Fuzziness and Approximate Reasoning

Abstract

We have presented a notion that paradoxes in sciences, mathematics and logic come to us as temporary and permanent within the logical environment of their creation. The resolution of temporary paradox is intra-paradigm in nature while the resolution of permanent paradox is an inter-paradigm process. The former is an internal movement in terms of sub-paradigm changes while the latter is a revolution in paradigm with inter-paradigm changes. In this respect, it is useful to introduce the concept of global paradigm into the analysis. Every global paradigm is a family of sub-paradigms. A resolution of a temporary paradox may result in intra-paradigm changes and hence inter-sub-paradigm shifting. Intra-paradigm changes are merely refinements of existing paradigm. A resolution of a permanent paradox results in inter-paradigm shifting from one global paradigm to another global paradigm. The new global paradigm may have the old paradigm as its sub-paradigm in the sense that it offers solutions to solved and unsolved problems in the old paradigm as well as providing new epistemic look and rationality in knowledge acceptance process. An example of a permanent paradox in logic and philosophy is that of sorites (the paradox of heap), the resolution of which we have provided through a paradigm shifting from classical paradigm to fuzzy paradigm in a companion volume [R17.24]. © 2009 Springer-Verlag Berlin Heidelberg.