Well, 'unfalsifiable' is a trickier concept in "sciences" like linguistics, in which almost everything is unfalsifiable in a strict sense. Ultimately, this is because linguistics is a narrative tradition - like botany, political science, history or theology - rather than an experimental process like the sciences in a narrow sense. Rather than making predictions tested by specific, independent experiments, linguistics attempts to fit the most congenial narrative to an (almost-entirely) already-existing field of data (even if it's not all been codified yet). Each narrative will - being a narrative and not reality - fail to be congenial in some way, but each narrative can be progressively elaborated or reframed (maintaining the same data) to appeal to critics. In other words, almost all of linguistics is the sort of post-hoc explanation that the falsifiability criterion was meant to exclude.
This is also why theories are much harder to kill off in linguistics, and why totally different theories can continue to survive in competition: there is no clear procedure for eliminating them, as judging the most congenial narrative is a subjective exercise (far more so than judging experimental failure) and there will always be wide divergences in aesthetic taste when it comes to narratives.
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Specific to this question: I think the remarkable thing is that anyone would ask it, and that nobody would question it. It seems to me that the entire attempt to provide a "theory" of phonology is misguided. Consider a closely-related subject: nobody would seriously ask for a theory of animals, which neatly explains all observed animals, neither overgenerating (predicting animals that don't exist) nor undergenerating (failing to predict the existence of the platypus). Yet animals and languages are very similar things: both are complex structures that have emerged through evolutionary pressures acting upon stochastically-generated mutations over time, both are linked both through cladistic hierarchies of relatedness and through processes of convergent evolution, both are found in a bewildering (but non-random) diversity of forms arranged through space and time, and both develop almost entirely prior to the introduction of experimental observation and hence are conceptually "given". Indeed, languages are animals taken a step further, in the sense of being even less amenable to empirical study on account of greater degrees of indeterminacy and subjectivity.
Hoping to develop a "theory" that "generates" the features of a language from some universal is exactly parallel (only worse) to hoping to develop a "theory" that "generates" the platypus from some Ideal Animal. It's a bizarrely 19th century notion. Well, it's actually a bizarrely ancient greek notion (this sort of linguistics is really just an acceptable form of Platonism), but versions of it remained popular in some other subjects into the 19th century - think of the way Comte, Hegel, Spencer and Marx attempted to create "theories" of history that, through modulation of various parameters, could "generate" observed historical societies (societies are much like animals or languages in this respect - zoology, linguistics and sociology/history should probably be considered branches of a single discipline of, let's call it, "myriology"*). This approach has long since been recognised to be both infertile and confused in every area EXCEPT linguistics.
[Indeed, taking another branch of myriology: it's equivalent to asking for a "theory" of psychology that "generates" individual personalities... (neither over- nor under-generating!). Even psychologists no longer claim to do that, and they're not exactly paragons of rigour themselves.]
But what about the Universal Grammar (or whatever you call it when you don't want to call it Universal Grammar but want to continue as though it were a Universal Grammar)? Doesn't the existence of Universal Grammar entail the generatability of languages?
No, clearly it doesn't. Philosophically, universal grammar is only necessary in a very minimal form: there must be some general contours of more and less congenial assumptions about meaning (otherwise it would never be possible to narrow down the infinite range of possible interpretatons to the point where learning through affirmation and elimination becomes feasible), particular in the area of assent and dissent, but there is absolutely no need for, or even really plausibility for, a positive common grammar, or even for a determinate number of commensurable 'rules'. Beyond this is just faith, not reason.
*I'm calling it that because at core 'myriology' is the study of commonalities and differences between the myriad outcomes of common processes. It's not the best word, to be sure.
_________________ Blog:
But the river tripped on her by and by, lapping
as though her heart was brook: Why, why, why! Weh, O weh
I'se so silly to be flowing but I no canna stay!
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