You say:
Analytic philosophy tends to not be concerned with meta questions and resolves a distinction between analytic truths and synthetic truths, favouring an analysis on the analytic aspect, usually in relation to meaning and linguistics.
I'm not sure that there's much value outside of historical analysis of observing the analytic-synthetic distinction in language, the typical philosopher's preoccupation with Kant aside. In a naturalized epistemology, the dominance of psychologism as a means of framing one's metaphysical principles and the authority of linguistics takes front seat in analytic philosophy. The analytic-synthetic distinction has been noted as problematic since the 1940's (SEP). From the article The Analytic/Synthetic Distinct:
if the claim Brothers are male siblings should be synonymous with Brothers are brothers, and thinking the one should be no different from thinking the other. But, aside from such simple cases as brother and bachelor, proposed analyses, if successful, often seemed quite non-obvious and philosophically informative... This is “the paradox of analysis,” which can be seen as dormant in Frege’s own move from his (1884) focus on definitions to his more controversial (1892a) doctrine of “sense,” where two senses are distinct if and only if someone can think a thought containing the one but not other, as in the case of the senses of “the morning star” and “the evening star.”
This paradox of analysis was resolved by Quine in the Two Dogmas satisfactorily through the introduction of the term "cognitive synonymy". In modern linguistics, the rule of thumb is ANY distinction in syntax represents some difference in semantics, and Quine's cognitive synonymy anticipated work in linguistics where every unique context is an instance of monosemanticity. This accords nicely with a traditional application of the Identity of Indiscernibles since intension can be seen not just a one or more propositions, but holophrastic continuum. Linguistic holophrasis, for instance, is the use of a single word that conveys a potentially contextually complex meaning. Words are a shallow medium to describe thought, and they introduce ambiguities. Thus, science, on this reading, also supports Quine's inscrutability of reference.
You ask some questions:
Yet, there are still two fundamental questions need to be resolved: a) How can analytic truths be established as truths non-circularly, in a warranted way? b) How can the concrete, finite thinker establish its own reasoning as accessing/producing such truths? Especially in the context of the usual naturalism and secularism of analytic philosophy that has an anthropic conception of man as a finite, evolved creature through blind processes not teleologically oriented towards analytical truths, and without a transcendental access to a universal realm of truths?
The short answer is that because propositions can be logically consistent but somewhat meaningless, truth-conditional semantics is not sufficient to warrant anything more than the coherence of the logical structure of claims. In other words, the theory of coherent truth is insufficient for adequate warrant because it doesn't ensure that true statements are meaningful. This would seem to imply that logicism itself as a solution to all of meaning and metaphysical grounding is insufficient. This of course would come as no surprise to those who read the mathematical philosophy of C.S. Pierce or L.E.J. Brouwer who rely on an interpretation of meaning, at least in mathematics, that is empirical or intuitional in nature.
Another different response to this problem, and one response that comes from the meta-semantic disputes of the Linguistic Wars, is an alternative class of semantics known as cognitive semantics. For instance instance, while logic constants may permeate discourse, the semantics of morphemes and lexemes are not logical at all, but are rooted in context and experience. This sort of theorizing is handy at clearing up most of the mysteries of exophoric reference. From the WP article:
The main tenets of cognitive semantics are:
That grammar manifests a conception of the world held in a culture;
That knowledge of language is acquired and contextual;
That the ability to use language draws upon general cognitive resources and not a special language module.
One last strategy for metaphysical grounding is the notion that cognition itself is embodied. Instead of seeing semantics as grounded in logical systems, it is possible instead to believe that meaning is derived from bodily experience (something that hardly would have displeased the Classical Empiricists, no?). This is the notion of embodied cognition (SEP).
Dummett held that the origins of analytic philosophy and the Linguistic Turn rested with Frege, and clearly the logicist agenda has been and continues to be influential in thinkers, particularly those swayed by his Platonic, anti-psychological thinking about language and meaning. But since the 1950's, analytic philosophy has taken an increasingly empirical approach to answering questions with Quine clearly being a bellwether for rejecting the idea that words are bearers of meaning, and philosophy operating distinctly from science. It is in this more contemporary attitude towards analyticity, one that rejects the analytic-synthetic divide entirely, that much modern analytic philosophy is conducted.
