So, I took a short pause before giving a thoughtful response. I really enjoyed your post. As far as I understand, you're proposing a more integrated model of faith and knowledge, one where the paradox is resolved through a redefinition of concepts.
We all know that “certain” knowledge is aspirational. We all know that we know nothing certain. So, we should always qualify our “knowledge” claims with “at least that is what I believe to be the case.” All scientific knowledge is subject to future falsification. — Fire Ologist
Here I partially agree. Everything we call knowledge (including in the scientific sense) is ultimately based, to some extent, on belief. None of us possesses absolute knowledge in any field, science, or judgment. We possess knowledge that is sufficiently justified (for us). Knowledge that is sufficiently justified (for us) is everything that a person accepts as true and acts upon (including both rationality and belief). Sufficiently justified knowledge, however, includes both a rational (verifiable) component and an unverifiable component.
I agree with this statement.
Expressed mathematically, this formula would be roughly as follows:
[Sufficiently justified (for the subject) knowledge] minus [Rational knowledge] equals [Faith]
In Russian, there is a special word for "sufficiently justified (for the subject) knowledge" – "pravda." In everyday speech, we say, "This is my pravda"—that is, it is how I reasonably believe, based on rational and irrational judgments, and act in accordance with it. Example: someone who says, "My pravda is that the Egyptians built the pyramids" expresses their reasonably well-founded knowledge, based on archaeological evidence (the rational part) and the decision to stop doubting (faith). This is their "pravda," which motivates them to take action (for example, writing articles or teaching). In Russian, there's also the word "istina" (truth), which is equivalent to "truth" in English. But the concept of "pravda" (truth) is not the same as "truth" (truth), although translators will translate it that way. There are many other cultural features associated with Pravda that I thought you might find interesting, and that are relevant to our discussion.
However, I would like to clarify your answer in another part:
The difference between what religious faith is and what scientific knowledge is has to do with what justification is employed. It’s not a difference that creates this preacher’s paradox. The preacher has to remain logical and provide evidence and make knowledge claims, just like any other person who seeks to communicate with other people and persuade them.
So really, there is no difference in the mind between a religious belief and a scientific belief - these are objects someone knows. They are both knowledge. The difference has to do with what counts as evidence, and the timing of when one judges enough evidence and logic have been gathered and applied, and it is time to assert belief and to act. — Fire Ologist
In the previous text, I distinguished between the concepts of rational knowledge and faith. So, when it comes to religion, the part I called faith is dogmatized and not subject to criticism. When it comes to science, the part of our judgment that I call faith is presupposed, but can be refuted. This resonates with Popper's ideas.
That is, you and I, as educated people with a scientific bent, can debate this or any other topic, but our discussion has the potential to evolve: I can agree with you; you can agree with me; we can come to something new together. But this is completely impossible when it comes to intra-dogmatic discussion.
Returning to our paradox, which you've certainly mitigated with your judgment: the paradox still exists. If dogmas were subject to revision, that would be fine, I'd agree with you, but dogmas are not subject to revision (that's what religion is for). Therefore, I conclude that the paradox remains.