Abstract
SOME PHILOSOPHICAL AND SOCIAL SIGNIFICATIONS OF SETS IN LOGIC
This paper discusses the philosophical and social significations of sets in three logical systems; two-valued logic, many-valued logic, and fuzzy logic. Here is an attempt to infer these significations from thedefinition of sets; graphically represented by Venn diagrams or membership functions, and the basic operations on sets.
This paper explains that each set is a reflection, either explicitly or implicitly, of human thinking's ways. Two-valued set as a representation of binary and strict thinking, many-valued set as a representation of multiple thinking, which is less strict than binary thinking, but also lessopen than fuzzy or open and freethinking, which is represented by fuzzy set.
Unlike those who say that the one, but not the other, of these three logical systems can represent real world, and reflect human thinking’s ways, this paper detect that each one of these systems has more suitable scope than the other, and can reflect one way of thinking better than the other does. Therefore, each logical system has its importance and role in real life, and has scope that is more appropriate to represent it.Finally, it asserts that logical systems do not exhaust human beings' life.
Keywords
Sets -membership values- basic operations.
