I think you're right, OP, to recognize that measurements don't validate themselves—they require what we might call interpretive faith in the adequacy of our theoretical frameworks.
Let's consider the structure: A measurement only means something within a theoretical context that tells us (1) what we're measuring, (2) why this particular quantity matters, and (3) how to interpret the numerical result.
But how do we know if that theoretical context itself is correct? After all, we have no "view from nowhere" to confirm that our theoretical schema actually carves reality at its joints. We can't step outside our conceptual frameworks to verify they correspond to reality-as-it-is-in-itself. Indeed, we learned from Heisenberg that those kinds of confirmations can't be done – we, the observer-participants, are part of the mix.
Your comments reminded me of the Duhem-Quine thesis: when measurements conflict with predictions, we face underdetermination—we can preserve theory by adjusting auxiliary hypotheses, or vice versa. The choice of what to revise involves commitments that transcend the measurements themselves.
I take it, OP, that you are pointing to something like this: scientists must have faith that their measurement practices track real features of the world, not merely that instruments produce consistent numbers. The leap from "my REW software outputs these frequency response curves" to "these curves represent the actual acoustic properties of my room" requires trusting that our theoretical apparatus (wave theory, Fourier analysis, transducer calibration assumptions) adequately maps reality.
Perhaps, OP, you overstate calling this "faith" in the religious sense—implying it's evidence-free. A better framing might be that it's not "faith" but a "provisional commitment" – to fallible frameworks that have proven pragmatically successful, which we hold with appropriate epistemic humility about their completeness. The faith isn't blind; it's a bet that inquiry converges, down the road, on pragmatic truth.
