UNDECIDABILITY, UNCOMPUTABILITY AND UNPREDICTABILITY: Paradigmatic Reflections in the Space of Classical-Fuzzy Logical Duality by KOFI KISSI DOMPERE

KOFI DOMPERE

Essay Abstract

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.

Author Bio

Dr. Kofi Kissi Dompere is an emeritus professor of economics at Howard University and a founder and a distinguished Research professor of a new Research Institute of Information Decision and Economic Sciences (RIIDES). His areas of teaching and research are economic theory, mathematical economics, OR, decision theory and international economics. He has published several scholarly essays om economic theory, and over ten monographs on foundations on fuzzy sets and systems and fuzzy decisions with Springer Science; economic dynamics and methodology of development economics with Greenwood publishers, and foundations of African philosophy with Adonis-Abbey Publishers. His current research is on epistemic

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Satyavarapu Gupta

Wonderful words Prof KOFI KISSI DOMPERE !!!!

........................................With reference to any phenomenon of interest, where decidability, computability and predictability are logically sought without fuzzy-stochastic conditionality, the axiomatic model representation of any variety must meet completeness conditions. These conditions are such that the system's propositions in the model, must reflect the exactness of the variety characteristic disposition; the rules of inference from the laws of thought must be made exactly as the objective laws governing the variety's behavior. additionally, the defined initial conditions in the characteristic disposition must correspond exactly to the variety's identity and behavior. These completeness conditions are equivalent to Gödel-completeness , and hence if the initial system is decidable and computable then all subsequent points of decidability, computability and predictability must be derivable from the initial truth of the characteristic dispositions of decidability, computability and predictability. To achieve this completeness, the knowledge by acquaintance must be exact, true and empirically perfect. The laws of thought must be the same as the objective laws governing the variety's behavior. These completeness conditions are the demands of the classical paradigm of thought. They require a perfect paradigm of thought, a perfect language and a perfect information with no deficiencies of vagueness.....................

I am requesting you to please apply these conditions to my essay:

"A properly deciding, Computing and Predicting new theory's Philosophy"

Where I just elaborated in terms of what should be the freedom available to an author when the "real open thinking" is supported. How I got these on Dynamic Universe Model.............

I request you to please apply your theory on this and give an unbiased reply

Best Regards

Snp.gupta

Wilhelmus de Wilde

Dear Professor Dompere

You have written a thorough essay and analysed the problems of undecidability, unpredictability and uncomputability in our reality deeply.

You are really giving the righteous answer when you write: "The completeness conditions are unattainable due to the cognitive capacity limitations of cognitive agents". This is in my perception the real cause of the unpredictability of our future.

Every conscious agent has his own (uncomplete relative to others) set of information. When working together it will still be by a restricted amount of others (and these co-operators are having the same direction of thought, with the same goal).

So every prediction will be a "gamble". Also, each prediction is taking place in the past. (because the NOW is unattainable), so is the time that we are "consuming" by processing information in order to arrive at a conclusion (prediction). Already the brain of a conscious agent needs time to make the observation an experience (see my essay).

I understand your conclusions and respect them, as you say "there is no absolute truth" (note 2) and it is especially note 3 that has an important meaning for me.

I hope that you will find some time to read my entry in this contest and maybe if you have some remarks or questions I will be glad to answer them.

Best regards

Wilhelmus de Wilde

Martin Staveren

Dear prof. Dompere,

The rather ad hoc "fuzzy paradigm" has been replaced by Bayesian estimation, which is based on elementary logic. It is then not necessary to refer to true/false oppositions, etc.

KOFI DOMPERE

One of the greatest ignorance about fuzziness ii the failure to understand the differences of fussy paradigm and its processing modules over fuzzy information and the classical paradigm of thought over the classical information with exactness and volume limitation. The added confusion is failure to understand that the universal varieties exist in dualistic-polar conditions for their identities and not in yes or no with excluded middle to exclude vagueness in language, thinking, reasoning and thought. There are demands on thinkers to realize that decidability has a corresponding undicidablity that are subjected to decision-choice actions under neuro-decision choice conditions. The classical paradigm of thought that is generally used has a problem with an internal paradox that results from the principle of excluded middle. over fuzzy paradigm of thought relates to the processing capability of fuzzy information with vagueness. The classical paradigm of thought relates to classical information with exactness where the development of the theory of approximation is an attempt to recue the classical paradigm fro its contradiction. More exposition will follow.