Abstract

The purpose of this study is to focus on three interrelated topics concerning the logical and ontological nature of relations. These topics are: the delineation of the Bonding Theory of Relations as found in the works of Gottlob Frege and Bertrand Russell, an analysis of the classic Bradley-type infinite regress argument against relations, and the development of a means of distinguishing between valid and invalid self-reference and so be able to diagnose and solve some of the classic self-referential paradoxes. ;Subsequent to its exposition and that of the more general principles it exemplifies, the bonding theory of relations is formalized. Alternate interpretations for the outlined system are discussed, and the system is then refined to include instances of relations. So refined, the system then provides a criterion for distinguishing between valid and invalid self-predication. The formal system is then extended by an axiom prohibiting a relation complex from being an n-embedded constituent of itself. This prohibition, together with their analysis using relation instances, makes it possible to diagnose and block the Liar-type paradoxes. The analysis of the remaining paradoxes shows their violation of the standard restriction that no individual or predicate should be defined in terms of itself, i.e., idem per idem. Rules are proposed that prevent this error and at the same time admit the defining of a relation instance in terms of other instances of itself, a situation necessary for recursive definitions but one not taken into account by standard rules of definition. ;Bradley's regress argument is shown to be self-referentially inconsistent. Also, using results from the analysis of the bonding theory, it is argued that the regress argument consists of four premises, the first three of which are mutually contradictory and the fourth simply drags out this contradiction into an infinite regress. The contradictory premise states that a relation has the same logical status as its relata, the denial of which is the very heart of the bonding theory