There seems to be two concepts of what constitutes a "meaningful" proposition in logic: one is that you can build up the proposition via the syntactical rules. However, another approach is to say that a meaningful sentence is that it is assigned a set in a model (even if it's only the empty set). (That is, that there is a model in which it is either true or false.) By the first approach, a contradiction is clearly meaningful. In the second one, however, I see a problem: yes, it can be assigned the empty set, so at first glance one would say that it is meaningful. On the other hand, a theory with a contradiction, i.e., an inconsistent theory, has no model, and therefore there cannot be a model to contain the empty set to which the contradiction should be assigned. Hence, it would seem that the contradiction is meaningless. So, which is it? False under all interpretations, or meaningless?