"It's pretty clear at this point that foundation projects in all areas have failed. There's no foundations to logic, there is no foundations to mathematics, and therefore, there's no foundation to science, there's noBoth "foundational" and "infinite regress" projects in science, logic, and philosophy have all failed. Religion fails at this also, but Christian just won't own up to it and admit it - they are in denial. The only real available recourse is "coherentism", which those in the religious community dislike. They crave their "certainty", even at the expense of intellectual integrity. So, abandoning the attempt at having "ultimate knowledge", we have an important difference between science and religion - science generates results that happen to strongly agree with what is happening in the real world, and religion does not. As Hilary Putnam put it: "Realism
foundation to any other belief system or way of acting. What we need is a different metaphor." And that different metaphor is the "network" of knowledge metaphor. Your insistence on finding a "basis" for all knowledge is old fashioned and no longer seriously considered by most philosophers, who instead prefer a "coherentist" or network approach which emphasizes the discovery of an intereconnected, mutually consistent, coherent network of information about the world, not an ultimate foundation. As Gödel and others showed, attempts to find the foundation of even the most solid logical systems is ultimately doomed. Russell, after years trying to derive a basis for Mathematics, finally gave up.
Religion generates none of the same types of useful and consistent results as science - it entails no novel predictions, is unable to retro-dict past events, and has generated no increased understanding of the cosmos (in fact, has been behind many historical misconceptions about how things work). The last time religion did anything useful in advancing knowledge was 800 years ago during the era of Medieval scholasticism. Its been downhill ever since.
Accepting the inherent uncertainty in all knowledge and the impossibility of certain knowledge, Naturalism is probably the correct way to see the world. Barbara Forrest, for example, describes Naturalism as "a generalization of the cumulative results of scientific inquiry". In other words, the best explanation for the success of science is that Naturalism is true. Given the proliferation of successful scientific explanations for phenomena, Forrest concludes that there is "an asymptotic decrease in the existential possibility of the supernatural to the point at which it is wholly negligible". If Naturalism were false, there would be some phenomena that could not be explained solely in terms of natural causes. However, because science can explain all of the "uncontroversial phenomena" we have encountered (i.e., known to have actually occurred) in terms of natural causes, there probably are no phenomena which cannot be explained in terms of natural causes. Therefore, Naturalism is probably true.
To quote Donald Simanek, of Lock Haven State College:
Some people are profoundly disturbed by the fact that reason alone can't generate truths. When the use of mathematics and logic in science is explained to them they respond, "If mathematics and logic can't produce absolute truths, then they produce only untruths or partial truths, and are therefore worthless." This sentence is itself an example of nonsense clothed in the appearance of logic.
It must be admitted at the outset that science is not in the business of finding absolute truths. Science proceeds as if there are no absolute truths, or if there are such truths, we can never know what they are. As the pre-Socratic skeptics observed: If we were to stumble upon an absolute truth, we'd have no way to be certain it is an absolute truth. The models and theories of science are approximations to nature—never perfect. But in most cases we know rather well how good they are. We can state quantitatively the limits of uncertainty of numeric results, and their range of applicability. Yet there's always the possibility that we may find exceptions to one of our accepted laws, or may even find alternative theories that do a better job than older ones.
Some critics of science attack this process of science, on the grounds that it cannot produce absolute truths. Theirs is a black/white view of the scientific process. Never mind that they have not proposed any other process that is capable of producing anything near the power and comprehensiveness of present science. They say that "Theory X" isn't perfect therefore it is "wrong".
There is no evidence of, or compelling reason to believe in, a metaphysical/religious teleology (an externally imposed purpose). We cannot detect any conscious entity or force that shapes our destinies, that cares about us, that reveals knowledge to us, or which has a stake in our existence. In other words, there is no evidence of an "intelligent design" or overall purpose or goal for the universe other than to continue to do what it does - exist. That minimal, modest, and economical claim is the only claim that the form of Naturalism I subscribe to asserts. It even allows for non-natural (supernatural) things to exist. But, if they do exist, they don't appear impact the natural world in any detectable way. This form of Naturalism doesn't restrict the natural world to the known forms of material existence with which we are familiar, and avoids the messy issue of the existence of abstract entities such as mathematical concepts, properties of objects, love, beauty, ideas, etc. It only subtracts teleology / supernatural causation, because we don't see it happening.