It sometimes happens that one is analyzing some theory and one discovers that the theory in some sense implies something meaningless.
But that doesn’t make sense when we think about it. Meaningfulness/meaninglessness is only applicable to sentences, and not to propositions. Implication is only defined in relation to propositions. So when we encounter the scenario that a theory “implies something meaningless” we should say that the theory implies that some sentence is meaningful but it isn’t. In that way we can use an inference (MT) to conclude that the theory is false. We can’t do that with something meaningless.
When I write ‘applicable’ I mean only in meaning, not some possibility of some sort.