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Mathematics is constantly proving things true. Physics also has theorems, for instance, the Stone–von Neumann theorem. The scientific method is a method for testing of hypotheses, yes, but that is simply one way of discovering what is true. Logic, testimony, written accounts and records, mathematical proofs, and so on are all other ways of discovering truth. For instance, you cannot prove who was the Emperor of Rome at a particular date in the past with experiments. You must use historical record to do so. Unless you call your experiment opening a book - but that's not a controlled experiment. And even if all books said that Marcus Aurelius was the Emperor of Rome on March 16, 180 you still wouldn't be able to prove it mathematically or using logic. You're using inference to the best explanation in a form of Bayesian probabilities. Even though it is a matter of fact that either he was or wasn't, there's no experiment you can run on that hypothesis that could tell you the truth. On your point 2, "X=>Y" indeed means X implies Y, so given X is true, Y is true as well. It could mean causality, but it could also mean necessity. So saying "X is true means Y is true" can be applied to numerous different contexts, including one of causality. I let go of the apple, and the apple falls. This last statement being equivalent to every body that is not subject to forces follows the geodesic created by the spacetime manifold. Which can be put in a logical form X=>Y. And on your first point: the natural world is clearly following mathematical truths, and that is the entire point of the conversation. The ask of "Why is nature consistent" implies something much much deeper about the nature of reality than what scientific experiments can show. It is a metaphysical question, not a scientific question. |
Well here I soundly agree with you. I believe that's what I was trying to communicate at the very start, when I said "those 'why' questions are exactly what math and science do not answer."
I suppose our difference relates to how we conceive of other kinds of "why" questions.
> Mathematics is constantly proving things true.
Also agreed with you there. That's one key difference between math and science, in my mind. For that reason, I suppose I'd put theoretical physics more in the "math" realm than the "science" realm, at least w/respect to the theorem you mention, and similar.
Small aside: thank you for the tenacious-but-respectful discussion — I always worry when a thread goes 3+ replies deep that it'll just become an angsty flamewar, so it's nice to have a counterexample in my training set (: