Yes, I figured something your view is something like that from your responses. There are other tegermak fans on here as well and I don't want to start yet another argument against it.
As you probably already guessed, I do not share tegemarks reasoning.
I have tried to explain my conceptual position position to other realists on here before. But I definitely have answers to your questions of "what is in it's place" etc, they challange is to provide an argument in a form that is acceptable, from your point of view so to speak, which has proved tricky.
I might comment more later, but not that I do not deny existence of laws, I just claim that from the point of view of something that makes a real difference - the action of a system - the only importance is the inferrable laws, and the inferrable laws are relative to the inference system, and thus observer dependent, and thus evolving with the observer.
Objectivity is simply emergent consensus to the exten possible, in a local group of interacting observers, but there is always a residual disagreement, and this residual disagreement becomes not "relative law" but rather defining the symmetry groups and gauges that are part of describing interactins. Ie. the residual subjectivity is the set of observer frames, and the emergent objectivity is the symmetry transformation that allows for some kind of invariant formulation.
But even this objectivity is evolving, since it's constrained to the inferrability condition.
// Note that I am more radical, or perhasp more definite that smolins idea here, but I share the basic arguments of smolin against timeless law
The predictive power in my view is the fact that the action of such a system, depends on these things. The fact tht a system can not infer a particular regularity in it's environment, means that systems action is invariant to the choice of regularity.
I think if you insist in tegemarks terms, my objections would amount to insisting that his mathematics is uesless or lacking predictive power unelss the computability and representation capacity is taken into account. Can you even define the say the set of all mathematics? it makes no sense ot me. Also a mathematical system tht isn't computable by a computer at hand (rather than imaginary computers larger than the universe itself) doesn't offer predictive power. The predictive power comes only when you actually complete a computation. Also the computational time is an issue.
With inferrability law, I more or less talk about the constraint on "mathematical regularties" that come from the limtis of complexity of the inside observer.
The size of somebodies brain pretty much sets a limit of what can be comprehended. I think there is an analogy to physical law, to the extent what regularities in the action one system can infere from another system.
Sorry to not have more at the moment. This is a bried motivation only. The ultimate exposition of this in terms of something that is doing real predictions is still owrk in progress in my part. I'm not aware of anyone else either that has more than fragments implemented.
As for Tegemarks resoninng, I would similarly ask how tegemarks idea can help solve open problems in physics, and the unification of QM and GR etc. This is the real question. all this prior to that are just motivation in different directions.
Not sure if that makes anything clearer, probably not
/Fredrik