It is imperative for the Church in all times and places to be in dialogue without the culture of the world, and therefore for the Church to be able to couch her theology in the language of the world. Christians have done this to varying degrees of success over the ages. Part of the problem is that each society has a multi-layered culture which incorporates a different lexicon, and so the "vernacular" changes depending on who one is speaking to.
Why is contemporary language important? Many reasons spring to mind: one cannot truly believe what one does not understand, one will not learn what one cannot understand, mental barriers emerge when somebody uses language that is foreign. In this sense, relatable language is evangelical.
Another important reason is that language furnishes our conceptual framework. According to some people (in particular, adherents to linguistic determinism), the grammar and vocabulary of a language structures and could even limit and determine human knowledge and thought. Even if a theory of strong linguistic determinism is false, it remains clearly true that language provides clarity to concepts which would be too vague to communicate otherwise. Since language defines concepts for communication, it follows that understandable language is crucial for communication of the Gospel.
The fact that concepts appear in linguistic form is part of the reason why Christians have been hesitant to translate their conceptual frameworks into the vernacular of an age: precision arises when one uses a particular language, and dead languages have the bonus of remaining static and precise. Ecclesiastical Latin is an instance of a language the Church has declared "sacred", simply for the reason that theology most precise in Latin, in part because much theology was developed in Latin, in part because it is now dead and immutable.
This hesitation is not without due reason, as the East-West schism shows: according to the 1995 document "The Greek and Latin Traditions Regarding the Procession of the Holy Spirit" from the Pontifical Council for Promoting Christian Unity, the famous filioque clause which separates the Western and Eastern Church doctrinally may not be a doctrinal difference at all, but a linguistic issue. "Procedere" has been used to translate "ἐκπορεύεσθαι" and "προϊέναι", whereas only the latter translation would reflect the doctrine affirmed by the Catholic Church, the former indeed being heretical. Whilst the East-West schism is more complicated historically than one simple doctrinal difference, the filioque controversy does indeed highlight the problems that can result when doctrines readily understood in one language are transferred to another. Less fundamental issues may well lie at the heart of other doctrines, such as papal infallibility, as John Ford points out in a recent article.
Whilst theological orthodoxy is important, it is no substitute for the essence of the Church's apostolate, which is its missionary commission. So the Church must, despite risks, translate her theology into language which can be understood by the receivers of her missionary impulse. Who are these people? The Church's "preferential option for the poor", as well as her Master's anointing "to preach good news to the poor" (Luke 4:17, quoting Isaiah) makes clear that those who live in poverty are the first port of call for the missionary Church. So language appropriate to that context is required, and a rhetoric which is intelligible to the poor necessary.
Without minimizing the important duty towards the poor, the missionary comission is to preach the Gospel to all the nations, which includes those that are not marked distinctly by poverty (understood at least in part in material terms). This means that other groups need the Gospel translated into language fitting for their context - including my own, the analytic tradition in philosophy and the natural sciences. What does it mean to couch Christian theological concepts in the language and vocabulary of these groups?
I will not here embark on such a monumental project, although any Christian who lives in a particular cultural context must address the issue of formulating the core tenets of Christianity at some point, lest they deny their core vocation as Christians as missionaries. What I will do is make a few comments about past re-formulations of Christian theology, and ones underway at present.
It is important to note that this has been done before, in the hands of one of the greatest theological minds in the Western tradition, St Thomas Aquinas. In his day, Greek philosophy was the prevailing intellectual norm, and his Christianizing of Aristsotelian philosophy has profoundly marked the Western Church. St Thomas therefore presents us with the paradigmatic case of theology in dialogue with philosophy, even the philosophy of pagans like the ancient Greeks. It is true that some elements of Aristotelianism had to be condemned, but it equally true that the insights of Aristotle were important for theology, and if nothing else, allowed greater intellectual rigor in Christian theology.
Unfortunately, a large portion of Catholic philosophy has attempted to emulate St Thomas' Aristotelianism in a time in which it is untenable, instead of taking the dialogue insight and Christianizing the new "pagan philosophy." Just like in St Thomas' time, there will be many sceptics that such a venture is possible - a quick look at the Condemnations at the University of Paris will suffice to show that they abounded - and yet he managed to pull of an incredible feat. We must now turn to modern philosophy to see how current language can be used to express Christian truths, and so give renewed intellectual rigor to Christianity. The work of saints like St Edith Stein and St John Paul II are good places to start in the continental tradition's sub-area of phenomenology (I am unaware of any analytic philosophers in phenomenology), and perhaps John Joseph Haldane and Richard Swinburne, not to mention the Protestants Alvin Plantinga and William Lane Craig, can form some sort of beginning of the analytic tradition's side of things.
The natural sciences must also be addressed with the eye's of a theologian, and I can think of no better starting place than the Anglican theologian Alister McGrath's trilogy A Scientific Theology, which I have the treat of delving into his first volume later on this year. Just like Greek philosophy might have been considered out of bounds for theology because it was pagan, so now the naturalism that prevails in scientific circles should not deter Christians from entering into it with the firm convictions of Christ.
I do not know what form a scientific theology would take, and yet it is undoubtedly necessary for a fruitful dialogue between religion and science, which is probably considered the most important intellectual authority in the West today. I do not know what an analytical philosophical theology would look like, and yet for intellectual dialogue between Christianity and what probably should be considered the highest intellectual authority, philosophy, it is crucial.
I find myself in the strange position of being in the middle of the three: a Christian, and therefore a theologian, a philosopher, and a scientist. Whilst this characterization is certainly unfair, some might consider my area of science the very pinnacle - physics - if only because of the reductionism that is virally present in society. Misconceptions notwithstanding, if it is the case that I continue to learn about these fields of study upon which I am embarked, I should in principle be particularly capable of the task at hand. It is not a nice idea; it is a necessary one.
 Ford, John, "Infallibility - terminology, textual analysis and theological interpretation - a response to Mark Powell", Theological Studies, 74 (2013).