Hartry Field
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199230747
- eISBN:
- 9780191710933
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230747.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter is a short introduction to the ways of dealing with the Liar paradox within classical logic. It distinguishes classical gap theories, classical glut theories, and weakly classical ...
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This chapter is a short introduction to the ways of dealing with the Liar paradox within classical logic. It distinguishes classical gap theories, classical glut theories, and weakly classical theories (a heading that includes both supervaluation theories and revision theories, in their ‘internal’ versions). It introduces some natural ‘Incoherence Principles’, jointly unsatisfiable in classical logic. The gap, glut, and weakly classical theories can be understood as different choices as to which incoherence principle to reject.Less
This chapter is a short introduction to the ways of dealing with the Liar paradox within classical logic. It distinguishes classical gap theories, classical glut theories, and weakly classical theories (a heading that includes both supervaluation theories and revision theories, in their ‘internal’ versions). It introduces some natural ‘Incoherence Principles’, jointly unsatisfiable in classical logic. The gap, glut, and weakly classical theories can be understood as different choices as to which incoherence principle to reject.
Jc Beall
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199268733
- eISBN:
- 9780191708527
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199268733.001.0001
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
Among the various conceptions of truth is one according to which ‘is true’ is a transparent, entirely see-through device introduced for only practical (expressive) reasons. This device, when ...
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Among the various conceptions of truth is one according to which ‘is true’ is a transparent, entirely see-through device introduced for only practical (expressive) reasons. This device, when introduced into the language, brings about truth-theoretic paradoxes (particularly, the notorious Liar and Curry paradoxes). The options for dealing with the paradoxes while preserving the full transparency of ‘true’ are limited. This book presents and defends a modest, so-called dialetheic theory of transparent truth.Less
Among the various conceptions of truth is one according to which ‘is true’ is a transparent, entirely see-through device introduced for only practical (expressive) reasons. This device, when introduced into the language, brings about truth-theoretic paradoxes (particularly, the notorious Liar and Curry paradoxes). The options for dealing with the paradoxes while preserving the full transparency of ‘true’ are limited. This book presents and defends a modest, so-called dialetheic theory of transparent truth.
Scott Soames
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780195123357
- eISBN:
- 9780199872114
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195123352.001.0001
- Subject:
- Philosophy, Philosophy of Language
Understanding Truth aims to illuminate the notion of truth, and the role it plays in our ordinary thought, as well as in our logical, philosophical, and scientific theories. Part 1 is ...
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Understanding Truth aims to illuminate the notion of truth, and the role it plays in our ordinary thought, as well as in our logical, philosophical, and scientific theories. Part 1 is concerned with substantive background issues: the identification of the bearers of truth, the basis for distinguishing truth from other notions, like certainty, with which it is often confused, and the formulation of positive responses to well‐known forms of philosophical skepticism about truth. Having cleared away the grounds for truth skepticism, the discussion turns in Part 2 to an explication of the formal theories of Alfred Tarski and Saul Kripke, including their treatments of the Liar paradox (illustrated by sentences like This sentence is not true). The success of Tarski's definition of truth in avoiding the Liar, and his ingenious use of the paradox in proving the arithmetical indefinability of arithmetical truth, are explained, and the fruitfulness of his definition in laying the foundations for the characterization of logical consequence in terms of truth in a model is defended against objections. Nevertheless, it is argued that the notion of truth defined by Tarski does not provide an adequate analysis of our ordinary notion because there are intellectual tasks for which we need a notion of truth other than Tarski's. There are also problems with applying his hierarchical approach to the Liar as it arises in natural language – problems that are avoided by Kripke's more sophisticated model. Part 2 concludes with an explanation of Kripke's theory of truth, which is used to motivate a philosophical conception of partially defined predicates – i.e., predicates that are governed by sufficient conditions for them to apply to an object, and sufficient conditions for them to fail to apply, but no conditions that are both individually sufficient and jointly necessary for the predicates to apply, or for them to fail to apply. While the advantages of understanding are true, to be a predicate of this sort are stressed at the end of Part 2, a theory of vague predicates according to which they are both partially defined and context sensitive is presented in Part 3. This theory is used to illuminate and resolve certain important puzzles posed by the Sorites paradox: a newborn baby is young, if someone is young at a certain moment, then that person is still young one second later, so everyone is young. The book closes with an attempt to incorporate important insights of Tarski and Kripke into a broadly deflationary conception of truth, as we ordinarily understand it in natural language and use it in philosophy.Less
Understanding Truth aims to illuminate the notion of truth, and the role it plays in our ordinary thought, as well as in our logical, philosophical, and scientific theories. Part 1 is concerned with substantive background issues: the identification of the bearers of truth, the basis for distinguishing truth from other notions, like certainty, with which it is often confused, and the formulation of positive responses to well‐known forms of philosophical skepticism about truth. Having cleared away the grounds for truth skepticism, the discussion turns in Part 2 to an explication of the formal theories of Alfred Tarski and Saul Kripke, including their treatments of the Liar paradox (illustrated by sentences like This sentence is not true). The success of Tarski's definition of truth in avoiding the Liar, and his ingenious use of the paradox in proving the arithmetical indefinability of arithmetical truth, are explained, and the fruitfulness of his definition in laying the foundations for the characterization of logical consequence in terms of truth in a model is defended against objections. Nevertheless, it is argued that the notion of truth defined by Tarski does not provide an adequate analysis of our ordinary notion because there are intellectual tasks for which we need a notion of truth other than Tarski's. There are also problems with applying his hierarchical approach to the Liar as it arises in natural language – problems that are avoided by Kripke's more sophisticated model. Part 2 concludes with an explanation of Kripke's theory of truth, which is used to motivate a philosophical conception of partially defined predicates – i.e., predicates that are governed by sufficient conditions for them to apply to an object, and sufficient conditions for them to fail to apply, but no conditions that are both individually sufficient and jointly necessary for the predicates to apply, or for them to fail to apply. While the advantages of understanding are true, to be a predicate of this sort are stressed at the end of Part 2, a theory of vague predicates according to which they are both partially defined and context sensitive is presented in Part 3. This theory is used to illuminate and resolve certain important puzzles posed by the Sorites paradox: a newborn baby is young, if someone is young at a certain moment, then that person is still young one second later, so everyone is young. The book closes with an attempt to incorporate important insights of Tarski and Kripke into a broadly deflationary conception of truth, as we ordinarily understand it in natural language and use it in philosophy.
Tim Maudlin
- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199247295
- eISBN:
- 9780191601781
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199247293.001.0001
- Subject:
- Philosophy, Philosophy of Language
At least since the work of Tarski, the Liar paradox has stood in the way of an acceptable account of the notion of truth. It has been less noticed that once one admits a truth predicate into a formal ...
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At least since the work of Tarski, the Liar paradox has stood in the way of an acceptable account of the notion of truth. It has been less noticed that once one admits a truth predicate into a formal language, along with intuitively valid inferences involving the truth predicate, standard classical logic becomes inconsistent. So, any acceptable account of truth must both explicate how sentences get the truth values they have and amend classical logic to avoid the inconsistency. A natural account of a trivalent semantics arises from treating the problem of assigning truth values to sentences as akin to a boundary‐value problem in physics. The resulting theory solves the Liar paradox while avoiding the usual ‘revenge’ problems. It also suggests a natural modification of classical logic that blocks the paradoxical reasoning. This semantic theory is wedded to an account of the normative standards governing assertion and denial of sentence and a metaphysical analysis truth and factuality. The result is an account in which sentences like the Liar sentence are neither true nor false, and correspond to no facts.Less
At least since the work of Tarski, the Liar paradox has stood in the way of an acceptable account of the notion of truth. It has been less noticed that once one admits a truth predicate into a formal language, along with intuitively valid inferences involving the truth predicate, standard classical logic becomes inconsistent. So, any acceptable account of truth must both explicate how sentences get the truth values they have and amend classical logic to avoid the inconsistency. A natural account of a trivalent semantics arises from treating the problem of assigning truth values to sentences as akin to a boundary‐value problem in physics. The resulting theory solves the Liar paradox while avoiding the usual ‘revenge’ problems. It also suggests a natural modification of classical logic that blocks the paradoxical reasoning. This semantic theory is wedded to an account of the normative standards governing assertion and denial of sentence and a metaphysical analysis truth and factuality. The result is an account in which sentences like the Liar sentence are neither true nor false, and correspond to no facts.
Gyula Klima
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195176223
- eISBN:
- 9780199871957
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195176223.003.0010
- Subject:
- Religion, Church History
This chapter provides a comprehensive survey of Buridan’s conception of logical validity in a semantically closed token-based system, as he conceives of natural languages. The chapter argues first ...
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This chapter provides a comprehensive survey of Buridan’s conception of logical validity in a semantically closed token-based system, as he conceives of natural languages. The chapter argues first that Buridan has very good logical, as well as merely metaphysical, reasons to conceive of natural languages as compositional systems of significative token-symbols. Next, the chapter discusses the peculiar Buridanian conception truth and validity, according to which validity must not be based on truth, and truth need not always follow upon correspondence. These results are presented as the consequences of Buridan’s pursuit of a consistently nominalist semantics for natural languages, able to handle the Liar Paradox and its kin involving reflective uses of language without the Tarskian distinction between object-language and meta-language, rejected for systematic reasons in the seventh chapter.Less
This chapter provides a comprehensive survey of Buridan’s conception of logical validity in a semantically closed token-based system, as he conceives of natural languages. The chapter argues first that Buridan has very good logical, as well as merely metaphysical, reasons to conceive of natural languages as compositional systems of significative token-symbols. Next, the chapter discusses the peculiar Buridanian conception truth and validity, according to which validity must not be based on truth, and truth need not always follow upon correspondence. These results are presented as the consequences of Buridan’s pursuit of a consistently nominalist semantics for natural languages, able to handle the Liar Paradox and its kin involving reflective uses of language without the Tarskian distinction between object-language and meta-language, rejected for systematic reasons in the seventh chapter.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0021
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter discusses and replies to a number of the more important objections that have been made to dialetheism since the publication of the first edition of the book. The topics covered include ...
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This chapter discusses and replies to a number of the more important objections that have been made to dialetheism since the publication of the first edition of the book. The topics covered include dialetheic logic, the Extended Liar Paradox, expressability, and motion.Less
This chapter discusses and replies to a number of the more important objections that have been made to dialetheism since the publication of the first edition of the book. The topics covered include dialetheic logic, the Extended Liar Paradox, expressability, and motion.
B. F. Taylor
- Published in print:
- 2006
- Published Online:
- July 2012
- ISBN:
- 9780719069086
- eISBN:
- 9781781701218
- Item type:
- book
- Publisher:
- Manchester University Press
- DOI:
- 10.7228/manchester/9780719069086.001.0001
- Subject:
- Film, Television and Radio, Film
This book offers an opportunity to reconsider the films of the British New Wave in the light of forty years of heated debate. By eschewing the usual tendency to view films such as A Kind of Loving ...
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This book offers an opportunity to reconsider the films of the British New Wave in the light of forty years of heated debate. By eschewing the usual tendency to view films such as A Kind of Loving and The Entertainer collectively and include them in broader debates about class, gender and ideology, it presents a new look at this famous cycle of British films. Refuting the long-standing view that films such as Billy Liar and Look Back in Anger are flawed and therefore indicative of an under-achieving national cinema, the book also challenges the widely held belief in the continued importance of the relationship between the British New Wave and questions of realism. Drawing upon existing sources and returning to unchallenged assumptions about British cinema, this book allows the reader to return to the films and consider them anew. In order to achieve this, the book also offers a practical demonstration of the activity of film interpretation. This is essential, because the usual tendency is to consider such a process unnecessary when it comes to writing about British films. The book demonstrates that close readings of films need not be reserved for films from other cinemas.Less
This book offers an opportunity to reconsider the films of the British New Wave in the light of forty years of heated debate. By eschewing the usual tendency to view films such as A Kind of Loving and The Entertainer collectively and include them in broader debates about class, gender and ideology, it presents a new look at this famous cycle of British films. Refuting the long-standing view that films such as Billy Liar and Look Back in Anger are flawed and therefore indicative of an under-achieving national cinema, the book also challenges the widely held belief in the continued importance of the relationship between the British New Wave and questions of realism. Drawing upon existing sources and returning to unchallenged assumptions about British cinema, this book allows the reader to return to the films and consider them anew. In order to achieve this, the book also offers a practical demonstration of the activity of film interpretation. This is essential, because the usual tendency is to consider such a process unnecessary when it comes to writing about British films. The book demonstrates that close readings of films need not be reserved for films from other cinemas.
Hartry Field
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199230747
- eISBN:
- 9780191710933
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230747.003.0017
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter looks at two ways of meeting the goal of naïvety. Yablo's is technically simpler, but involves extreme failures of intersubstitutivity of logical truths within conditionals. The ...
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This chapter looks at two ways of meeting the goal of naïvety. Yablo's is technically simpler, but involves extreme failures of intersubstitutivity of logical truths within conditionals. The alternative involves a revision-theoretic ideas, but applied to the conditional instead of the truth predicate, in combination with an iterated Kripke fixed point construction. A general non-triviality theorem is proved, and examples are given, especially to a ‘transfinite Liar hierarchy’.Less
This chapter looks at two ways of meeting the goal of naïvety. Yablo's is technically simpler, but involves extreme failures of intersubstitutivity of logical truths within conditionals. The alternative involves a revision-theoretic ideas, but applied to the conditional instead of the truth predicate, in combination with an iterated Kripke fixed point construction. A general non-triviality theorem is proved, and examples are given, especially to a ‘transfinite Liar hierarchy’.
Sten Lindström
- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780195367881
- eISBN:
- 9780199867585
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195367881.003.0007
- Subject:
- Philosophy, Philosophy of Language
This chapter discusses a paradox that, in Kaplan's view, threatens the use of possible worlds semantics as a model‐theoretic framework for intensional logic. Kaplan's paradox starts out from an ...
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This chapter discusses a paradox that, in Kaplan's view, threatens the use of possible worlds semantics as a model‐theoretic framework for intensional logic. Kaplan's paradox starts out from an intuitively reasonable principle referred to as the principle of plenitude. From this principle he derives a contradiction in what he calls naive possible world theory. Kaplan's metatheoretic argument can be restated in the modal object language as an intensional version of the Liar paradox.Less
This chapter discusses a paradox that, in Kaplan's view, threatens the use of possible worlds semantics as a model‐theoretic framework for intensional logic. Kaplan's paradox starts out from an intuitively reasonable principle referred to as the principle of plenitude. From this principle he derives a contradiction in what he calls naive possible world theory. Kaplan's metatheoretic argument can be restated in the modal object language as an intensional version of the Liar paradox.
Jeanne Pitre Soileau
- Published in print:
- 2021
- Published Online:
- May 2022
- ISBN:
- 9781496835734
- eISBN:
- 9781496835789
- Item type:
- chapter
- Publisher:
- University Press of Mississippi
- DOI:
- 10.14325/mississippi/9781496835734.003.0008
- Subject:
- Sociology, Culture
This chapter is very short because it seems that the children interviewed could not recall many teases and taunts. The author remembered many more. The quote by C. W. Sullivan III succinctly stated ...
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This chapter is very short because it seems that the children interviewed could not recall many teases and taunts. The author remembered many more. The quote by C. W. Sullivan III succinctly stated that teases and taunts are used by children to “enforce conformity.”Less
This chapter is very short because it seems that the children interviewed could not recall many teases and taunts. The author remembered many more. The quote by C. W. Sullivan III succinctly stated that teases and taunts are used by children to “enforce conformity.”
J. R. LUCAS
- Published in print:
- 1970
- Published Online:
- October 2011
- ISBN:
- 9780198243434
- eISBN:
- 9780191680687
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198243434.003.0024
- Subject:
- Philosophy, Metaphysics/Epistemology, Moral Philosophy
Gödel devised a method whereby the formulae of a given formal language could be put in a 1-1 correspondence with a subset of the natural numbers: that is to say, to every number there is correlated ...
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Gödel devised a method whereby the formulae of a given formal language could be put in a 1-1 correspondence with a subset of the natural numbers: that is to say, to every number there is correlated only one formula, and to every formula there is correlated one and only one number, which we call its Gödel number. In order to pursue the possibility of reproducing the Liar paradox within formal mathematics we need to follow up Gödel's scheme for correlating numbers and formulae with a method of making up properties of numbers and relations between numbers that will correspond to logically important properties of formulae and relations between formulae. But it turns out that this is not possible. Truth — and similarly falsity — are not representable in the logistic calculus L, though provability-in-the-logistic-calculus L — the next best thing — is. In Gödel's theorem, therefore, the Liar paradox is altered by substituting ‘unprovable-in-the-logistic-calculus-L’ for ‘untrue’.Less
Gödel devised a method whereby the formulae of a given formal language could be put in a 1-1 correspondence with a subset of the natural numbers: that is to say, to every number there is correlated only one formula, and to every formula there is correlated one and only one number, which we call its Gödel number. In order to pursue the possibility of reproducing the Liar paradox within formal mathematics we need to follow up Gödel's scheme for correlating numbers and formulae with a method of making up properties of numbers and relations between numbers that will correspond to logically important properties of formulae and relations between formulae. But it turns out that this is not possible. Truth — and similarly falsity — are not representable in the logistic calculus L, though provability-in-the-logistic-calculus L — the next best thing — is. In Gödel's theorem, therefore, the Liar paradox is altered by substituting ‘unprovable-in-the-logistic-calculus-L’ for ‘untrue’.
Scott Soames
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780195123357
- eISBN:
- 9780199872114
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195123352.003.0003
- Subject:
- Philosophy, Philosophy of Language
Five different forms of truth skepticism are examined and defused: the view that truth is indefinable, that it is unattainable and unknowable, that it is inextricably metaphysical and hence not ...
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Five different forms of truth skepticism are examined and defused: the view that truth is indefinable, that it is unattainable and unknowable, that it is inextricably metaphysical and hence not scientifically respectable, that there is no such thing as truth, and that truth is inherently paradoxical, and so must either be abandoned or revised. An intriguing formulation of the last of these views is owing to Alfred Tarski, who argued that the Liar paradox shows natural languages to be inconsistent because they contain defective, and ultimately incoherent truth predicates. Here, it is argued in response that on a plausible interpretation of his puzzling notion of an inconsistent language, Tarski's argument is, though logically valid, almost certainly unsound, since one of its premises is highly problematic. Similar results are achieved for other forms of truth skepticism.Less
Five different forms of truth skepticism are examined and defused: the view that truth is indefinable, that it is unattainable and unknowable, that it is inextricably metaphysical and hence not scientifically respectable, that there is no such thing as truth, and that truth is inherently paradoxical, and so must either be abandoned or revised. An intriguing formulation of the last of these views is owing to Alfred Tarski, who argued that the Liar paradox shows natural languages to be inconsistent because they contain defective, and ultimately incoherent truth predicates. Here, it is argued in response that on a plausible interpretation of his puzzling notion of an inconsistent language, Tarski's argument is, though logically valid, almost certainly unsound, since one of its premises is highly problematic. Similar results are achieved for other forms of truth skepticism.
Scott Soames
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780195123357
- eISBN:
- 9780199872114
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195123352.003.0006
- Subject:
- Philosophy, Philosophy of Language
In proving that the language of arithmetic does not contain its own truth predicate, Tarski demonstrated that the claim that a language both satisfies certain minimal conditions and contains its own ...
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In proving that the language of arithmetic does not contain its own truth predicate, Tarski demonstrated that the claim that a language both satisfies certain minimal conditions and contains its own truth predicate leads to a contradiction – a result that can seem puzzling in light of the fact that it seems obvious that English does satisfy the relevant conditions, while containing its own truth predicate (though of course this cannot be). Chapter 5 explores the well‐known response to this problem (a version of the Liar paradox), which maintains that English is really an infinite hierarchy of languages defined by a hierarchy of Tarski‐style truth predicates. The construction of the hierarchy is explained, and the ways in which it is used to block different versions of the paradox are illustrated. The discussion then turns to problems with the approach, the most serious being the irresistible urge to violate the hierarchy's restrictions on intelligibility in the very process of setting it up – something we tend to forget because we imagine ourselves taking a position outside the hierarchy from which it can be described. Once we realize that the hierarchy is supposed to apply to the language we are using to describe it, the paradox returns with a vengeance, threatening to destroy the very construction that was introduced to avoid it.Less
In proving that the language of arithmetic does not contain its own truth predicate, Tarski demonstrated that the claim that a language both satisfies certain minimal conditions and contains its own truth predicate leads to a contradiction – a result that can seem puzzling in light of the fact that it seems obvious that English does satisfy the relevant conditions, while containing its own truth predicate (though of course this cannot be). Chapter 5 explores the well‐known response to this problem (a version of the Liar paradox), which maintains that English is really an infinite hierarchy of languages defined by a hierarchy of Tarski‐style truth predicates. The construction of the hierarchy is explained, and the ways in which it is used to block different versions of the paradox are illustrated. The discussion then turns to problems with the approach, the most serious being the irresistible urge to violate the hierarchy's restrictions on intelligibility in the very process of setting it up – something we tend to forget because we imagine ourselves taking a position outside the hierarchy from which it can be described. Once we realize that the hierarchy is supposed to apply to the language we are using to describe it, the paradox returns with a vengeance, threatening to destroy the very construction that was introduced to avoid it.
Scott Soames
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780195123357
- eISBN:
- 9780199872114
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195123352.003.0007
- Subject:
- Philosophy, Philosophy of Language
Presents a philosophical model of partially defined predicates, illustrates how a language could come to contain them, and provides a natural way of understanding the truth predicate in which it ...
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Presents a philosophical model of partially defined predicates, illustrates how a language could come to contain them, and provides a natural way of understanding the truth predicate in which it conforms to this model. On this view, there are sentences, including Liar sentences like this sentence is not true and “Truth Tellers” like This sentence is true, about which the rules determining whether or not a sentence is true provide no result (either to the effect that it is true, or to the effect that it is not true) – thereby blocking the usual derivation of the paradox. However, despite these promising results, it is shown that a general solution to the Liar paradox is not forthcoming, since the very activity of solving the paradox in a particular limited case provides material for recreating it in a new and strengthened form. In the second half of the chapter, it is argued that this philosophical model provides the best way of understanding Saul Kripke's formal theory of truth (despite certain uncharacteristically misleading remarks of his to the contrary). In addition to laying out the philosophical basis for Kripke's theory of truth, explanations are given of his basic technical apparatus and formal results – including fixed points, minimal fixed points, monotonicity, intrinsic fixed points, ungrounded sentences, and paradoxical sentences.Less
Presents a philosophical model of partially defined predicates, illustrates how a language could come to contain them, and provides a natural way of understanding the truth predicate in which it conforms to this model. On this view, there are sentences, including Liar sentences like this sentence is not true and “Truth Tellers” like This sentence is true, about which the rules determining whether or not a sentence is true provide no result (either to the effect that it is true, or to the effect that it is not true) – thereby blocking the usual derivation of the paradox. However, despite these promising results, it is shown that a general solution to the Liar paradox is not forthcoming, since the very activity of solving the paradox in a particular limited case provides material for recreating it in a new and strengthened form. In the second half of the chapter, it is argued that this philosophical model provides the best way of understanding Saul Kripke's formal theory of truth (despite certain uncharacteristically misleading remarks of his to the contrary). In addition to laying out the philosophical basis for Kripke's theory of truth, explanations are given of his basic technical apparatus and formal results – including fixed points, minimal fixed points, monotonicity, intrinsic fixed points, ungrounded sentences, and paradoxical sentences.
Tim Maudlin
- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199247295
- eISBN:
- 9780191601781
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199247293.003.0001
- Subject:
- Philosophy, Philosophy of Language
Reviews the standard semantic paradoxes, and constructs a simple formal language in which the paradoxical reasoning can be reconstructed. Particular attention is paid to Löb's paradox, which allows ...
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Reviews the standard semantic paradoxes, and constructs a simple formal language in which the paradoxical reasoning can be reconstructed. Particular attention is paid to Löb's paradox, which allows for the derivation of any sentence in the language as a theorem. The advantages of a natural deduction system over an axiomatic logic is discussed.Less
Reviews the standard semantic paradoxes, and constructs a simple formal language in which the paradoxical reasoning can be reconstructed. Particular attention is paid to Löb's paradox, which allows for the derivation of any sentence in the language as a theorem. The advantages of a natural deduction system over an axiomatic logic is discussed.
William G. Lycan
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199697519
- eISBN:
- 9780191742316
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199697519.003.0006
- Subject:
- Philosophy, Philosophy of Language, Philosophy of Mind
In “Truth and Meaning”, Davidson acknowledged that the Liar Paradox is a problem for his semantic program; but he did not seem to take it very seriously. This chapter joins Lepore and Ludwig in ...
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In “Truth and Meaning”, Davidson acknowledged that the Liar Paradox is a problem for his semantic program; but he did not seem to take it very seriously. This chapter joins Lepore and Ludwig in deploring that. They offer Davidson a way out, in a quite different way, by suggesting a “solution” to the Liar Paradox that is adequate to the facts of natural language, that is fairly simple, and that will make linguistic semantics safe from Tarski's famous argument, in the sense that it will keep truth definitions for particular natural languages from blowing up. (It is a linguist’s solution, not a logician’s. Nor is it intended to reveal anything conceptually deep.) The preferred approach is hierarchical, in the spirit of Tarski’s treatment of formal languages, but is shown to resist the usual objections to hierarchical approaches. Contra Tarski, there is a good and clear, if somewhat grotesque, sense in which a natural language can contain its own truth predicate without paradox.Less
In “Truth and Meaning”, Davidson acknowledged that the Liar Paradox is a problem for his semantic program; but he did not seem to take it very seriously. This chapter joins Lepore and Ludwig in deploring that. They offer Davidson a way out, in a quite different way, by suggesting a “solution” to the Liar Paradox that is adequate to the facts of natural language, that is fairly simple, and that will make linguistic semantics safe from Tarski's famous argument, in the sense that it will keep truth definitions for particular natural languages from blowing up. (It is a linguist’s solution, not a logician’s. Nor is it intended to reveal anything conceptually deep.) The preferred approach is hierarchical, in the spirit of Tarski’s treatment of formal languages, but is shown to resist the usual objections to hierarchical approaches. Contra Tarski, there is a good and clear, if somewhat grotesque, sense in which a natural language can contain its own truth predicate without paradox.
John C. Waldmeir
- Published in print:
- 2009
- Published Online:
- March 2011
- ISBN:
- 9780823230600
- eISBN:
- 9780823236923
- Item type:
- chapter
- Publisher:
- Fordham University Press
- DOI:
- 10.5422/fso/9780823230600.003.0006
- Subject:
- Religion, Religion and Literature
This chapter examines the presentation of clergy sexual abuse and its consequences in literature. In Robert Cooperman's collection of poems titled The Trials of Mary McCormick, he tries to dramatize ...
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This chapter examines the presentation of clergy sexual abuse and its consequences in literature. In Robert Cooperman's collection of poems titled The Trials of Mary McCormick, he tries to dramatize how the actions of individual abusers and victims occur in institutional frameworks. In Doubt: A Parable, playwright John Patrick Shanley raises the issue of doubt in Sister Aloysius's suspicion that Father Flynn is sexually abusing Mrs. Muller's teenage son. In Mary Karr' 1995 novel The Liar's Club, she relates her experience in being sexually abused as a child by figures she understood to be in positions of authority.Less
This chapter examines the presentation of clergy sexual abuse and its consequences in literature. In Robert Cooperman's collection of poems titled The Trials of Mary McCormick, he tries to dramatize how the actions of individual abusers and victims occur in institutional frameworks. In Doubt: A Parable, playwright John Patrick Shanley raises the issue of doubt in Sister Aloysius's suspicion that Father Flynn is sexually abusing Mrs. Muller's teenage son. In Mary Karr' 1995 novel The Liar's Club, she relates her experience in being sexually abused as a child by figures she understood to be in positions of authority.
B. F. Taylor
- Published in print:
- 2006
- Published Online:
- July 2012
- ISBN:
- 9780719069086
- eISBN:
- 9781781701218
- Item type:
- chapter
- Publisher:
- Manchester University Press
- DOI:
- 10.7228/manchester/9780719069086.003.0020
- Subject:
- Film, Television and Radio, Film
This chapter provides a detailed reading of John Schlesinger's 1963 film Billy Liar. It aims to demonstrate that a British film such as this sustains the kind of detailed aesthetic discussion that is ...
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This chapter provides a detailed reading of John Schlesinger's 1963 film Billy Liar. It aims to demonstrate that a British film such as this sustains the kind of detailed aesthetic discussion that is usually reserved for films from other modes of cinema. Towards the end of Billy Liar, Billy Fisher, the liar of the title, having previously arranged to go to London with his friend Liz, is faced with the possibility that he might finally have to go. The time for talking has now finished and Billy needs to act but it becomes increasingly clear that he cannot go through with his plan. The spaces and places of Billy Liar are vital and a fully integrated component in this film's specific examination of the sometimes contradictory and often problematic relationship between one man and the world in which he lives.Less
This chapter provides a detailed reading of John Schlesinger's 1963 film Billy Liar. It aims to demonstrate that a British film such as this sustains the kind of detailed aesthetic discussion that is usually reserved for films from other modes of cinema. Towards the end of Billy Liar, Billy Fisher, the liar of the title, having previously arranged to go to London with his friend Liz, is faced with the possibility that he might finally have to go. The time for talking has now finished and Billy needs to act but it becomes increasingly clear that he cannot go through with his plan. The spaces and places of Billy Liar are vital and a fully integrated component in this film's specific examination of the sometimes contradictory and often problematic relationship between one man and the world in which he lives.
Keith Simmons
- Published in print:
- 2018
- Published Online:
- July 2018
- ISBN:
- 9780198791546
- eISBN:
- 9780191852923
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198791546.001.0001
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by the concepts of reference or denotation, predicate extension, and truth. ...
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This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by the concepts of reference or denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions ‘denotes’, ‘extension’, and ‘true’ are context-sensitive. The second, inspired by a brief, tantalizing remark of Gödel’s, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities is presented and applied to a wide variety of versions of the definability paradoxes, Russell’s paradox, and the Liar paradox. The book argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski’s intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. The book examines the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism.Less
This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by the concepts of reference or denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions ‘denotes’, ‘extension’, and ‘true’ are context-sensitive. The second, inspired by a brief, tantalizing remark of Gödel’s, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities is presented and applied to a wide variety of versions of the definability paradoxes, Russell’s paradox, and the Liar paradox. The book argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski’s intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. The book examines the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism.
Mark Jago
- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780198823810
- eISBN:
- 9780191862595
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198823810.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language
What Truth Is presents and defends a novel theory of what truth is, in terms of the metaphysical notion of truthmaking. This is the relation which holds between a truth and some entity in the world, ...
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What Truth Is presents and defends a novel theory of what truth is, in terms of the metaphysical notion of truthmaking. This is the relation which holds between a truth and some entity in the world, in virtue of which that truth is true. By coming to an understanding of this relation, I argue, we gain better insight into the metaphysics of truth. The first part of the book discusses the property being true, and how we should understand it in terms of truthmaking. The second part focuses on truthmakers, the worldly entities which make various kinds of truths true, and how they do so. I argue for a metaphysics of states of affairs, which account for things having properties and standing in relations. The third part analyses the logic and metaphysics of the truthmaking relation itself, and links it to the metaphysical concept of grounding. The final part discusses consequences of the theory for language and logic. I show how the theory delivers a novel and useful theory of propositions, the entities which are true or false, depending on how things are. One feature of this approach is that it avoids the Liar paradox and other puzzling paradoxes of truth.Less
What Truth Is presents and defends a novel theory of what truth is, in terms of the metaphysical notion of truthmaking. This is the relation which holds between a truth and some entity in the world, in virtue of which that truth is true. By coming to an understanding of this relation, I argue, we gain better insight into the metaphysics of truth. The first part of the book discusses the property being true, and how we should understand it in terms of truthmaking. The second part focuses on truthmakers, the worldly entities which make various kinds of truths true, and how they do so. I argue for a metaphysics of states of affairs, which account for things having properties and standing in relations. The third part analyses the logic and metaphysics of the truthmaking relation itself, and links it to the metaphysical concept of grounding. The final part discusses consequences of the theory for language and logic. I show how the theory delivers a novel and useful theory of propositions, the entities which are true or false, depending on how things are. One feature of this approach is that it avoids the Liar paradox and other puzzling paradoxes of truth.
