An abstract approach to bivalence

Abstract

This paper outlines an approach to the principle of bivalence based on very general, but still elementary, semantic considerations. The principle of bivalence states that (a) "every sentence is either true or false". Clearly, some logics are bivalent while others are not. A more general formulation of (a) uses the concept of designated and non-designated logical values and is captured by (b) "every sentence is either designated or non- designated". Yet this formulation seems trivial, because the concept of non-designated value is negative. In order to refine the analysis, the class of anti-designated values has been distinguished. The non-trivial version of the principle of bivalence is expressed by (c) "every sentence is either designated or anti-designated". The last part of the paper mentions some extralogical reasons for considering the principle of bivalence with truth being a designated value as intimately connected to human thinking and behavior. ©2013 by Nicolaus Copernicus University.