivity, and Mathematics
Author: Claire Ortiz Hill,Guillermo E. Rosado Haddock
Publisher: Open Court Publishing
ISBN: 9780812694178
Category: Philosophy
Page: 315
View: 8064
Most areas of philosopher Edmund Husserl’s thought have been explored, but his views on logic, mathematics, and semantics have been largely ignored. These essays offer an alternative to discussions of the philosophy of contemporary mathematics. The book covers areas of disagreement between Husserl and Gottlob Frege, the father of analytical philosophy, and explores new perspectives seen in their work.

    • Philosophy

Modality

Metaphysics, Logic, and Epistemology
Author: Bob Hale,Aviv Hoffmann
Publisher: Oxford University Press
ISBN: 0199565813
Category: Philosophy
Page: 363
View: 1089
Modality brings together contributions from both well-established leaders in the field and up-and-coming philosophers. Between them, the papers address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal logic and its relations to necessary existence and to counterfactual reasoning, and other issues central to thecurrently highly active debate among philosophers in this area. The general introduction locates the individual contributions both in the specific context of the research project for which they were produced, and in the wider context of the contemporary discussion of the metaphysics and epistemology of modality.

    • Philosophy

Philosophy of Mathematics

Structure and Ontology
Author: Stewart Shapiro
Publisher: Oxford University Press
ISBN: 9780198025450
Category: Philosophy
Page: 296
View: 7636
Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.

    • Philosophy

The Worlds of Possibility

Modal Realism and the Semantics of Modal Logic
Author: Charles S. Chihara
Publisher: Oxford University Press
ISBN: 9780199246557
Category: Philosophy
Page: 342
View: 4845
Charles Chihara gives a thorough critical exposition of modal realism, the philosophical doctrine that there exist many possible worlds of which the actual world -- the universe in which we live -- is just one. The striking success of possible-worlds semantics in modal logic has made this ontological doctrine attractive. Modal realists maintain that philosophers must accept the existence of possible worlds if they wish to have the benefit of using possible-worlds semantics to assess modalarguments and explain modal principles. Chihara challenges this claim, and argues instead for modality without worlds; he offers a new account of the role of interpretations or structures of the formal languages of logic.

    • Science

Structural Realism

Structure, Object, and Causality
Author: Elaine Landry,Dean Rickles
Publisher: Springer Science & Business Media
ISBN: 9400725795
Category: Science
Page: 212
View: 1771
Structural realism has rapidly gained in popularity in recent years, but it has splintered into many distinct denominations, often underpinned by diverse motivations. There is, no monolithic position known as ‘structural realism,’ but there is a general convergence on the idea that a central role is to be played by relational aspects over object-based aspects of ontology. What becomes of causality in a world without fundamental objects? In this book, the foremost authorities on structural realism attempt to answer this and related questions: ‘what is structure?’ and ‘what is an object?’ Also featured are the most recent advances in structural realism, including the intersection of mathematical structuralism and structural realism, and the latest treatments of laws and modality in the context of structural realism. The book will be of interest to philosophers of science, philosophers of physics, metaphysicians, and those interested in foundational aspects of science.

    • Religion

Actuality, Possibility, and Worlds


Author: Alexander R. Pruss
Publisher: Bloomsbury Publishing USA
ISBN: 1441120629
Category: Religion
Page: 320
View: 4006
Actuality, Possibility and Worlds is an exploration of the Aristotelian account that sees possibilities as grounded in causal powers. On his way to that account, Pruss surveys a number of historical approaches and argues that logicist approaches to possibility are implausible.The notion of possible worlds appears to be useful for many purposes, such as the analysis of counterfactuals or elucidating the nature of propositions and properties. This usefulness of possible worlds makes for a second general question: Are there any possible worlds and, if so, what are they? Are they concrete universes as David Lewis thinks, Platonic abstracta as per Robert M. Adams and Alvin Plantinga, or maybe linguistic or mathematical constructs such as Heller thinks? Or is perhaps Leibniz right in thinking that possibilia are not on par with actualities and that abstracta can only exist in a mind, so that possible worlds are ideas in the mind of God?

    • Philosophy

Thoughts

Papers on Mind, Meaning, and Modality
Author: Stephen Yablo
Publisher: Oxford University Press
ISBN: 0199266468
Category: Philosophy
Page: 327
View: 5320
In these twelve essays Stephen Yablo presents a modern-day examination of Cartesian themes in the metaphysics of mind, including mental/physical dualism, the possibility of disembodied existence, conceivability as a guide to possibility, the nature of solipsistic content, and how the mind affects the course of physical events.

    • Philosophy

Meaning and Method

Essays in Honor of Hilary Putnam
Author: George Boolos
Publisher: Cambridge University Press
ISBN: 9780521360838
Category: Philosophy
Page: 380
View: 9565
This volume is a report on the state of philosophy in a number of significant areas.

    • Philosophy

Reference, Truth and Conceptual Schemes

A Defense of Internal Realism
Author: G. Forrai
Publisher: Springer Science & Business Media
ISBN: 9401728682
Category: Philosophy
Page: 163
View: 1165
1. HISTORICAL BACKGROUND The purpose of the book is to develop internal realism, the metaphysical-episte mological doctrine initiated by Hilary Putnam (Reason, Truth and History, "Introduction", Many Faces). In doing so I shall rely - sometimes quite heavily - on the notion of conceptual scheme. I shall use the notion in a somewhat idiosyncratic way, which, however, has some affinities with the ways the notion has been used during its history. So I shall start by sketching the history of the notion. This will provide some background, and it will also give opportunity to raise some of the most important problems I will have to solve in the later chapters. The story starts with Kant. Kant thought that the world as we know it, the world of tables, chairs and hippopotami, is constituted in part by the human mind. His cen tral argument relied on an analysis of space and time, and presupposed his famous doctrine that knowledge cannot extend beyond all possible experience. It is a central property of experience - he claimed - that it is structured spatially and temporally. However, for various reasons, space and time cannot be features of the world, as it is independently of our experience. So he concluded that they must be the forms of human sensibility, i. e. necessary ingredients of the way things appear to our senses.