Two seemingly unrelated approaches to (propositional) logical consequence will be compared in this tutorial. According to the former one, rooted in Kant'ss notion of analyticity but especially championed by exponents of the C.I. Lewis school at Harvard (Baylis, Nelson, Parry) in the debate about paradoxes of entailment, a conclusion
φ validly follows from certain premisses in
Γ in case the meaning of
φ is "analytically contained" in the meanings of the members of
Γ . In this approach, only
significant sentences are taken to be of interest to the logician. In the latter perspective, defended among others by Bochvar, Halldén, Kleene, Goddard and Routley, consequence is more traditionally viewed as truth preservation (or as preservation of some other semantic property), but in the presence of possibly
non-significant (e.g. meaningless) sentences. The early discussion on these
logics of significance has focussed on many-valued propositional logics with
infectious truth values, namely, values that are assigned to a sentence
φ if and only if they are assigned to some propositional variable occurring in
φ.