Scott Soames
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780195123357
- eISBN:
- 9780199872114
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195123352.003.0008
- Subject:
- Philosophy, Philosophy of Language
Presents a theory of partially defined, context sensitive, vague predicates, each of which is associated with a default determinate‐extension – i.e., a set of things to which the rules of the ...
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Presents a theory of partially defined, context sensitive, vague predicates, each of which is associated with a default determinate‐extension – i.e., a set of things to which the rules of the language determine that it applies – and a default determinate‐antiextension – a set of things to which the rules of the language determine that it does not apply. Since these sets do not exhaust all cases, speakers have the discretion of adjusting the extension and antiextension of such a predicate F so as to include initially undefined cases – often by explicitly characterizing an object o for which F is initially undefined as being F, or as being not F. When a speaker does this, the extension (or antiextension) of F is adjusted so as to include o plus all objects indistinguishable, or virtually indistinguishable from o. This analysis is used to illuminate and defuse the Sorites paradox, the main lesson of which is taken to be that the boundary lines fixing the extensions and antiextensions of many vague predicates are inherently unstable. Although this is not a practical problem for speakers in ordinary situations, and although it does not represent any theoretical incoherence in the meanings of vague predicates, it does explain the discomfort typically generated by standard versions of the Sorites paradox.Less
Presents a theory of partially defined, context sensitive, vague predicates, each of which is associated with a default determinate‐extension – i.e., a set of things to which the rules of the language determine that it applies – and a default determinate‐antiextension – a set of things to which the rules of the language determine that it does not apply. Since these sets do not exhaust all cases, speakers have the discretion of adjusting the extension and antiextension of such a predicate F so as to include initially undefined cases – often by explicitly characterizing an object o for which F is initially undefined as being F, or as being not F. When a speaker does this, the extension (or antiextension) of F is adjusted so as to include o plus all objects indistinguishable, or virtually indistinguishable from o. This analysis is used to illuminate and defuse the Sorites paradox, the main lesson of which is taken to be that the boundary lines fixing the extensions and antiextensions of many vague predicates are inherently unstable. Although this is not a practical problem for speakers in ordinary situations, and although it does not represent any theoretical incoherence in the meanings of vague predicates, it does explain the discomfort typically generated by standard versions of the Sorites paradox.
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.
Ian Rumfitt
- Published in print:
- 2015
- Published Online:
- June 2015
- ISBN:
- 9780198733638
- eISBN:
- 9780191798016
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198733638.003.0008
- Subject:
- Philosophy, Philosophy of Mind
Vague terms have for centuries presented a challenge to classical logic: in paradoxes like the Sorites, the application of classical laws takes us from true premisses to apparently absurd ...
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Vague terms have for centuries presented a challenge to classical logic: in paradoxes like the Sorites, the application of classical laws takes us from true premisses to apparently absurd conclusions. This chapter focuses on Crispin Wright’s ‘Paradox of no sharp boundaries’, which presents the difficulty acutely. Wright recommends using intuitionistic logic when reasoning with vague terms, but provides no semantics to justify that choice. The chapter proposes a semantic theory for a large class of vague predicates, so-called ‘polar’ predicates, whose extensions are defined by reference to paradigms or poles. It is argued that the extensions of such predicates are regular open sets in a suitable topology, and that the use of classical logic when reasoning with them is sustained. The paradoxes are resolved, though, because under the recommended semantics their apparently absurd conclusions are acceptable.Less
Vague terms have for centuries presented a challenge to classical logic: in paradoxes like the Sorites, the application of classical laws takes us from true premisses to apparently absurd conclusions. This chapter focuses on Crispin Wright’s ‘Paradox of no sharp boundaries’, which presents the difficulty acutely. Wright recommends using intuitionistic logic when reasoning with vague terms, but provides no semantics to justify that choice. The chapter proposes a semantic theory for a large class of vague predicates, so-called ‘polar’ predicates, whose extensions are defined by reference to paradigms or poles. It is argued that the extensions of such predicates are regular open sets in a suitable topology, and that the use of classical logic when reasoning with them is sustained. The paradoxes are resolved, though, because under the recommended semantics their apparently absurd conclusions are acceptable.
