Measuring and Modeling Truth
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Philosophers, linguists and others interested in problems
concerning natural language frequently employ tools from
logic and model theory. The question arises as to the
proper interpretation of the formal methods employed -- of
the relationship between, on the one hand, the formal
languages and their set-theoretic models and, on the other
hand, the objects of ultimate interest: natural language and
the meanings and truth conditions of its constituent words,
phrases and sentences. Two familiar answers to this
question are descriptivism and instrumentalism. More
recently, a third answer has been proposed: the
logic-as-modeling view. This paper seeks to clarify and
assess this view of logic. The conclusion is that we can
successfully adopt the modeling perspective on a given piece
of logical machinery only if we have to hand some other
machinery to which we take the descriptive attitude. Thus,
logic-as-modeling is not a full-fledged alternative to the
descriptive view -- for it cannot stand alone: it can at
best be an addition to the descriptive perspective. The
paper first presents the argument in a general, abstract
form, before working through a detailed case study. The
case examined is the one with respect to which the
logic-as-modeling view has been developed in the greatest
detail in the literature: the case of fuzzy model theory as
an account of vagueness in natural language.