I mentioned 'metalinguistic space' in the article about existence-assertions, so I want to apply the concept concretely to the pathetic Creationism "debate" that's sweeping the religiopolitical arena, as it makes its way into school programs. Of course this analysis in metalanguage is applicable to all areas of so-called debate. The analysis shows that there really is no debate, because there is nothing that can be debated; both parties are talking past each other, simply because the intersection of both lambdas yield the null set. This is tantamount to saying that there is no basis for argument.
To reiterate, the universes of discourse are the ontologies of paradigms, i.e., the set of admissible objects in paradigms and theories within paradigms. For example, a paradigm whose universe of discourse is based on the epistemological delimitation of its objects to empirical phenomena might “softly” consign non-empirical phenomena to the domain of conjectural, hypothetical, or inference-based objects, or with respect to a “hard” approach, it might consign such objects to the empty set ∅. As another example, if the paradigm were to be based on religious authority (or authorities), then its universe of discourse would likewise be delimited, demarcated with respect to the same, and all other objects that do not fall within the scope of its ontology would be equal to ∅.
Hence, if a paradigm θ1’s universe of discourse were Λ1 , then in the case in which a nonempty Λ2 were to intersect with Λ1 and the result is null, then Λ1 - Λ2 = Λ1 inasmuch as relative to Λ1, the nonempty universe of discourse Λ2 has no object(s) in common with Λ1. Logically speaking, relative to paradigm θ1, the universe of discourse Λ2 is equivalent to the null set, nonempty though it might be. It is simply “discarded” by θ1, and is outside the scope of its set of admissible objects, in which case the truth-functional valuation of the statement
∀x [x ∈ Λ1.⇒.x ∉ Λ2]
would always be true in paradigm θ1. Note that Λ2 will always “tag along” θ1 because the null set is a subset of every set, but it only tags along as that which simply “does not exist” with respect to paradigm θ1, because it has set its parameters to exclude Λ2, and the inflated union Λ1 ∪ Λ2 would no longer = Λ1, in which case it would be rejected by paradigm θ1, based on its epistemological selection-process. (Which, I suppose, could be (in)formally understood in terms of a specific operator ε1 over the set of all possible universes ∪Λi so that ε1(∪Λi) = Λ1)
Granted, in most cases there are overlaps of some kind, but the question is to what degree those overlaps are paradigmatically significant.
Which brings us to the metalinguistic analysis. To define: Let θs be a “soft” empirical paradigm of scientific method. Let θd be a religious-dogma-based paradigm, and let Λs and Λd be their respective universes of discourse.
θs consigns elements of Λd to the set of objects belonging in the category of conjectures, hypotheses, and (hitherto) unobservables. Though θs does not consider the set Λd to be null, the fact remains that Λd ∩ Λs is, if not equal to ∅, a set of elements that “sit on the fence,” as it were, and would for the most part be non-definitive with regard to the paradigm in question; i.e., the set ∂(Λd ∩ s) would be paradigmatically insignificant. This result, logically, would be the same in the case of a “hard” empirical paradigm with respect to the ontology of Λd. The same principle holds for θd with respect to Λs .
If both paradigms were “hardline,” then both would reject the “borderline” set ∂(Λd ∩ s) as spurious, as = ∅. We now apply the analysis concretely to the Evolution - Creationism debate. A "hard" paradigm which supports the universe of discourse of evolution theory excludes the universe of discourse supported by the hardline paradigm of creationism, and vice versa. It is only in this metalinguistic space in which it becomes evident that the two paradigms have nothing of ontological value in common (and whatever they do have in common is paradigmatically insignificant). If there is nothing of significance in common, then there is no ground, there is no basis for debate. I am not speaking of the tenacity of one’s faith in science or dogma. I am speaking strictly of the elements of the universes of discourse.
So, dropping a dimension and getting back to the world of language, the debate of Evolution - Creationism is actually a non-debate. It’s simply shadow-boxing, talking past each other; there will never be an agreement. There has been compromise for sure with “softer” θd, which I believe is sensible, because they have made the boundaries of Λd “fuzzy” enough to accommodate a universe of discourse Λs’ > ∂(Λd ∩ s) (though Λs’ < Λs) in their paradigm. But with regard to the allowance of more objects into their universe of discourse, that is where the matter ends; the paradigm gets enriched with a larger, more flexible ontology, and there is nothing more to debate. In fact, that is when the so-called debate has ended.
As long as paradigms θs and θd are such that their respective Λs and Λd yield ∂(Λd ∩ s) ≈ ∅, there is no logical basis for debate. Unless, of course, one can logically prove that oranges are better than apples.