Truth values, neither-true-nor-false, and supervaluations

Studia Logica 91 (3):305 - 334 (2009)
Abstract
The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds of sentences. In many cases, this facility is said to produce truth values for sentences that on the face of it seem neither true nor false. Often enough, in this situation appeal is made to the method of supervaluations, which operate by “quantifying out” auxiliary parameters, and thereby produce something like a truth value. Logics of this kind exhibit striking differences. I first consider the role that Tarski gives to supervaluation in first order logic (§2.2), and then, after an interlude that asks whether neither-true-nor-false is itself a truth value (§2.3), I consider sentences with non-denoting terms (§2.4), vague sentences (§2.5), ambiguous sentences (§2.6), paradoxical sentences (§2.7), and future-tensed sentences in indeterministic tense logic (§2.8). I conclude my survey with a look at alethic modal logic considered as a cousin (§2.9), and finish with a few sentences of “advice to supervaluationists” (2.10), advice that is largely negative. The case for supervaluations as a road to truth is strong only when the auxiliary parameter that is “quantified out” is in fact irrelevant to the sentences of interest—as in Tarski’s definition of truth for classical logic. In all other cases, the best policy when reporting the results of supervaluation is to use only explicit phrases such as “settled true” or “determinately true,” never dropping the qualification
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
Categories (categorize this paper)
DOI 10.1007/s11225-009-9177-2
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,167
Through your library
References found in this work BETA
Future Contingents and Relative Truth.John MacFarlane - 2003 - Philosophical Quarterly 53 (212):321–336.
Outline of a Theory of Truth.Saul A. Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Vagueness, Truth and Logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.

View all 19 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Relative Truth and the First Person.Friederike Moltmann - 2010 - Philosophical Studies 150 (2):187-220..
Fuzzy Logic and Approximate Reasoning.L. A. Zadeh - 1975 - Synthese 30 (3-4):407-428.
Propositional Logic.Kevin C. Klement - 2004 - Internet Encyclopedia of Philosophy.
Circularity or Lacunae in Tarski's Truth-Schemata.Dale Jacquette - 2010 - Journal of Logic, Language and Information 19 (3):315-326.
Truthmaker Gaps and the No-No Paradox.Patrick Greenough - 2011 - Philosophy and Phenomenological Research 82 (3):547 - 563.

Monthly downloads

Added to index

2009-04-04

Total downloads

88 ( #57,222 of 2,153,332 )

Recent downloads (6 months)

2 ( #281,037 of 2,153,332 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums