There are four big facts that undergird the generative enterprise:
1. Species specificity: Nothing talks like humans talk, not even sorta kinda.
2. Linguistic creativity: “a mature native speaker can produce a new sentence on the appropriate occasion, and other speakers can understand it immediately, though it is equally new to them’ (Chomsky, Current Issues: 7). In other words, a native speaker of a given L has command over a discrete (and for all practical and theoretical purposes) infinity of differently interpreted linguistic expressions.
3. Plato’s Problem: Any human child can acquire any language with native proficiency if placed in the appropriate speech community.
4. Darwin’s Problem: Human linguistic capacity is a very recent biological innovation (roughly 50-100 kya).
These four facts have two salient properties. First, they are more or less obviously true. That’s why nobody will win a Nobel prize for “discovering” any of them. It is obvious that nothing does language remotely like humans do, and that any kid can learn any language, and that there is for all practical and theoretical purposes an infinity of sentences a native speaker can use, and that the kind of linguistic facility we find in humans is a recentish innovation in biological terms (ok, the last is slightly more tendentious, but still pretty obviously correct). Second, these facts can usefully serve as boundary conditions on any adequate theory of language. Let’s consider them in a bit more detail.
(1) implies that there is something special about humans that allows them to be linguistically proficient in the unique way that they are. We can name the source of that proficiency: humans (and most likely only humans) have a linguistically dedicated faculty of language (FL) and “designed” to meet the computational exigencies peculiar to language.
(2) implies that native speakers acquire Gs (recursive /procedures or rules) able to generate an unbounded number of distinct linguistic objects that native speakers can use to express their thoughts and to understand the expressions that other native speakers utter. In other words, a key part of human linguistic proficiency consists in having an internalized grammar of a particular language able to generate an unbounded number of different linguistic expressions. Combined with (1), we get to the conclusion that part of what makes humans biologically unique is a capacity to acquire Gs of the kind that we do.
(3) implies that all human Gs have something in common; they are all acquirable by humans. This strongly suggests that there are some properties P that all humans have that allow them acquire Gs in the effortless reflexive way that they do.
Indeed, cursory inspection of the obvious facts allows us to say a bit more: (i) we know that the data available to the child vastly underdetermines the kinds of Gs that we know humans can acquire thus (ii) it must be the case that some of the limits on the acquirable Gs reflect “the general character his [the acquirers NH] learning capacity rather that the particular course of his experience” (Chomsky, Current Issues; 112). (1), (2) and (3) imply that FL consists in part of language specific capacities that enable humans to acquire some kinds of Gs more easily than others (and, perhaps, some not at all).
Here’s another way of saying this. Let’s call the linguo-centric aspect of FL, UG. More specifically, UG is those features of FL that are linguistically specific, in contrast to those features of FL that are part of human or biological cognition more generally. Note that this allows for FL to consist of features that are not parts of UG. All that it implies is that there are some features of FL that are linguistically proprietary. That some such features exist is a nearly apodictic conclusion given facts (1)-(3). Indeed, it is a pretty sure bet (one that I would be happy to give long odds on) that human cognition involves some biologically given computational capacities unique to humans that underlie our linguistic facility. In other words, the UG part of FL is not null.
The fourth fact implies a bit more about the “size” of UG: (4) implies that the UG part of FL is rather restricted. In other words, though there are some cognitively unique features of FL (i.e. UG is not empty), FL consists of many operations that FL shares with other cognitive components and that are likely shared across species. In other words, though UG has content, most of FL consists of operations and conditions not unique to FL.
Now, the argument outlined above is often taken to be very controversial and highly speculative. It isn’t. That humans have an FL with some unique UGish features is a trivial conclusion from very obvious facts. In short, the conclusion is a no-brainer, a virtual truism! What is controversial, and rightly so, is what UG consists in. This is quite definitely not obvious and this is what linguists (and others interested in language and its cognitive and biological underpinnings) are (or should be) trying to figure out. IMO, linguists have a pretty good working (i.e. effective) theory of FL/UG and have promising leads on its fundamental properties. But, and I really want to emphasize this, even if many/most of the details are wrong the basic conclusion that humans have an FL with UGish touches must be right. To repeat, that FL/UG is a human biological endowment is (or should be) uncontroversial, even if what FL/UG consists in isn’t.
Let me put this another way, with a small nod to 17th and 18th century discussions about skepticism. Thinkers of this era distinguished logical certainty from moral certainty. Something is logically certain iff its negation is logically false (i.e. only logical truths can be logically certain). Given this criteria, not surprisingly, virtually nothing is certain. Nonetheless, we can and do judge that many more or less certain that are neither tautologies nor contradictions. Those things that enjoy a high degree of certainty but are not logically certain are morally certain. In other words, it is worth a sizable bet with long odds given. My claim is the following: that UG exists is morally certain. That there is a species specific dedicated capacity based on some intrinsic linguistically specific computational capacities is as close to a sure thing as we can have. Of course, it might be wrong, but only in the way that our bet that birds are built to fly might be wrong, or fish are built to swim might be. Maybe there is nothing special about birds that allow them to fly (maybe as Chomsky once wrly suggested, eagles are just very good jumpers). Maybe fish swim like I do only more so. Maybe. And maybe you are interested in this beautiful bridge in NYC that I have to sell you. That FL/UG exists is a moral certainty. The interesting question is what’s in it, not if it’s there.
Why do I mention this? Because in my experience, discussions in and about linguistics often tend to run the whether/that and the what/how questions together. This is quite obvious in discussions of the Poverty of Stimulus (PoS). It is pretty easy to establish that/whether a given phenomenon is subject to PoS, i.e. that there is not enough data in the PLD to fix a given mature capacity. But this does not mean that any given solution for that problem is correct. Nonetheless, many regularly conclude that because a proposed solution is imperfect (or worse) that there is no PoS problem at all and that FL/UG is unnecessary. But this is a non-sequitur. Whether something has a PoS profile is independent of whether any of the extant proposed solutions are viable.
Similarly with evolutionary qualms regarding rich UGs: that something like island effects fall under the purview of FL/UG is, IMO, virtually uncontestable. What the relevant mechanisms are and how they got into FL/UG is a related but separable issue. Ok, I want to walk this back a bit: that some proposal runs afoul of Darwin’s Problem (or Plato’s) is a good reason for re-thinking it. But, this is a reason for rethinking the proposed specific mechanism, it is not a reason to reject the claim that FL has internal structure of a partially UGish nature. Confusing questions leads to baby/bathwater problems, so don’t do it!
So what’s the take home message: we can know that something is so without knowing how it is so. We know that FL has a UGish component by considering very simple evident facts. These simple evident facts do not suffice to reveal the fine structure of FL/UG but not knowing what the latter is does not undermine the former conclusion that it exists. Different questions, different data, different arguments. Keeping this in mind will help us avoid taking three steps backwards for every two steps forward.
 Note that this is a very weak claim. I return to this below.
 Actually, this needs to be very qualified, as done here and here.
 This is very like the mathematical distinction between an existence proof vs a constructive proof. We often have proofs that something is the case without knowing what that something is.