I'm speaking of Tolstoy, who said: "without faith it is impossible to live." He probably didn't mean it in the way I'm meaning it.
I mean that faith, which can be equated with trust (which in turn signifies inclinations of the will, i.e., you can't just "believe" without showing some type of change in your behavior), is needed to move and live for all of our philosophical assumptions which can't (because they're assumptions) be proven. Take the existence of the outer world, other selves, uniformity in nature, induction, etc. All these things are what we would call "common sense," but this doesn't undermine the fact that we can't (and no philosopher so far has) proven these using reason. They're intuitive or instinctual axioms we have about the world, arguably hard wired into us.
What happens if we doubt these? We can't possibly move or live; we're bound in a constant state of skeptical paralysis. Without faith we can't be human. Religious faith is another flavor of a faith that's essentially no different than the daily faith we have in our basic assumptions.
It seems to me that you want to establish a definition of "faith" that includes everything that isn´t known with 100% certainty.
And since we necessarily think within a given frame of reference, and this frame of reference can impossibly be proven correct, you want to establish a definition of "faith" that includes all fathomable statements and notions.
To be honest, I find that suspicious. It seems to me that you semantically wipe all the subtle and not so subtle differences in certainty, evidence, necessity between different notions - just so you can make metaphysical beliefs appear to be on equal footing with any other notion. From axiom to the wildest guess and conspiration theory: they are all "faith"-based.
I´m not willing to go there with you. Of course, you have the freedom to define "faith" any way you like - but if this is the definition you want us to use, I for one will insist that the substantial differences are henceforth represented by new words for these categories.
Apparently, when Tolstoi made his statement, he was indeed referring to axioms - assumptions that we can impossibly do without. These axioms are held by
everyone - and then there are these extra beliefs that we
can do and live without (like religious beliefs, conspiration theories, etc.). Some find them individually helpful, useful and convincing, but they aren´t axiomatic by any means.
Next, I don´t agree with your assertion that our behaviour represents our beliefs (as in: metaphysical truth claims). Personally, I do behave as if the outer world exists, as if it works the way we all observe it working - but I am not at all convinced that this is metaphysically true. I am accepting it as a useful (and often almost unavoidable) assumption - within the frame of reference of what our minds suggest to us (not individually, but collectively), but this doesn´t mean that I believe this very frame of reference to be metaphysically true. FWIW, we could all be brains in vat, we could be characters in a computer game, we could be ideas in a superbrain, I could be the only real person (and everyone else being a product of my imagination) or whatever: picking one of these frames of references over "the world as it appears to us is real" wouldn´t change my behaviour one iota. Whether the natural laws are real laws in a real nature, or virtual natural laws in a virtual nature that I am virtual part of, makes no difference whatsoever when it comes to my behaviour. They are reliable within the frame of reference I am existing in - no matter what this frame actually is (or what I believe it to be).
So, no, my behaviour doesn´t allow any conclusions on what I do or don´t consider metaphysically true.