Oxford, England: Oxford University Press (
2008)
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Abstract
In VAGUENESS AND DEGREES OF TRUTH, Nicholas Smith develops a
new theory of vagueness: fuzzy plurivaluationism.
A predicate is said to be VAGUE if there is no sharply
defined boundary between the things to which it applies and
the things to which it does not apply. For example, 'heavy'
is vague in a way that 'weighs over 20 kilograms' is not. A
great many predicates -- both in everyday talk, and in a
wide array of theoretical vocabularies, from law to
psychology to engineering -- are vague.
Smith argues, based on a detailed account of the defining
features of vagueness, that an accurate theory of vagueness
must involve the idea that truth comes in degrees. The core
idea of degrees of truth is that while some sentences are
true and some are false, others possess intermediate truth
values: they are truer than the false sentences, but not as
true as the true ones. Degree-theoretic treatments of
vagueness have been proposed in the past, but all have
encountered significant objections. In light of these,
Smith develops a new type of degree theory. Its innovations
include a definition of logical consequence that allows the
derivation of a classical consequence relation from the
degree-theoretic semantics, a unified account of degrees of
belief and their relationships with degrees of truth and
subjective probabilities, and the incorporation of semantic
indeterminacy -- the view that vague statements need not
have unique meanings -- into the degree-theoretic framework.
As well as being essential reading for those working on
vagueness, Smith's book provides an excellent entry-point
for newcomers to the area -- both from elsewhere in
philosophy, and from computer science, logic and
engineering. It contains a thorough introduction to
existing theories of vagueness and to the requisite logical
background.