Is Belief a Function of Evidence?
"A wise man," the great Enlightenment philosopher David Hume asserted famously, "proportions his belief to the evidence." Hume, readers may recall, was one of the leading spokesmen for the empiricists, those skeptical, science-minded types who maintained against their rationalist counterparts that a belief is justified only when founded firmly upon evidence borne of experience. Hume's modern-day disciples appear no less committed to that belief (though it's never been clear just what the evidence is that is supposed to justify it). In an age given to the glorification of natural science and its technological outgrowths, this sort of evidentialism-empiricism does hold a certain appeal as the outlook shared by most scientists and other professing intellectuals. Moreover, it has become the weapon of choice for atheists in arguments against Christian theism. Richard Carrier for example says:
So the supposed evidence that Christians try to offer for God's existence, creative activity, or goodness simply doesn't cut it. It turns out not to be evidence, but theories about otherwise ambiguous evidence, theories that themselves remain unproven, and often barely plausible when compared with more obvious alternatives that more readily explain the full range of evidence we have. Therefore, the Christian theory has insufficient support to justify believing it.
Carrier is clearly overstating his case. Yet it may come as a surprise to some that for many instances of belief, Christians like me would actually tend to agree with the empiricists. If someone were to tell me they have seen Bigfoot, for example, or a ghost, or an amputee restored to wholeness upon the utterance of an evangelist's prayer, I would not simply believe the claim without further substantiation of some kind. I would want to know answers to questions like, "Did other people see this, and if so, what kind of people are they?", or, "Was this sighting recorded or documented anywhere?", or "Are there any accessible sources of trace evidence for the event?" I'm sure Hume would approve of this cautious withholding of belief.
Hume's point about "proportion" is also well taken. Evidence increases the probability that a given hypothesis is true, and thereby strengthens belief in that hypothesis accordingly. It seems to follow that among rational thinkers belief grows stronger with the accumulation of supporting evidence; and conversely, belief weakens with the failure of evidence to support it. Philosophers often employ Bayes' theorem to express this positive relationship between belief and evidence in mathematical terms.
On the other hand, there seem to be limitations to how far Hume's empirical principle should extend. For starters, it's not always easy to say just what constitutes "evidence" in the first place. Evidence has been defined in terms of sense data, physical objects like documents and inscriptions, widely accepted true propositions, and even beliefs simply held with psychological certainty. Thomas Kelly observes:
Both in and outside of philosophy, the concept of evidence has often been called upon to fill a number of distinct roles. Although some of these roles are complementary, others stand in at least some measure of tension with one another. Indeed, as we will see below, it is far from obvious that any one thing could play all of the diverse roles that evidence has at various times been expected to play.
Evidence usually plays a significant role in supporting hypotheses; but this implies that at some point hypotheses have been proposed. Data by themselves have precious little to say. Apart from a hypothetical context put in place by the human imagination, potential sources of evidence like orbital motion, continental drift, interference patterns of light, specified complexity, the empty tomb of Jesus, the conversion of Saul of Tarsus, or even a smoking gun, would not have the power to suggest, let alone confirm, the truth of a hypothesis. In a sense, the "belief" that leads to the proposal of the hypothesis must precede its confirmation.
And the fact that many of our most basic, foundational beliefs (in the reality of the external world, say, or the veracity of logical axioms, or the reliability of our senses) cannot be confirmed by any form of evidence suggests, again, that there are limitations to how much epistemic work evidence can actually perform. Perhaps we have been designed to believe. Confirmation bias, meanwhile, appears to be a universal psychological tendency among humans – scientists included – which indicates that human beliefs are often impervious to evidence. Important as evidence is, clearly other factors drive our beliefs.
One of these factors is desire. As it's often said, "We believe what we want to believe." The fact is, even if it's true that we can't always choose whether to believe in a given proposition or worldview, we do generally choose what we want to believe. We strongly tend to feed those beliefs we want to affirm, and starve the beliefs we would rather repudiate. Thus an atheist who says he would really like to believe in God, but spends all his time on message boards and blogs arguing against that belief at every opportunity, is not being entirely honest. The same could be said of a Christian who complains that his faith is weak and he just can't help it, but spends little or no time in prayer or meditating on the words of Scripture. For all of us, belief has a way of aligning itself with the heart's desire and picking up where evidence leaves off. Or as Hebrews says it, "Faith is the substance of things hoped for, the evidence of things not seen" (Heb. 11:1).
 Richard Carrier, "Why I Am Not a Christian," The Secular Web (2006), https://infidels.org/library/modern/richard_carrier/whynotchristian.html#noevidence. Curiously, Carrier then adds, "And this would be so even if Christianity was true. For even if it is true, we still don't have enough evidence to know it is true." Is he hedging his bets here?
 For a couple of articles among many on this blog addressing evidence for Christianity, see my recent "Shreds of Evidence," http://christiancadre.blogspot.com/2017/04/shreds-of-evidence.html, or, "Evidence of Openness," http://christiancadre.blogspot.com/2016/02/evidence-of-openness_13.html.
 Thomas Kelly, "Evidence," Stanford Encyclopedia of Philosophy (July 28, 2014), https://plato.stanford.edu/entries/evidence/
 See for example Karl Albrecht, "The Real Reason We Believe What We Believe," Psychology Today (April 21, 2014), https://www.psychologytoday.com/blog/brainsnacks/201404/the-real-reason-we-believe-what-we-believe.