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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.
Truth and Paradox offers a comprehensive account of truth values and the norms governing claims about truth, based on a new approach to logic and semantics. Since the seminal work of Tarski in the mid-twentieth century, the Liar paradox and other related paradoxes have stood in the way of a precise philosophical account of truth. Tim Maudlin draws on analogies from mathematical physics to explicate the origin of classical truth-value gaps, and to provide an account of truth that avoids any hierarchy of languages or of truth predicates. He also closely investigates our reasoning about truth, including apparently unobjectionable reasoning about the paradoxical sentences. The fallacies in that reasoning are located not in any inferences concerning truth, but in the foundations of standard logic. Blocking the paradoxical arguments requires emendation of classical logic, and the requisite emendations call into question the existence of any a priori logical truths. Maudlin also includes a discussion of facts and factuality, most particularly the question of whether there are any facts about truth. All philosophers interested in logic and language will find this a stimulating read.
This is an 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.
This work is in two parts. It began as a general investigation of vagueness in natural languages. The Sorites Paradox came to dominate the work however, and the second part of the book consists in an discussion ofthat puzzle and related problems. The first part contains a general discussion ofthe nature ofvagueness and its sources. I discuss various conceptions of vagueness in chapter 1 and outline some of the problems to do with the conception of vagueness as a linguistic phenomenon. The most interesting of these is the Sorites paradox, which occurs where natural languages exhibit a particular variety of borderline case vagueness. I discuss some sources of vagueness of the borderline case variety, and views of the relation between linguistic behaviour and languages which are vague in this sense. I argue in chapter 2 that these problems are not to be easily avoided by statistical averaging techniques or attempts to provide a mathematical model of consensus in linguistic usage. I also consider in chapter 3 various approaches to the problem of providing an adequate logic and semantics for vague natural languages, and argue against two currently popular approaches to vagueness. These are supervaluation accounts which attempt to provide precise semantic models for vague languages based on the notion of specification spaces, and attempts to replace the laws ofclassical logic with systems offuzzy logic.
This volume explores how vagueness matters as a specific problem in the context of theories that are primarily about something else. After an introductory chapter on the Sorites paradox, which exposes the various forms the paradox can take and some of the responses that have been pursued, the book proceeds with a chapter on vagueness and metaphysics, which covers important questions concerning vagueness that arise in connection with the deployment of certain key metaphysical notions. Subsequent chapters address the following: vagueness and logic, which discusses the sort of model theory that is suggested by the main, rival accounts of vagueness; vagueness and meaning, which focuses on contextualist, epistemicist, and indeterminist theories; vagueness and observationality; vagueness within linguistics, which focuses on approaches that take comparison classes into account; and the idea that vagueness in law is typically extravagant and that extravagant vagueness is a necessary feature of legal systems.
Spandrels of Truth by Jc Beall,Jeffrey C. Beall Pdf
Jc Beall presents a new theory of 'transparent' truth. A prominent philosophical view of truth is as an entirely see-through device introduced for only practical (expressive) reasons. Beall's modest dialetheic theory shows how the notorious paradoxes associated with transparency can be dealt with.
Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions.
Author : Tim Maudlin,Department of Philosophy Tim Maudlin Publisher : Oxford University Press on Demand Page : 223 pages File Size : 45,6 Mb Release : 2004-05-13 Category : Language Arts & Disciplines ISBN : 9780199247295
Truth and Paradox by Tim Maudlin,Department of Philosophy Tim Maudlin Pdf
Consider the sentence 'This sentence is not true'. Certain notorious paradoxes like this have bedevilled philosophical theories of truth. Tim Maudlin presents an original account of logic and semantics which deals with these paradoxes, and allows him to set out a new theory of truth-values and the norms governing claims about truth.
Author : Robert L. Martin Publisher : Unknown Page : 334 pages File Size : 49,9 Mb Release : 1984 Category : Language Arts & Disciplines ISBN : UCAL:B3941883
Recent Essays on Truth and the Liar Paradox by Robert L. Martin Pdf
This collection of recent essays includes important and influential work on the concept of truth and the semantic pardoxes. Using techniques of mathematical logic, these philosophers tackle this age-old problem to offer new insights and widely varying analyses.
Did Buddha become a fat man in one second? Is there a tallest short giraffe? Epistemicists answer 'Yes!' They believe that any predicate that divides things divides them sharply. They solve the ancient sorites paradox by picturing vagueness as a kind of ignorance. The alternative solutions are radical. They either reject classical theorems or inference rules or reject our common sense view of what can exist. Epistemicists spare this central portion of our web of belief by challenging peripheral intuitions about the nature of language. So why is this continuation of the status quo so incredible? Why do epistemicists themselves have trouble believing their theory? In Vagueness and Contradiction Roy Sorensen traces our incredulity to linguistic norms that build upon our psychological tendencies to round off insignificant differences. These simplifying principles lead to massive inconsistency, rather like the rounding off errors of calculators with limited memory. English entitles speakers to believe each 'tolerance conditional' such as those of the form 'If n is small, then n + 1 is small.' The conjunction of these a priori beliefs entails absurd conditionals such as 'If 1 is small, then a billion is small.' Since the negation of this absurdity is an a priori truth, our a priori beliefs about small numbers are jointly inconsistent. One of the tolerance conditionals, at the threshold of smallness, must be an analytic falsehood that we are compelled to regard as a tautology. Since there are infinitely many analytic sorites arguments, Sorensen concludes that we are obliged to believe infinitely many contradictions. These contradictions are not specifically detectable. They are ineliminable, like the heat from a light bulb. Although the light bulb is not designed to produce heat, the heat is inevitably produced as a side-effect of illumination. Vagueness can be avoided by representational systems that make no concession to limits of perception, or memory, or testimony. But quick and rugged representational systems, such as natural languages, will trade 'rationality' for speed and flexibility. Roy Sorensen defends epistemicism in his own distinctive style, inventive and amusing. But he has some serious things to say about language and logic, about the way the world is and about our understanding of it.
This book is about one of the most baffling of all paradoxes--the famous Liar paradox. Suppose we say: "We are lying now." Then if we are lying, we are telling the truth; and if we are telling the truth we are lying. This paradox is more than an intriguing puzzle, since it involves the concept of truth. Thus any coherent theory of truth must deal with the Liar. Keith Simmons discusses the solutions proposed by medieval philosophers and offers his own solutions and in the process assesses other contemporary attempts to solve the paradox. Unlike such attempts, Simmons' "singularity" solution does not abandon classical semantics and does not appeal to the kind of hierarchical view found in Barwise's and Etchemendy's The Liar. Moreover, Simmons' solution resolves the vexing problem of semantic universality--the problem of whether there are semantic concepts beyond the expressive reach of a natural language such as English.
Logic is fundamental to thought and language. But which logical principles are correct? The paradoxes play a crucial role in answering that question. Written by leading figures in the field, this text discusses novel thoughts about the paradoxes.