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I don't follow the last part about insurmountable incompatibilities or conflicts between physical theories. The universe does not - at least as far as we can te
by danbruc 12y ago
I don't follow the last part about insurmountable incompatibilities or conflicts between physical theories. The universe does not - at least as far as we can tell - blue screen and present us a speed of light exceeded, unexpected singularity or unsupported particle interaction error. The laws of nature seem to work in a flawless and consistent manner.
Maybe we are just to dumb to discover a theory or set of theories that describe nature in its entirety in a consistent manner using the language of mathematics. Maybe we are not to dumb, maybe such an theory does not exist because for some deep reasons there ere just no mathematical expressions describing (some parts of) nature. Maybe we can only get away with using some really huge lookup tables to describe nature. Maybe even lookup tables are not up to the task.
But what seems absolutely impossible to me is that we have different correct theories, i.e. they describe nature flawlessly where they apply, but they nonetheless lead to inconsistencies or contradictions.
- phkahler 12y ago>> But what seems absolutely impossible to me is that we have different correct theories, i.e. they describe nature flawlessly where they apply, but they nonetheless lead to inconsistencies or contradictions. But isn't that exactly where we are with quantum mechanics and relativity? Everyone thinks that if we were smarter or given more time, a unified theory will emerge that looks like one or the other at the appropriate scale. What if that never happens? I think the author is asking "What if that's not even possible?". It seems possible to him because there is no known reason for the mathematics to fit the world in the first place.
- danbruc 12y agoNo, we know that neither relativity nor quantum mechanics is correct, so the premise is already not fulfilled. And, as I said, too, it is very possible that we or mathematics fails to give a unified and correct description. But I just read the part again and I probably misread it the first time. He is not talking about having absolutely correct but inconsistent or contradicting theories, but about theories that are correct, consistent and non-contradicting where we can test them and maybe even where we can ever expect to test them, but ultimately lead to inconsistencies or contradictions if we extrapolate them beyond experimental reach. This leaves us in a situation where the theories are in perfect agreement with reality but on purely theoretical grounds it seems impossible that they are correct. This is more similar to the situation of relativity and quantum mechanics but we have not yet reached the experimental limits and the theories are not even in perfect agreement with all available data. (I will read it a third time, I am still not totally convinced that I got it right.)
- DenisM 12y ago>Maybe we are not to dumb, maybe such an theory does not exist because for some deep reasons there ere just no mathematical expressions describing (some parts of) nature. I find Godel's incompleteness theorem suggests there are fundamental limits to "knowledge" as we define it. http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_the...
- judk 12y agoThat only applies to infinity. A closed physical system (which a solar system approximates decently well) is not touched by it.
- eli_gottlieb 12y agoNo, that only puts limits on the provability of particular theorems in formal proof systems. Inductive reasoners have no such trouble.
- DenisM 12y agoI would think I that provability is of critical importance. Could you elaborate? Is there something I can read on this point of view?
- eli_gottlieb 12y agoFormal proof is not actually a part of real epistemology outside of mathematics.