Classical-logic analogue of a fuzzy "paradox"

Abstract

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 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.