Here is where I think we part ways, philosophically speaking:
> If we keep in mind the difference between what we can rigorously establish and what we’re fundamentally taking on faith (however well-founded)
From my perspective, we're taking everything in the real world "on faith" (and there is a loaded phrase ripe to be deliberately misinterpreted) to a certain extent, and not just because of brain-in-a-vat arguments. For example, I sit in chairs thinking they're solid objects, but they're made of solid objects and might well collapse under me. In my experience, that doesn't happen to me, so my heuristic is that chairs are safe, but a heuristic isn't rigorous. It's "faith" if you want to phrase things that way.
Moving deeper, I trust that my senses provide me with accurate-enough reflections of reality I can use them to navigate my world safely, but I know enough about neurology to know that that isn't a given. Vision is reconstructed by the visual cortex from messy and incomplete nerve signals from the retinas, our sense of 3D space is reconstructed (based on low-level heuristics) from a pair of 2D images reconstructed from those messy retinal signals, and so on, from the bottom of the neurological hierarchy to the top of the conscious sense of self. The human machine lives off of best-guess reconstructions from incomplete and messy data.
This isn't mere acatalepsy, however: I think humans live in a physical world we're capable of perceiving accurately enough, and comprehending well enough, that we can accurately say we live in a real and comprehensible external Universe, and that some things don't go away even if you don't believe in them. Therefore, it's possible for our heuristic judgements to become more accurate at predicting reality over time, which is what separates knowledge from dogma.
Accepting that an authority is probably more likely to be right than wrong is a heuristic, and that heuristic can and should be improved, but all of our knowledge of reality is heuristic, so trying to treat reality like an axiom system is philosophically wrong-headed and incapable of dealing with the full complexity of reality as well.
I'd agree with almost all of that, but with two additions: I think we can locally approximate reality as an axiomatic system, with the axioms just being the stuff we've decided to treat as true for the moment. When the context changes what counts as an axiom changes, but that only rarely happens to me with chairs.
Second, I think there's at least a rough partial order on the things people propose as axioms: the order of how surprised I am when someone contests one, if you like. Very surprised, if it's the existence of external reality; not too surprised at all, sadly, if it's whether biologists are to be trusted over the pastor at their church on the origin of species.
The nice thing about that machinery is that when you meet the second sort of person, you're not forced to believe that they're fundamentally irrational and immune to all reason.
One more thing: trusting experts is a very convenient heuristic for me individually, and I use it all the time, but it's not epistemelogically all that useful. In principle you can always replace an appeal to the authority of a genuine expert with the evidence that they rely on to come to their judgement: if you can't, then they're speaking outside of their expertise. No one of us can win an argument on the internet that way; time is finite and we each only know so much. But if we all chip away at it, by supplying evidence where and when we can, we might get somewhere.
> If we keep in mind the difference between what we can rigorously establish and what we’re fundamentally taking on faith (however well-founded)
From my perspective, we're taking everything in the real world "on faith" (and there is a loaded phrase ripe to be deliberately misinterpreted) to a certain extent, and not just because of brain-in-a-vat arguments. For example, I sit in chairs thinking they're solid objects, but they're made of solid objects and might well collapse under me. In my experience, that doesn't happen to me, so my heuristic is that chairs are safe, but a heuristic isn't rigorous. It's "faith" if you want to phrase things that way.
Moving deeper, I trust that my senses provide me with accurate-enough reflections of reality I can use them to navigate my world safely, but I know enough about neurology to know that that isn't a given. Vision is reconstructed by the visual cortex from messy and incomplete nerve signals from the retinas, our sense of 3D space is reconstructed (based on low-level heuristics) from a pair of 2D images reconstructed from those messy retinal signals, and so on, from the bottom of the neurological hierarchy to the top of the conscious sense of self. The human machine lives off of best-guess reconstructions from incomplete and messy data.
This isn't mere acatalepsy, however: I think humans live in a physical world we're capable of perceiving accurately enough, and comprehending well enough, that we can accurately say we live in a real and comprehensible external Universe, and that some things don't go away even if you don't believe in them. Therefore, it's possible for our heuristic judgements to become more accurate at predicting reality over time, which is what separates knowledge from dogma.
Accepting that an authority is probably more likely to be right than wrong is a heuristic, and that heuristic can and should be improved, but all of our knowledge of reality is heuristic, so trying to treat reality like an axiom system is philosophically wrong-headed and incapable of dealing with the full complexity of reality as well.