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Stewart Shapiro 《Studia Logica》2008,90(3):313-336
It is a commonplace that the extensions of most, perhaps all, vague predicates vary with such features as comparison class
and paradigm and contrasting cases. My view proposes another, more pervasive contextual parameter. Vague predicates exhibit
what I call open texture: in some circumstances, competent speakers can go either way in the borderline region. The shifting
extension and anti-extensions of vague predicates are tracked by what David Lewis calls the “conversational score”, and are
regulated by what Kit Fine calls penumbral connections, including a principle of tolerance. As I see it, vague predicates
are response-dependent, or, better, judgement-dependent, at least in their borderline regions. This raises questions concerning
how one reasons with such predicates.
In this paper, I present a model theory for vague predicates, so construed. It is based on an overall supervaluationist-style
framework, and it invokes analogues of Kripke structures for intuitionistic logic. I argue that the system captures, or at
least nicely models, how one ought to reason with the shifting extensions (and anti-extensions) of vague predicates, as borderline
cases are called and retracted in the course of a conversation. The model theory is illustrated with a forced march sorites
series, and also with a thought experiment in which vague predicates interact with so-called future contingents. I show how
to define various connectives and quantifiers in the language of the system, and how to express various penumbral connections
and the principle of tolerance. The project fits into one of the topics of this special issue. In the course of reasoning,
even with the external context held fixed, it is uncertain what the future extension of the vague predicates will be. Yet
we still manage to reason with them. The system is based on that developed, more fully, in my Vagueness in Context, Oxford, Oxford University Press, 2006, but some criticisms and replies to critics are incorporated. 相似文献
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Greg Frost-Arnold 《Journal of Philosophical Logic》2008,37(3):239-257
The logic of singular terms that refer to nothing, such as ‘Santa Claus,’ has been studied extensively under the heading of
free logic. The present essay examines expressions whose reference is defective in a different way: they signify more than one entity. The bulk of the effort aims to develop an acceptable formal semantics based upon an intuitive idea introduced informally
by Hartry Field and discussed by Joseph Camp; the basic strategy is to use supervaluations. This idea, as it stands, encounters
difficulties, but with suitable refinements it can be salvaged. Two other options for a formal semantics of multiply signifying
terms are also presented, and I discuss the relative merits of the three semantics briefly. Finally, possible modifications
to the standard logical regimentation of the notion of existence are considered. 相似文献
3.
We give a survey on truth theories for applicative theories. It comprises Frege structures, universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation. 相似文献
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