Evolution of Language
Consider a hypothetical species with the following profile: they have evolved by mutation and natural selection a language of thought, an internal symbolic system of infinite scope and finite base. This they use as the medium of their thought. They have not yet, however, evolved a public language of communication, so their use of language is wholly internal. Let us suppose that this language, call it IL (internal language), is fully conscious to members of the species: the words, phrases, and sentences that comprise it pass through the consciousness of its users. It is not an unconscious language, employed by the brain, but a language that can be introspected in all its glory—rather as we can introspect the language we speak when we employ it in inner speech. Let us suppose that it is innate and universal. In addition to IL the species has a vocal signaling system V that they use to warn each other of predators or to express their emotions, but V is not a real language in the sense that IL is—just a few unstructured sounds. We can suppose that V evolved well before IL in some ancestor species and has been inherited from those ancestors. The signaling system V is a separate faculty from the language IL, both in its evolutionary origin and inner nature. V cannot express the full semantic content of IL and members of our hypothetical species don’t expect it to. The two faculties merely coexist.
Now suppose that at a later time something novel happens: the species develops an external communicative language. This language EL is a sign language not a vocal language, and it recruits the earlier internal language of thought. It is, in fact, the externalization of IL, though it serves a different purpose—communication not cognition. The external language EL is capable of expressing all that is expressed in IL—the two languages are inter-translatable. EL is rather like a human natural language, except that it is paired with an internal language that is as accessible in its structure and lexicon as a natural language. It may be that EL will gradually diversify over time, so that there will come to be many versions of it, though all derive from IL. Notice that EL does not derive from the old signaling system V and isn’t even a vocal language; in no way does it share in the neural basis of the signaling system. This system predated both IL and EL, but those languages evolved without any reliance on it. We can say that IL was a preadaptation for EL and essential for its appearance, but the system V played no role in the origin of either. Exactly why and how IL evolved is not known, though it certainly greatly expanded cognitive power; and it is also a question why EL evolved, given that the species did perfectly well without it for thousands of years. In any case, IL came first and EL built upon it, without input from V.
We can imagine that speakers of EL might wonder whether this new capacity deserves to be called a language, since they originally applied this term to IL and take that to be the paradigm case of a language. The fact that it is public and embodied might for them count as reasons to withhold the name “language” from it, because for them a genuine language should be something interior and hidden. For them, a language is by definition a mental language not a public physical language, though they can appreciate the motivation for extending the notion to the external language. Some cautious souls might insist on putting the word in scare quotes when speaking of the external means of communication. And there may be bolder types who write books with titles like The Language of Communication or External Syntactic Structures, well aware that they are flouting linguistic convention and received opinion—for it is generally held that there is no real language but the language of thought and no syntax of anything outside the head. After all, they can introspect the language of thought within their own consciousness, and there is no doubt that a language is what it is (some skeptics maintain that we can never be certain that an external language exists, though it is apodictic that an internal language does).
This hypothetical species appears perfectly logically possible. It contrasts with another hypothetical species, which may not be logically possible, that first develops a public language and only later internalizes that language to produce inner speech; and that public language evolved from a prior signaling system like V. The former hypothetical species first develops a language of thought and then develops an external language of communication, with no contribution from its inherited signaling system; that system need never have existed in order for language to evolve. The latter hypothetical species models what many have believed about the origin of actual human language, namely that primitive vocal signaling came first and formed the basis for the evolution of sophisticated human language. But the former is also a coherent story that should be evaluated on its merits; it may, in fact, be the true theory. The question is an empirical one (though issues of logical possibility also arise); certainly we cannot just assume that the other theory is correct. It is not easy to see how we could set about answering the question, what with the remote origins of language and the difficulty of understanding thought, but there are some facts about human spoken language that are suggestive. 
First, natural languages mirror thought, but they do not mirror animal signaling systems: thought has the complexity and structure of language, but signaling systems don’t. If we maintain that human languages somehow derive from primitive signaling systems, we have the problem of the poverty of the precursor: those systems just don’t have the internal structure that is present in a normal human language. But a system of inner thought, especially when coded in an internal language, has exactly the right kind and degree of structure to provide a platform for external language to develop. People tend to suppose that just because signaling systems and human languages are both vocal the one must have evolved from the other, but this is a superficial point of view—in my hypothetical species the external language is stipulated to be a sign language (visual) not a vocal language (auditory). It is not physical form that matters but constitutive structure—the formal object not its contingent physical medium.
There is a lot to say, and a lot that has been said, about these matters, but I don’t propose to delve into the evidence and arguments now; my point has been to set the issue up in a perspicuous manner by describing a stipulated hypothetical species. The question is whether that species models how things actually are (were) with humans. Is spoken language externalized symbolic thought or is it elaborated vocal signaling? Once we have accepted the prior existence of a language of thought, isn’t this the obvious place to look for the origin of spoken language? I would venture that the more advanced mammals all have fairly sophisticated thought but that their signaling systems fail to do justice to their thought processes—they can’t properly express what they think (this is why we always have to guess what dogs and cats want and think from their rather limited sounds and gestures). They thus lack what humans manifestly possess—a full-blown articulate external language. Why this should be is hard to say, but it is clearly a fact. We have IL, EL, and signaling; they have (primitive) IL and signaling. The idea that both thought and language evolved from signaling by some process of augmentation is hard to believe—like thinking that eyes might have evolved from fingernails. Of course, the linguistic behavior we observe in humans today incorporates vocal signaling, alongside the linguistic competence that derives from the internal language; but that doesn’t mean these have the same evolutionary origin or intrinsic structure. Natural languages as we find them are really hybrids of distinct systems with distinct evolutionary origins: they result from a combination of the initial language of thought, contingent embodiment in a specific sensory-motor system, and the ancient system of calls and cries that we inherited from our ancestors. These three systems are now interwoven in the phenomenon of human communication, but that doesn’t mean they don’t retain their separate identities. If I shout out the sentence “Your hair is on fire!” I exploit my vocal apparatus, my instinct to warn, and my internal competence in an abstract computational structure—all in one. But these are separate psychological systems with complex interrelations. Thus language as we use it can be both “cognitive” and “expressive”—reflecting its origins in inner thought as well as in more primitive forms of communication.
The naïve view of thought and language is that thought comes first, in the species and the child, and that we then go on to express it in spoken words. That view has been challenged, particularly by twentieth century thinkers, who invert the order of explanation: spoken words come first and from these thought develops. Thought is language internalized, instead of language being thought externalized. The naïve view seems to me to have more going for it, and my hypothetical species agrees. To them it is quite self-evident that a language of thought precedes and explains a language of communication and not vice versa.
 This is complex contested territory; I intend only to skim over the subject here. For those familiar with modern linguistics, I am siding with Chomsky on these matters: my hypothetical species closely follows the view of language he has defended, most recently in Robert C. Berwick and Noam Chomsky, Why Only Us: Language and Evolution (MIT Press, 2016).