Contradictions at the Borders

Ripley, David

doi:10.1007/978-3-642-18446-8_10

Cited by 46 publications

(46 citation statements)

References 19 publications

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“…In this our treatment of assertion agrees with the pragmatic account of vague predicates recently proposed by Alxatib and Pelletier in [1]. In the second part of this section, we relate our framework to the experimental data they obtained, as well as to the earlier findings reported by Ripley in [23] and by Serchuk, Hargreaves and Zach in [25].…”

Section: The Pragmatics Of Vague Predicatessupporting

confidence: 84%

“…To substantiate our discussion, we confront our treatment of penumbral connections with some recent psycholinguistic data on the semantic treatment of vague predicates established independently by [1,23] and [25]. Overall, the data suggest that subjects do not preserve classical logical truths for borderline cases.…”

Section: Psycholinguistic Evidencementioning

confidence: 85%

“…Prima facie, these data are therefore consistent with the view that sentences of the form Pa ∧ ¬Pa can be used tolerantly for borderline cases. Moreover, they indicate that the predictions of either subvaluationism or supervaluationism for borderline cases are not empirically adequate (see [1,23] for discussions).…”

Section: Contradictions and Borderline Casesmentioning

confidence: 99%

“…In Section 3, we enlarge the space of consequence relations and discuss various notions of mixed consequence, in particular van Rooij's consequence from classical to tolerant truth and its kin, and discuss the application of this framework to the sorites paradox. In Section 4, finally, we close this paper with the discussion of some applications of the semantics to the pragmatics and psycholinguistics of vague predicates, in relation to recent experiments by Alxatib and Pelletier [1], Ripley [23] and Serchuk, Hargreaves and Zach [25]. The focus of that section concerns the predictions of tolerant and strict semantics for borderline cases, and in particular the choice between tolerant and strict interpretations for vague predicates.…”

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confidence: 96%

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Tolerant, Classical, Strict

et al. 2010

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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.

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Section: The Pragmatics Of Vague Predicatessupporting

confidence: 84%

Section: Psycholinguistic Evidencementioning

confidence: 85%

Section: Contradictions and Borderline Casesmentioning

confidence: 99%

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confidence: 96%

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Tolerant, Classical, Strict

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“…There have been only a few examples of such studies reported in the literature and broadly speaking the results are mixed (see [28] for an overview). However, in one such study Ripley [24] finds that there is evidence that people are willing to accept contradictions in borderline cases. We will return to the issue of penumbral connection in the discussion in section 8.…”

Section: Axioms For Three Valued Valuationsmentioning

confidence: 99%

Borderlines and probabilities of borderlines: On the interconnection between vagueness and uncertainty

Lawry

2016

Journal of Applied Logic

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We describe an integrated approach to vagueness and uncertainty within a propositional logic setting and based on a combination of three valued logic and probability. Three valued valuations are employed in order to model explicitly borderline cases and in this context we give an axiomatic characterisation of two well known three valued models; supervaluations and Kleene valuations. We then demonstrate the close relationship between Kleene valuations and a sub-class of supervaluations. Belief pairs are lower and upper measures on the sentences of the language generated from a probability distribution defined over a finite set of three valued valuations. We describe links between these measures and other uncertainty theories and we show the close relationship between Kleene belief pairs and a sub-class of supervaluation belief pairs. Finally, a probabilistic approach to conditioning is explored within this framework.

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Experimental Philosophical Logic

Ripley

2016

A Companion to Experimental Philosophy

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The purpose of this chapter is to explore the intersection of experimental philosophy and philosophical logic, an intersection I'll call experimental philosophical logic. In particular, I'll be looldng for and sketching some ways in which experimental results, and empirical results more broadly, can inform and have informed debates within philosophical logic. Here's the plan: first, I'll lay out a way of looking at the situation that makes plain at least one way in which we should expect experimental and logical concerns to overlap. Then, I'll turn to the phenomenon of vagueness, where we can see this overlap explored and developed from multiple angles, showing just how intimately related experiment and logic can be. Finally, I'll canvass some other cases where we have similar reasons to expect productive interactions between experimental methods and formal logic, and point to some examples of productive work in those areas. 3 6 .1 Logic, Pure and AppliedLet's open by briefly considering a distinction between pure and applied logic. This distinction is analogous to the one between pure and applied algebra, or between pure and applied topology, or between pure and applied versions of any branch of mathematics. (I don't pretend that any of these distinctions is precise, or that there are no problem cases; the gist is all that matters.) Roughly, pure logic is an exploration of the properties and relations occupied by logical sys-• terns in themselves, without attending to any particular use they may or may not have. Typical questions within pure logic: is proof system X sound and complete for model theory Y?; is suchand-such a logical system decidable? compact? finitely axiomatizable?; is this rule admissible in that system?; and so on. Pure logic is most naturally thought of as a subfield of mathematics, although it is of course also pursued by researchers in philosophy, linguistics, computer science, electrical engineering, and so on, in pursuit of our own varied research interests.

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Contradictions at the Borders

Cited by 46 publications

References 19 publications

Tolerant, Classical, Strict

Tolerant, Classical, Strict

Borderlines and probabilities of borderlines: On the interconnection between vagueness and uncertainty

Experimental Philosophical Logic

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