Vagueness, inexactness, and imprecision

Abstract
THERE IS OFTEN UNCERTAINTY ABOUT WHETHER SOME PREDICATE APPLIES TO SOME PHYSICAL OBJECT OR STATE. THIS UNCERTAINTY MAY HAVE ANY OF THREE SOURCES - VAGUENESS OF A TERM, INEXACTNESS OF A CONCEPT, OR PRACTICAL DIFFICULTY IN DETERMINING ITS APPLICABILITY. VARIOUS WAYS IN WHICH CONCEPTUAL INEXACTNESS OR PRACTICAL DIFFICULTY MAY PRODUCE UNCERTAINTY ARE DISTINGUISHED. NEITHER TERMINOLOGICAL VAGUENESS, NOR PRACTICAL DIFFICULTY IN DETERMINING THE APPLICABILITY OF A CONCEPT ARE NECESSARY FEATURES OF EVERY LANGUAGE IN EVERY PHYSICAL WORLD, BUT CONCEPTUAL INEXACTNESS IS A NECESSARY FEATURE OF EMPIRICAL CONCEPTS. THESE RESULTS ARE UTILIZED TO DETERMINE THE SOURCES AND NECESSITY OF IMPRECISION IN MEASUREMENT
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