The essay presents a paradigmatic viewpoint of the meanings of undecidability, uncomputability and unpredictability, and their roles in knowing. A discussion on the epistemic conditions are offered to show the analytical similarities and differences among them. The methodological approach is based on the principle of opposites composed of dualistic-polar conditions of varieties. The principle of opposites is linked separately to the classical paradigm of thought with excluded middle and non-acceptance of contradiction to examine decidability, computability and predictability. It is then linked to the fuzzy paradigm of thought with relational continuum, unity and acceptance of logical contradiction as a logical value. It is argued that the questions and problems of undecidability, uncomputability and unpredictability are the results of deficiencies induced by the classical paradigm with exact information, decision, excluded middle and non-acceptance of contradiction that generate paradoxes, ill-posed problems especially when the reality are within the excluded middle of dualistic-polar conditions. The problems of undecidability, uncomputability and unpredictability do not arise in fuzzy paradigm with inexact information, relational continuum, unity and acceptance of contradiction as a logical value. The undecidable, uncomputable and upredictable problems are considered in dualities and formulated in the fuzzy decision-choice space, solved and analyzed with the method of fuzzy optimization to illustrate the paradigmatic nature of the problems and their conditions of existence. These problems are continuations of contest discussions of on reality as well as the question of information-knowledge representations and epistemic questions of knowing. The rise of these decision-choice problems depends on the choice between with classical paradigm or with the fuzzy paradigm. The classical absoluteness of on problem-solution conditions approximates fuzzy relativity of problem-solution conditions in all decision-choice actions with fuzzy-stochastic conditionality.
KOFI KISSI DOMPERE