That's absurd, if it cannot be observed (Perceived) it doesn't exist (For you).
Oh, it's observed all right -- but the observation is personal, not verifiable.
To explain a little better, many Christians accept the "Bible" as an authority of divine revelation. It's the starting place and foundation of their beliefs... a premise.
As such, it is also the lens through which they observe.
So now they observe and credit God as being present in situations that non-Christians would not, which in turn reinforces what they've already accepted as divine revelation. It's a circular loop.
(Note, that does not say they're wrong, nor that they're right... just that there is no way to evaluate something that claims to be "divine revelation.")
You might have as your premise that "truth must be observable." That is an assumption the presupposes that divine revelation does not exist. It colors all of your observations.
We always bring some type of presupposition to our observations.
That's exactly what I want to do. Hmmm, so you say it's not doable?
For the reasons I said above, I don't think that two people who possess differing presuppositions/authorities can convince each other of anything, because they do not share common ground rules.
At best, you are forced to find the common ground -- some sort of sensible life experience that seems similar for you both -- and this means the argument becomes less about what can be "specifically proven" and more about what seems "more reasonable" to the typical human being.
I think some sorts of observations are quantifiable... which means in part that anyone who measures/evaluates the object in question will come up with the same answer. (The most obvious are size, weight, color, things like that.)
But objects just are not objects. We attach meaning to every object we run into. For example a pencil is to write with -- but it could also serve as a stabbing tool, or a thing to pry open a stuck desk drawer, or something to break when you are mad, or a host of other uses. Those uses are not predetermined and are based in large part on what assumptions the person is bringing with them.
Now imagine something INTANGIBLE, where two people assume different things right off the bat (God is the "God of the Bible" versus no God, or God is something else entirely) and how much more difficult it is to reach a consensus between them. Until one of them changes their framework (the foundation shifts), they will never agree or even really comprehend.
So you want to deal with the foundation, if anything, and not the cosmetic issues. (i.e., don't argue about what functions a pencil is good for, argue about why a pencil is being perceived a certain way and whether that makes sense as the only valid framework).
Does this mean that impressions like the one with the deity are nothing more then concepts?
How about "choices" based on "concepts"? There is a strong element of choice involved: "I choose to believe this is true because I think it is worth believing in."
But if impressions are concepts then I think one would need a context to place them in, or perhaps they could be described through their internal context, things they are associated with. For example, multiplication could be quantifiable if we observe it as some kind of a sequence of operations, addition would be one, multiplication two, exponentiation three and so on or we could view it as a member of the family of operations on numbers, or both.
Well, that's one way people do argue about God and other things -- by trying to reduce the discussion to a progression of internally consistent algorithms/proofs. (If this = this, and that = that, then this = that.) It's just that things such as the Bible are assumed to be God's divine revelation, so the only way around it is why making that assumption might be unreasonable or unlikely. Once you bump someone into your own frame of reference (or vice versa), a real discussion can occur.
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I am trying to get past all the abstract language we've both used to get to the kernel of your post, just a little fuzzy yet for me here...
You probably would also benefit from trying to see things from their frame of reference, even if you disagree with it, especially if you plan to try to bump them into yours. It's only fair, right? And making that sort of effort would only be aided, the more you can momentarily see things the way they do.
You can try to observe something not by looking at it directly, but by looking "around" it or noting it much from the effect it seems to cause on its surroundings. (Just like we "see" black holes, for example, from all the radiation pouring off of them. We see what's around them, but we do not actually see them.)
If you want to see the Christian God, for example, I would look at how it impacts the people who claim to be in God's proximity -- who did they used to be, have they changed, do they behave differently because of their faith, how much have they changed, does it inform their life, is their life a "desirable" one, do they seem at peace while still being very engaged in life, and so on. Would the person be different today if they did not believe in God? If they were just trying to be "good on their own," could they maintain the same level of compassion/goodness/whatever they are showing now?
Is that the sort of thing you are thinking?