Ontology, Epistemology, Explication and Exactness in Mathematics and Sciences

Abstract

All the questions raised in the previous chapters fall under either the set of questions of ontological type or the set of questions of epistemological type. Most of the questions are of epistemological type. The theory of the knowledge square is a meta-theory on epistemology and knowledge production. The point of entry of the meta-theory is that the information input for knowledge production is defective due to fuzziness and incompleteness that create qualitative and quantitative inexactness for all sciences. Fuzziness is associated with qualitative disposition of information while incompleteness is associated with quantitative disposition of information about epistemic objects with neutrality of time. The point of departure is a search for an appropriate symbolism that will incorporate fuzziness and incompleteness of information with a further search for appropriate logic of operations that will allow exact equivalences to be abstracted from inexactness. All the debates in the last analysis are about what we claim to know about what there is in the ontological space and the process of knowing. In the epistemic process of knowing, the solution to the problem of exactness forces us to choose between two principles that must be taken as intuitive assumptions. They are the ontological principle of exactness and inexactness, on one hand, and the epistemological principle of exactness and inexactness on the other. The inter-relational structures between ontology and epistemology regarding exactness and inexactness are displayed in Figure 7.0.1. In the process of the knowledge production, are we willing to assume the ontological principle of exactness about the elements in the universal object set as defined in the potential space relative to knowing? In other words, are we willing to accept the fundamental principle that ontological objects, processes and states are exact, and hence there are no vague objects and there is no defective ontological information structure associated with them as in Cohort II? Alternatively, are we to accept ontological vagueness and epistemic exactness as in Cohort III? Another choice that is to be faced is that of accepting complete exactness in both spaces where the epistemological information is the exact replica of the ontological information as in Cohort I. The final choice is to accept complete inexactness in both the spaces with vague ontological and epistemic objects as in Cohort IV. Let us examine these in a little more detail.