Vagueness and Degrees of Truth

Smith, Nicholas J. J.

doi:10.1093/acprof:oso/9780199233007.001.0001

Cited by 178 publications

(27 citation statements)

References 131 publications

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“…First, it implies that two individuals are P -similar on that view provided the application of the predicate P yields truth values that are sufficiently close. This interpretation of P -similarity in terms of closeness in truth values is faithful to what Smith calls the closeness principle, according to which, if two individuals a and b are sufficiently similar in P -relevant respects, then the degrees of truth of the corresponding sentences P a and P b should not be too far apart [Smith, 2008]. Secondly, the relation of similarity is, for each predicate, reflexive and symmetric, but it need not be transitive.…”

Section: Stvpmentioning

confidence: 62%

“…Some may find more appeal in the distinction between strict truth and tolerant truth as two levels of truth proper. [Smith, 2008] for example defends a notion of permissive consequence for fuzzy logic in writing (pg. 223):…”

Section: What Do 'Strict' and 'Tolerant' Mean?mentioning

confidence: 99%

“…Our goal in this paper is to show the interest of such a notion of permissive consequence, whereby consequence is no longer defined as the preservation of some designated truth-value (or set thereof) from premises to conclusion, but rather, as the enlargement of the set of designated truth-values, or as a weakening of standards when going from premises to conclusion (see, in order of appearance, [Nait-Abdallah, 1995], [Bennett, 1998], [Frankowski, 2004], [Zardini, 2008], [Smith, 2008], , [Cobreros et al, 2012b]). More specifically, we intend to show the fruitfulness of this notion for the prospect of getting a unified treatment of the paradoxes of vagueness and of the paradoxes of self-referential truth.…”

Section: Introductionmentioning

confidence: 99%

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Vagueness, Truth and Permissive Consequence

Cobreros

Égré

Ripley

et al. 2015

Unifying the Philosophy of Truth

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We say that a sentence A is a permissive consequence of a set of premises Γ whenever, if all the premises of Γ hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisit of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference.

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Section: Stvpmentioning

confidence: 62%

Section: What Do 'Strict' and 'Tolerant' Mean?mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vagueness, Truth and Permissive Consequence

Cobreros

Égré

Ripley

et al. 2015

Unifying the Philosophy of Truth

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“…In particular, the epistemic theory would seem to assume the existence of some objectively correct boundary threshold between, for example, short and not short. This assumption lies at the heart of one of the main criticisms of epistemicism in the literature, that it does not provide a satisfactory account of the relationship between the semantics and the use of language (Keefe and Smith 2002;Smith 2008). That is, it seems clear that the meaning of vague concepts are in large part determined by their use over time by a diverse population of communicators.…”

Section: The Uncertain Threshold Model Of Vaguenessmentioning

confidence: 99%

“…Now clearly this model can also act as a source of stochasticity if, for example, when deciding whether or not to describe the robber as short, each witness picks a precisification at random according to the probability weighting and then checks if the robber's height is contained in the particular extension of short that they have chosen. Finally, a general degree-based view of vagueness defines the membership of the extension of a predicate as a function into [0, 1], but where there is no probabilistic interpretation of this membership function (Smith 2008). Even for this nonprobabilistic model, stochastic channels can still be relevant provided that assertion decisions are made by employing a threshold on membership functions.…”

Section: The Uncertain Threshold Model Of Vaguenessmentioning

confidence: 99%

Vagueness and Aggregation in Multiple Sender Channels

Lawry

James

2017

Erkenn

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Vagueness is an extremely common feature of natural language, but does it actually play a positive, efficiency enhancing, role in communication? Adopting a probabilistic interpretation of vague terms, we propose that vagueness might act as a source of randomness when deciding what to assert. In this context we investigate the efficacy of multiple sender channels in which senders choose assertions stochastically according to vague definitions of the relevant words, and a receiver then aggregates the different signals. These vague channels are then compared with Boolean channels in which assertions are selected deterministically based on classical (crisp) definitions. We show that given a sufficient number of senders, a linear stochastic channel outperforms Boolean channels when performance is measured by the expected squared error between the actual value described by the senders and the receiver's estimate of it based on the signals they receive. The number of senders required for vague channels to be at least as accurate as Boolean channels is shown to be a decreasing function of the size of the language i.e. the number of description labels available to the senders. Vague channels are then shown to be robust to transmission error provided the error rate is not too large. In addition, we investigate the behaviour of both Boolean and vague channels for a parametrised family of distributions on the input values. Finally, we consider optimal vague channels assuming a fixed number of senders and show that, provided there are more than two senders, a vague channel can be found that outperforms the optimal Boolean channel. In this context, we show that for channels with relatively low numbers of senders S-curve production functions are optimal.

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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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Vagueness and Degrees of Truth

Cited by 178 publications

References 131 publications

Vagueness, Truth and Permissive Consequence

Vagueness, Truth and Permissive Consequence

Vagueness and Aggregation in Multiple Sender Channels

Experimental Philosophical Logic

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