Fuzzy Approach, Graded Truth, and Structures of Truth Values

Paradoxes of vague terms. Human description of the world provides us with remarkable situations of a special kind. Consider the following form of the ancient sorites paradox (paradox of heap). “A heap consisting of just one grain of sand is small. If you add one grain to a small heap, it remains small. Therefore, each heap is small.” Note that various forms of sorites paradoxes (e.g. the phalakros paradox, i.e. a paradox of a bald man that will be mentioned shortly) were known in antiquity and their formulation is attributed to Eubulides of Miletus (fourth century B.C.).