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@magitweeter @Radical_EgoCom perceptible means you can sense it with your senses. Quarks are imperceptible and all the evidence for their existence is circumstantial. The world reacts to inquiries as we would expect it to if quarks exist. This can't reasonably be called proof since it's essentially deducing the antecedent from the consequent, but it's all we can do in science. Even freaking Karl popper thought so.

But that's exactly the kind of evidence there is for the existence of God. Assuming God exists has adequate explanatory force in some people's authentic worldviews. Just not yours, though.

None of this is anything like mathematical existence proofs, which are either constructive=perceptual, like your group example, or non-constructive, like nothing outside of mathematics.