The logic of inexact concepts

The 'hard' sciences, such as physics and chemistry, construct exact mathematical models of empirical phenomena, and then use these models to make predictions. Certain aspects of reality always escape such models, and we look hopefully to future refinements. But sometimes there is an elusive fuzziness, a readjustment to context, or an effect of observer upon observed. These phenomena are particularly indigenous to natural language, and are common in the 'soft' sciences, such as biology and psychology. This paper examines problems of f i t zz iness , i.e., vagueness, ambiguity, and ambivalence. Although the theory is called a 'logic of inexact concepts', we do not endorse belief in some Platonic ideal 'concepts' or logic embodying their essence. Rather we suggest a method for constructing and studying models of the way we use words; and we use the word 'concept' metaphorically in discussing meaning. 'Exact concepts' are the sort envisaged in pure mathematics, while 'inexact concepts' are rampant in everyday life. This distinction is complicated by the fact that whenever a human being interacts with mathematics, it becomes part of his ordinary experience, and therefore subject to inexactness. Ordinary logic is much used in mathematics, but applications to everyday life have been criticized because our normal language habits seem so different. Various modifications of orthodox logic have been suggested as remedies, particularly omission of the Law of the Excluded Middle. Ordinary logic represents exact concepts syntactically: that is a concept is given a name (such as 'man') which becomes an object for manipulation in a formal language. Aristotelian logic and the predicate calculus are both such systems, in which rules are given to distinguish valid from