The Laws of Thought and Exact Science

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Given that the justified belief in support of exactness of the primary category of logical reality is accepted, we still have a problem of establishing the exactness of logical transformations among epistemic categories as well as to establish the conversion chain of derived categories by the method of constructionism. Let us keep in mind that the acceptance of exactness of the primary category means that the defective information structure over the epistemic space is due to incompleteness and free from defectiveness due to vagueness and ambiguities. In this way the possibility space is assumed to be exact and so also the incomplete information in the probability space. The first step is to present an exact representation of the elements in the primary category that is empirically or axiomatically defined on which the laws of thought will be applied. The representation involves a language presentation of ideas and meanings through words or symbols for analysis and synthesis to arrive at the derived logical categories. Examples of the primary and the derived categories in mathematics are that the advanced mathematical levels are derivative from the basic number system which is a derivative from our linguistic number system.