ABSTRACT
This essay originally appeared in 1989 as chapter 2 o f BG. [Editors]
4.1 Type of connection, and sorts of sociative and relevant logics
A sociative or connectional logic involves a definite connection in its implicational or inferential part, it is broadly relevant.31 Trivial connections (such as being either the same or different, or as implying or not implying) are not definite; they provide no genuine linkage of components. Nor, though the claim does not go undisputed, do the implicational connections exhibited in the basic paradoxes of implication-(A &; —> B and B —> (A V ~A) in standard notation-afford definite connections. For A and B may have nothing whatsoever to do with one another, share no content. Later we will look hard at the implausible theme that the modal ecology of the universe is such, the modal web spun so tight, that impossible and necessaiy statements, whatever they concern, have definite connections with everything else. To begin however, we make the preanalytic assumption that implication requires connection. The main type of connection that has been emphasized recently is relevance, whence “relevance logic”. But relevance does not constitute the only relation of definite connection, or the only one of historical importance-consider inclusion of content, sharing of terms, etc. Moreover, as is well known, relevance in general (not pinned down to specific determinates) is an elusive notion.
