I hope you don’t mind my input... I’ve been into this stuff for a long time, from two different avenues-- the evolutionary perspective (conscious intelligence (and thus language) as products of natural selection, finding the loci of consciousness in the brain, neurophysiology , etc) and the philosophical perspective – language as an inherent part of understanding ‘objectivist’ epistemology. And the role of syntax that actually shapes the nature of the concept itself (I hope that's what your talking about, if not... sorry, this will be wasting words).
The one thing that could be agreed upon philosophically is that "existence exists" (which incidently is a way of putting it into the form of a proposition, and thus into the form of an axiom, the primary fact of which is existence) -- and the primary basis of existence (anthropocentrically) is consciousness--and the process of consciousness (which I think is indeed ‘active’ (ergo, a ‘process’) rather than a passive ‘state’,although it’s not necessarily a volitional act) is parallel with the process of language right up to the step of "designation" ie. labelling a concept with a word(s).
Like you said to Harvey, basically ‘vocabulary’ is symbolic tagging, which I see as the ‘algebraic substitution’ of the phonetic/ symbolic ‘word’ in place of the integrated concept. Which, when you add what are called 'higher-level conceptualizations' (which includes syntaxic manipulation) language runs parallel to mathematics, like you said-- and despite the fact that it's much more formal and constrained in many ways, the big advantageous as a means of communication is that it's absolutely unambiguousness in spite of and because of the constraints. (eg. SETI transmissions use mathematics, prime-number sequences etc.)
Anyway, philosophy is an amateur passion, neurophysiology was part of my course load for 7 years of university, and for 2 of those years I did research in it (but only as a research assistant to my prof... which means I know he liked his coffee with one cream and two sugars...)
Anyway one well-supported hypothesis about the mental process of language is that every element of it, including what we know as the metaphysical, phenomenological and psychological processes-- they all have neuro-physiological correlates that can be mapped. In other words, if you look deep enough into Broca’s Area, Wernickes Area and associated structures in the temporal lobes where language occurs, there are neuronal events which are directly associated with each step of language-- the conceptualization, the designation, etc... You can poke an electrode into a conscious subject in a given spot in Wernickes' Area and produce the corresponding phonemic paraphasias (they know the mental concept but can't produce the actual word) and/ or semantic paraphasias, etc.
That’s why a reasonably good understanding of the language process requires a holistic (philosophy + psychology + physiology ) approach, and that’s why you wouldn't find the answer from Wittgenstein, Heidegger, Kirkegarde, Sartre et al --As philosophers, they can’t give ‘enough’ of the answer to satisfy you... I can say that because I have had that very same question that you have -- and I’ve already searched in philosophy! I mentioned those four existentialists because they all wrote copiously on ‘language’, because of how central that process is to the state "of being" and although you didn’t find anything from Wittgenstein, he (as one of the fathers of existential analytic philosophy) wrote half a book on the subject of language (called ‘Philosophical Investigations’) and you're right-- the question that you posed is not addressed. I don’t have a copy but I have a good synopsis from it in a fairly decent anthology of existentialism.
But the point remains : As neurophysiological (and pyschological) research is accumulated, the less valuable the purely philosophical theories of language become. We now understand the rough (neurophysiological) architecture of consciousness itself! Almost all the pathways and processes!
And I make that claim knowing full well that it seems to conflict with several ontological models – ones that reject ‘consciousness’ as a purely mechanistic/ naturalistic process, ie. we have a ‘soul’ or that consciousness (ie. our existence) is too awesome and beautiful a thing to be simply mechanistic in origin. Although I do actually subscribe to the former view, I don’t think that mapping consciousness in the brain explicitly eliminates the latter view, so neurophysiology still leaves room for the dualists (and the concept of ‘soul’...)
Aurino, I need to run... but I hope you don’t mind, I will put together an answer to your question to Harvey and I’ll post it as soon as I can.