Yes, at times these concepts are interchangeable because faith (and knowledge) can be viewed as subsets of belief. Knowledge is justified belief, while faith represents belief held in the face of uncertainty. Faith often entails elements like optimism, trust, or hope, while knowledge is grounded in beliefs that have been substantiated. Belief, more broadly, is the acceptance of something as true. We are in agreement on these distinctions. We only began discussing subsets when you mentioned that I "interchange" these terms. The fact is, it’s not problematic to do so occasionally, as we both acknowledged, and yet there remain important distinctions, as we both agreed.
The point of contention seems to be your assertion that “you don’t need faith (or optimism) if you have evidence.” Perhaps you intended to say, “You don’t need faith (or optimism) if you have all the evidence (which is equivalent to proof).” In that case, I would agree. If all the evidence is present, faith becomes unnecessary, as certainty is achieved. However, as I pointed out earlier, sometimes some evidence (such as a good movie trailer & cast) doesn’t fully prove a proposition (whether the movie will be good). If you choose to trust the claim and fill the gap of uncertainty with faith, you’re still holding a belief, albeit one under uncertainty. This exemplifies that it’s possible to have both faith and evidence for the same proposition, thereby countering the claim that “faith is belief without evidence.” Faith, therefore, must be more accurately defined as “belief in a proposition despite incomplete certainty, lacking definitive proof, or full evidence.”
After I clarify next my concept of evidence, I’m confident we can integrate all these ideas more cohesively.
The final point of disagreement is in your criteria for evidence. I, too, differentiate between evidence and proof. Evidence refers to any information, facts, or materials that may support or substantiate a claim, argument, or belief.
By "information," I mean that it could be subjective and, perhaps, unconvincing to some (and maybe even to me). However, the crucial point is that it remains information related to a proposition. You are not compelled to irrationally accept or believe this evidence if it’s insufficient, but it is still considered evidence.
Consider a situation where a friend claims that your neighbor won five million dollars in the lottery. The strongest evidence would be the lottery ticket itself, bank statements, signs of wealth and so forth. But what if for now you just have your friend who says, “My wife who knows a friend of your neighbor’s wife told me…”? In this instance, the evidence is hearsay, which is weaker and less reliable. While it’s still technically evidence, its worth is diminished because it lacks the immediacy and trustworthiness needed to reliably validate the claim. It still serves as a piece of information pointing toward the proposition. No one is forcing you to believe it. Acting on that evidence irrationally is the issue, not the evidence itself.
Evidence, in and of itself, isn’t classified as rational or irrational—those judgments apply to the conclusions drawn from it. Evidence is merely the material or information used to support a claim, and whether it’s rational or not depends entirely on how it is interpreted and applied when forming conclusions.
Just as many Christians possess a range of evidence supporting their beliefs, but the conclusions they draw are often not rational or logically consistent, the problem lies not with the evidence but with how it is used to form conclusions. The evidence may be weak, misinterpreted, or insufficient to conclusively support the claims, rendering the conclusions irrational, not the evidence itself.
Now, you may want to discuss how much uncertainty faith can reasonably fill before it becomes irrational, which I’m sure is something we both care about. But that’s a separate issue.
For example, after watching a well-crafted movie trailer featuring a talented director, producer, and cast, based on an acclaimed book, you may be 85% certain the movie will be good. In this case, faith isn’t bridging too large a gap. The belief that the movie will be good is justified by the available evidence, though it remains uncertain. In such a case, faith can coexist with evidence.
However, if you only know the movie title and have no further information, but you believe it will be good simply because you like the title, this would be an irrational faith/belief. This is when faith is used to fill an overly large gap of uncertainty, making the belief disproportionate.