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In this paper I describe the main Lvov-Warsaw School contributions to the proper analysis of the phenomenon of vagueness. I mention the following members of the School: Henryk Mehlberg (whose theory might be seen as an early version of supervaluationism), Stanisław Jaśkowski (whose discussive logic has been used as the logic of subvaluationism) and Marian Przełęcki. I’ll focus on the views of Przełęcki, who offered two different theories of vagueness. The better known is the one suggested in his book The Logic of Empirical Theories, which is another early version of supervaluationism. Of special interest however is his paper “W sprawie terminów nieostrych” [On the issue of vague terms], which has never been translated into English and in which Przełęcki advocates a radical theory – different from his later one – according to which statements concerning borderline cases are devoid of sense.