Sorry I’m a year late to the party. Just wanted to remark on this:

“Thinking about it like a mathematician, I see no reason whatsoever to privilege statements with a single universal quantifier, over statements with any other combination of quantifiers.”

We do have Universal Algebra going for that one 😛

]]>Anybody with basic knowlegde about mathematics, logic, computabilty theory and propabilty theory immeditaly undertands that this is naive at least.

1) There is nothing like a “set of all mathematical structures” (Russel). This directly leads to inconsistency!

2) For probability theory to work we need a countable sample space.

What is possible is to define a constructive subset of mathematics defined by certain (countable many) turing machines. This has been done by Jürgen Schmidhuber and is at least a proper consistent theory of Mathematics/computabilty theory.

But as of today real world Physics does not even seem to be computable. This means following standard Physics, our universe is not one of the universes defined by Jürgen Schmidhuber!

I could now go into detais, but the sheer fact that the author does not seem to be aware of this basically takes away all credibilty.

The next step would be taking into account quickly computable universes and to play around with those.

Two easy predictions:

If our universe is constructive (based on any turing machine) then QM is ontologically wrong (Whatever exactly this means).

Second if our universe is quickly computable, then QM is wrong and experiments should eventually show this

(Quantum computing does not scale in such a universe).

I’m not a huge fan, but I am willing to cut the string theorists some some slack. Relativity and QM (1) fit the world exceedingly well, even better than Newtonian mechanics and Maxwell’s E&M did, and (2) hate each others mathematical guts at least as fiercely as Newton’s and Maxwell’s equations did. By thinking very hard about the mathematical inconsistencies between successful theories, the string theorists are continuing a tradition which has enjoyed considerable success in the past. Unfortunately in practice there is room for a lot of nonsense in thinking very hard — we have mercifully forgotten a lot of the silly dead end things that were pondered in trying to work out QM especially — but in principle it’s not obviously a waste of time, even if all you really care about is the falsifiable stuff that (you hope) comes out at the very end.

Thinking very hard about how to reconcile Newton with Maxwell was very fruitful for Einstein, thinking very hard about how to reconcile Schroedinger/Heisenberg with Einstein was very fruitful for Dirac and for Feynman/Schwinger/Tomonaga — after which I lose the thread ’cause I mostly know about stuff that can be seen without enormous particle accelerators and sensitive cosmological experiments, but there are probably a few other names after that. Out of that thinking very hard fell falsifiable predictions about e.g. mass and energy, about antimatter, and about volumes of precise spectroscopic data for weakly bound electrons and — unfortunately largely obscured by nasty computational difficulties of computational chemistry and solid-state physics — rather large effects in behavior of strongly bound electrons in ordinary materials and chemical reactions. I think by the time you get to QED people had a pretty good idea what kind of falsifiable results they were looking for while they were poking around in the math, but I think Einstein and Dirac would have had a hard time telling you in advance that their theories would tell you about mass-energy equivalence and antimatter respectively.:-| So it’s not always realistic to demand that mathematical physicists pay their falsifiability rent in advance.

]]>Now, regarding string/M-theory, you’ve put your finger on exactly the sorts of issues people argue about today. As I understand it, string theory has passed some stringent mathematical consistency checks, and it’s also arguably made striking “mathematical predictions”—mostly concerning dualities and mirror symmetries—that were then confirmed by more rigorous methods. So, a string-theory supporter might ask, *why isn’t that good enough?*

Other people might respond that it’s not good enough because there are many beautiful areas of pure math (e.g., elliptic curve theory) that *also* “pass stringent consistency checks” and *also* “make striking mathematical predictions,” but that need not have anything directly to do with the physical universe. So, passing this sort of test can at most establish string theory as a beautiful branch of math, not as a correct physical theory.

As you point out, another argument that’s often made is that string theory “predicts” many of the same things that established physical theories do: e.g., it “predicts” that, at low enough energies, the world should look like it’s described by general relativity plus quantum field theory. However, skeptics would reply that that’s not good enough, because GR and QFT were already known at the time string theory was formulated! Indeed, the way you get string theory is (essentially) to start with all the tools for doing calculations in QFT, and then “upgrade” the point particles to extended objects.

Now, when you do that, you find that you get out GR as a “free, unexpected bonus.” That is indeed a remarkable fact: it’s the fact that got Witten and others excited about string theory in the first place, and that’s helped keep interest in the field alive for decades. But again, skeptics would say that it’s not remarkable *enough*, if one wants to establish string theory as the true fundamental theory, rather than “just” a good mathematical tool for understanding other theories. For a theory to achieve the status of (say) GR or quantum mechanics, many people would demand more: they’d demand that the theory tell us things about the physical world that we *didn’t* already know, and which we can then go out and verify are correct. (And of course, many string theorists themselves fully accept that as the standard, and have been trying to meet it.)

Obviously, I’m asking in reference to the endless debate over whether string theory/m-theory are scientific or not. The fact that they do predict many of the same things that classical theory predicts says something doesn’t it?

]]>http://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3Daps&field-keywords=rafe+champion

To understand Popper it is necessary to come to grips with at least six themes in his work, some of which represent a significant turn from the mainstream of epistemology and the philosophy of science. These are (1) the idea that all our knowledge is radically conjectural (2) the idea of public or objective knowledge in addition to our subjective beliefs, (3) the rejection of the quest for the essential meaning of terms, (4) the “rules of the game” or the social turn as Ian Jarvie called it to take full account of the social nature of science and the role of methodological conventions, practices and protocols (5) the evolutionary approach to take full account of the Darwinian revolution and (6) the return of metaphysics to the heart of science and the philosophy of science in defiance of the positivists who wanted to cast it out.

Happy reading!

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