Classical-Logic Analogue of a Fuzzy “Paradox”

One of the main reasons why classical logic is not always the most adequate tool for describing human knowledge is that in many real-life situations, we have some arguments in favor of a certain statement A and some arguments in favor of its negation ¬A. As a result, we want to consider both A and ¬A to be (to some extent) true. Classical logic does not allow us to do that, while in fuzzy logic, if the degree of belief in A is different from 0 and 1, then we have a positive degree of belief in a statement A&¬A. In classical logic, A&¬A is always false, so, when we get both A and ¬A in classical logic (a paradox), this means that something was wrong. In view of that, the fact that A&¬A is possible in fuzzy logic, is viewed by some logicians as a “paradox” of fuzzy logic. In this paper, we show that in classical logic, although we cannot directly have A&¬A, we can, in some sense, have confidence in both A and ¬A. In other words, we show that what classical logicians consider a fuzzy paradox has a direct analogue in classical logic.