The Paradox of the Heap of Grains in Respect to Roughness, Fuzziness and Negligibility

Abstract

In a first step, roughness and fuzziness fail to account for the type of grad-uality (vagueness) involved in the concept of a heap, as it is conceived in the famous Eubulides’ paradox. One can partially bridge this gap by means of tolerance rough sets. Even in this case, a non-concordance persists between the empirical finiteness and the theoretical infinity of a heap. Another way to approach this problem could be via negligibility (be it cardinal, measure-theoretic or topological)