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Message: <blockquote data-quote="EzekielRaiden" data-source="post: 9576192" data-attributes="member: 6790260">The only axioms it requires are the ones required to do calculus. That's it. If you think calculus works, then this works. (Mostly because Lagrangians are just systems of differential equations.)Solipsism is not a particularly productive or useful philosophical approach.It is not possible that they could derive mathematics that also work but which deny Noether's theorem. Your insistence on the total absence of any form of knowledge does you a disservice.If they develop something that is of equivalent descriptive power to calculus, they will derive their equivalent of Noether's theorem. It is not logically possible for them to develop something that can do what calculus does and somehow disprove Noether's theorem. It is one of the most fundamental, bedrock parts of mathematical physics--and it is a mathematical proof. All you need to do is observe a symmetry in nature to find the conservation law. E.g. the fact that physics works the same at time t0 and different time t1 requires that energy is conserved. (And, importantly, if it isn't conserved, the theorem also proves that there must be some kind of damping effect.)Frankly? I don't trust most scientists to say a damned thing about philosophy, which is what they're doing here; that's not a physical claim, it's a metaphysical one. Mostly because--from experience, as someone who actually has studied both--most hard-science scientists couldn't philosophize their way out of a paper bag with the bottom cut out. What passes for "philosophy" amongst most physicists, biologists, and chemists rarely rises to the level of an introductory freshman course.</blockquote>

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