On the ‘transitivity’ of consequence relations
David Ripley · Journal of Logic and Computation · 2017
A binary relation |$R$| on a set |$S$| is transitive iff for all |$a, b, c \in S$|, if |$aRb$| and |$bRc$|, then |$aRc$|. This almost never applies to the relations logicians tend to think of as consequence relations; where such relations are relations on a set at all, they are rarely transitive. Yet it is common to hear consequence relations described as ‘transitive’, and to see rules imposed to ensure ‘transitivity’ of these relations. This article attempts to clarify the situation.