That question is the origin of the entire discussion! If you don’t think there is an important distinction between: a) most people need to use faith to believe most science; and b) most people do not need to use faith to believe in most science then what on Earth have we been arguing about?
You said that most people basically have faith in scientific conclusions, other said that’s not faith, argument ensued. If you think the question of what to call “faith” is entirely beside the point then we aren’t talking about anything.
If your point regarding direct experience is that you had a subjectively different experience by learning something through one method than by learning it through another, then I still disagree (I think the depths of self-deceit we are capable of extend to being wrong about our own direct experiences - and that goes doubly for experiences we had in the past; its uncontroversial that I could be very mistaken about whether I was hearing a ringing in my ears yesterday) but I don’t think the point is worth belabouring. My question is, why is that difference in your experience at all relevant to the question of whether:
A) We should call belief based on reports of scientific consensus “faith”; and
B) We should call belief based on direct verification of facts for ourselves “faith”
You feel differently and you behave differently if you have understood the proof. But I feel differently and behave differently if I have a slice of cake in front of me than if I don’t. You have to meaningfully connect that feeling and behaviour to the idea of “proof” if you want to argue that one state constitutes “belief without proof” while the other does not. If you really don’t want to argue that point then I would simply say “case closed.”
To answer your question about the epistemic difference between people who actually do the experiments and people who merely hear reports of them, I would say there is none. It is the method that determines the truth, no the people who do it. The result of any experiment has to be filtered through some medium to get to us and we can’t observe anything without changing it, and more people in the chain of broken telephone means there is more likely to be errors, and certain people have more competency to carry out the experiments than others and lots of other factors go into making a reasonable decision about whether to believe something or not. But it never comes down to taking someone’s word for it.
As I say above, I see points 1 and 2 having no impact on whether or not something constitutes proof. I also don’t see how 3 is relevant. In math you give credit to the person that finds the first proof, but you don’t go on using their proof if a better one is found. We improve things all the time, so priority doesn’t make something better or more proofy.
On 4 you are just wrong. If there is a consensus and a series of experiments are done to challenge it (because people like to see things reproduced) then the consensus will change because of published journals, not because everyone goes and verifies those experiments themselves. Reality is, consensus changes through second hand accounts.
My argument is that there is that the difference between the two things is not that one gives “proof” and the other does not. And thus, the difference between them does not allow us to distinguish between “belief without proof” or not. And thus, if we say that believing in a scientific consensus require “faith” in science then we are basically saying that believing the results of experiment we conduct ourselves in an exercise in “faith” as well. And by doing so, we have reduced the concept of “faith” to meaninglessness.