John Karakonstantis
Keywords: characteristic function, fuzzy logic, membership function, classical logic, entitlement system, hyper-cubes, propositional type, fuzzy set, fuzzy entropy.
Abstract: In this paper, the main paradoxes are interpreted in such a way that they lead to the equivalence of a sentence and its negative s ????sc. In classical logic, paradoxes define sentences that contradict themselves. These sentences support strategies for proving theorems. In fuzzy logic, paradoxes lie at the center of hyper-cubes. It can then be established that changing the framework eliminates paradoxes. Paradoxes therefore show us how to change the “teaching process” framework so as to transcend the obstacles they bring about to teaching and learning. • The meaning of “nearby”1 is examined in two research frameworks. • A criterion for evaluating the “teaching process” is developed through a classification of mental activity by means of the measurement of the “fuzzy entropy” determining the internalization of concepts in every context. Finally, the contextual approach to mathematical certainties is accepted.
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