Just to put it out, I’m absolutely loving this discussion😛

But on one of the points you raised

“All sciences must work with tolerances to some specified resolution, be it in measurement or statistical.”

I don’t think this is true either, if a theory is in fact true it should be able to predict occurrences to the utmost amount of scrutiny possible and it should do so reproducibly.

If it fails to do so there is something wrong with it.

If you mean resolution of the measurement devices, then that’s a limitation on the device not the science or theory if the theory is true it must be true for when we have better devices.

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Newtonian physics works perfectly well as a theory until you move to quantum or cosmological scales. Nothing wrong with using in the correct scope. Theories will always be correct until they aren't, and then (hopefully) new theories emerge which are able to be applied more generally. Those theories will also be true, until they aren't 😉

Yes and we should not treat Newtonian gravity as a right theory anymore since we now know by measurement that it’s not, and even when we thought it was, it was reproducible at the known scales. Not sure how this is contradicts what I said previously though.