I think of faith as code that is running on your brain, shaping what you perceive to be true in the absence of evidence. Making faith fully compatible with evidential truth and reason is hard, and usually requires minimizing its ontological claims?
I know the proof for the undecidability of the Halting Problem. Measuring and quantification don't come into play. If by "proof of God" you mean a logical proof of the existence of an entity denoted by a concept formed over phenomenological facts, you may make a category mistake.
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I don’t like either terms in this context - “proof” or “God”. When people use the term proof they often mean evidence. When people use the word God they are often referencing the mythology of formalized religion and not the ontology of the “God Concept”.
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