 The relationship between (L2) and (L3) was briefly addressed above. They seem to be closely related because a logical truth can be understood as one that follows from an empty set of premises, and A being a logical consequence of B can be understood as it being a logical truth that if A then B. There are some questions to be ironed out about how this is supposed to go more precisely. How should we understand cases of logical consequence from infinitely many premises? Are logical truths all finitely statable? But for our purposes we can say that they are rather closely related.