The context this in which this comes up here generally requires something like “there’s a way to compare the complexity of numbers which always produces the same results independent of language, except in a finite set of cases. Since that set is finite and my argument doesn’t depend on any specific number, I can always base my argument on a case that’s not in that set.”
If that’s how you’re using it, then you don’t get to pick the languages first.
You do get to pick the languages first because there is a large but finite (say no more than 10^6) set of reasonable languages-modulo-trivial-details that could form the basis for such a measurement.
The context this in which this comes up here generally requires something like “there’s a way to compare the complexity of numbers which always produces the same results independent of language, except in a finite set of cases. Since that set is finite and my argument doesn’t depend on any specific number, I can always base my argument on a case that’s not in that set.”
If that’s how you’re using it, then you don’t get to pick the languages first.
You do get to pick the languages first because there is a large but finite (say no more than 10^6) set of reasonable languages-modulo-trivial-details that could form the basis for such a measurement.