(a) The conflict model. Here the aims, objects, or methods of reason and faith seem to be very much the same. Thus when they seem to be saying different things, there is genuine rivalry. This model is thus assumed both by religious fundamentalists, who resolve the rivalry on the side of faith, and scientific naturalists, who resolve it on the side of reason.
(b) The incompatibilist model. Here the aims, objects, and methods of reason and faith are understood to be distinct. Compartmentalization of each is possible. Reason aims at empirical truth; religion aims at divine truths. Thus no rivalry exists between them. This model subdivides further into three subdivisions. First, one can hold faith is transrational, inasmuch as it is higher than reason. This latter strategy has been employed by some Christian existentialists. Reason can only reconstruct what is already implicit in faith or religious practice. Second, one can hold that religious belief is irrational, thus not subject to rational evaluation at all. This is the position taken ordinarily by those who adopt negative theology, the method that assumes that all speculation about God can only arrive at what God is not. The latter subdivision also includes those theories of belief that claim that religious language is only metaphorical in nature. This and other forms of irrationalism result in what is ordinarily considered fideism: the conviction that faith ought not to be subjected to any rational elucidation or justification.
(c) The weak compatibilist model. Here it is understood that dialogue is possible between reason and faith, though both maintain distinct realms of evaluation and cogency. For example, the substance of faith can be seen to involve miracles; that of reason to involve the scientific method of hypothesis testing. Much of the Reformed model of Christianity adopts this basic model.
(d) The strong compatibilist model. Here it is understood that faith and reason have an organic connection, and perhaps even parity. A typical form of strong compatibilism is termed natural theology. Articles of faith can be demonstrated by reason, either deductively (from widely shared theological premises) or inductively (from common experiences). It can take one of two forms: either it begins with justified scientific claims and supplements them with valid theological claims unavailable to science, or it starts with typical claims within a theological tradition and refines them by using scientific thinking. An example of the former would be the cosmological proof for God's existence; an example of the latter would be the argument that science would not be possible unless God's goodness ensured that the world is intelligible. Many, but certainly not all, Roman Catholic philosophers and theologians hold to the possibility of natural theology. Some natural theologians have attempted to unite faith and reason into a comprehensive metaphysical system. The strong compatibilist model, however, must explain why God chose to reveal Himself at all since we have such access to him through reason alone.
Feel free to add your own thoughts to this conversation by going here.
Although I've weighed in on some of these issues previously, I'd like to add some more thoughts on faith (and reason) by once again drawing on the work of H. Richard Niebuhr.
Here's what Victor Anderson, Assistant Professor of Christian Ethics at Vanderbilt University, says about Niebuhr's conception of faith:
"Like [John] Dewey, Niebuhr also understood faith as the human abode in which value and being cohere in a unity of experience. Faith points to the universal in human experience. Niebuhr writes: '[Faith is a] fundamental personal attitude which, whether we call it faith or give it some other name, is apparently universal and general enough to be widely recognized' [Radical Monotheism and Western Culture (Westminster/John Knox Press, 1960), p. 16]. It is 'the attitude and action of confidence in, and fidelity to, certain realities as the sources of value and the objects of loyalty' [ibid.]. Faith exhibits a dupliclity in Niebuhr's analysis. Both passive and active aspects are present. Passively, faith is the confidence and trust that give value to the self. Actively, faith points to the value toward which the self is directed. Thus, in Niebuhr's analysis, trust is the passive side of faith and loyalty is the active" [Victor Anderson, Pragmatic Theology: Negotiating the Intersections of an American Philosophy of Religion and Public Theology (SUNY, 1998), p. 89].
(An outstanding explication of the active side of faith may be found in the American philosopher Josiah Royce's book The Philosophy of Loyalty, originally published in 1908 and reissued in paperback by Vanderbilt University Press in 1995. You can read more about Royce here.]
Niebuhr's analysis goes to a level deeper than definitions or models of faith that correlate it with beliefs that can be put in propositional form. Before we even get to that level, faith is more fundamentally an attitude, a basic posture towards the world and others. And, as Niebuhr points out, in its active form, that attitude or posture may take the form of faith as trust or faith as distrust. If I do not trust that the world makes sense, for example, I am not likely to engage in scientific research. Likewise, if I don't trust there is any meaning, purpose, or value to my life, I may consider suicide.
What or who do I trust? To what person(s) or cause(s) am I loyal?
How persons answer these questions tells them the object(s) and the content of their faith.
If Niebuhr is right, it makes no sense to exclude faith from science (or any other mode of inquiry, for that matter). For scientists exhibit both aspects of faith. There's faith as trust that the universe makes sense, it's worth investigating, and that the process of submitting one's work for peer review is necessary and worthwhile in the pursuit of truth. There's also faith as loyalty - in this case, loyalty to the scientific method and to the scientific community to which one submits the results of one's work. And the willingness to adjust and revise one's views in light of new evidence exhibits marks of both faith as trust and faith as loyalty.
If Niebuhr is right about faith at this basic dimension of attitude or posture towards the world and others, then the passive and active sides of faith are present in all human activity. So if we understand faith in terms of trust and loyalty, then science is just as much a "faith-based" enterprise as any mode of inquiry.
It does not follow from this that every scientist does or should embrace a particular religious faith or set of beliefs about God (much less claims of special revelation). To make that case would require additional argument. Nevertheless, Niebuhr makes an inescapably true point: "To deny the reality of a supernatural being called God is one thing; to live without confidence in some center of value and without loyalty to a cause is another" [Radical Monotheism and Western Culture (Westminster/John Knox, 1960), p. 25].