Tolerant, Classical, Strict
By Pablo Cobreros, Paul Égré, David Ripley, Robert van Rooij. Journal of Philosophical Logic, 2010
336 citations recorded by the source corpus.
In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.
Subfields: Artificial Intelligence, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/19a09e6281ce947fd0a4407b29115d12f08604eb
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Citations in the corpus
- On measurement and quantification: The case of most and more than half (2016, background): “9In a related approach, van Rooij (2011a) and Cobreros et al. (2012) develop a logical system based on the notion of tolerance which they apply to the analysis of vague predicates such as tall; see also Burnett (2012) for a further extension.”
- Paraconsistent Logic (2015, background): “For further discussion that shows in more detail how paraconsistent logics of various stripes can be useful here, see [1, 12, 38, 51].”