I think it is an error to turn faith into any kind of epistemic category—and I don’t think that’s what Paul, (as for the example quoted byJS357) had in mind. One has faith—confidence/trust—in the face of uncertainty. This is particularly emphasized in the Young's Literal Translation he listed:
“And faith is of things hoped for a confidence, of matters not seen a conviction.”
{This is not so difference from a similar use in sports psychology, in which confidence/faith/”belief” is counseled—not as a rational conclusion based on the evidence, but as an instrumental attitude that will enhance the likelihood of success in the face of uncertain conditions. Philosophically, faith can be seen as an existential attitude of hope and confidence in the face of existential uncertainty—and I think that theological usage—e.g. in St. Paul—can best be seen as an extension of this usage.}
Let’s take logic for example: one does not need to have faith that ~(A & ~A), or [If p then q; p; therefore q]. The opposite of these is not falsity, but absurdity. Similarly, one can prove that the set of all integers is infinite, and one need not then have faith.
Knowledge is standardly defined epistemologically as “justified, true belief”—that is a belief (opinion/conclusion) that one can justify rationally or empirically, and turns out to be true. Thus, there is also a kind of ex post facto element to empirical knowledge. If it turns out to no be true after all, that does not mean that the underlying belief (opinion/conclusion) was not justified at the time—it just means that it wasn’t really knowledge.*
{All that is why I think the word “believe”, in modern conventional or epistemic usages, is no longer a good translation (or is, at best, confusing) of the Greek pisteo—at least not in a New Testament context. }
A soteriology based on fear (by which I mean “fright” or terror or anxiety, which is not the Proverbial “fear of God” ) may well push people beyond faith into desperate (and even idolatrous) demands for certainty. I am not attributing that to anyone here (I certainly cannot), but just making a general observation. And, according to Paul, it is not faith that casts out fear by giving certain knowledge—it is love that casts out fear, as we forget ourselves and act for the beloved.
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* Note, however, that knowledge in the NT does not principally refer to epistemia or oidos, but gnosis, especially, I think, in Paul. Gnosis especially refers to direct apprehension or recognition or intimate familiarity—for example, I see my wife across the room. I know that it is her without any further investigation. This is the kind of knowing, I think that Wittgenstein (in his On Certainty) argued makes the grammatical addition of “I know”—as in “I know that is my wife”—both redundant and somehow confusing; it is sufficient to say, “That’s my wife over there.” [Barring some weird fantasy/science fiction scenarios—none of which would make me actually investigate who belongs to that lovely face that I recognize as my wife’s.]
Gnosis can also refer to esoteric or mystical knowledge—but need not. It is also used to refer to sexual intercourse.
The following statement by Paul seems almost to be like a Zen koan, intended to elicit at least some uneasiness about knowledge claims (and I think that the generalization reaches beyond the immediate context):
NRS 1 Corinthians 8:1 Now concerning food sacrificed to idols: we know that "all of us possess knowledge." Knowledge puffs up, but love builds up.
2 [/i]Anyone who claims to know something does not yet have the necessary knowledge[/i];
3 but anyone who loves God is known by him.