Many Worlds Interpretation: Does Quantum Mechanics Work This Way?

[Ken G]

As I said, I am using the word "model" in the model theoretic sense -- a model of a theory is, by definition, an interpretation for which the axioms of the theory are valid.

You still have it wrong, but I have to amend my language as well. The theory does give rise to a model, in the language you defined, so in that sense we have "models of the theory" not models of the universe. However, the universe is still not a model of the theory. This is the point, everything you listed in your "model theory" definitions are in our heads, and the universe isn't. So when I said the theory is a "model of the universe", in the language you are using, I meant the theory generates a model of the theory which is then tested as a "good" model when confronted with observations of the universe. Separating "the universe" from "what's happening in our heads" is the central concept of objectivity, so it is the very beating heart of the scientific method.

In science, it is more common to use the other meaning of "model" that you also mention, whereby we talk about "a good model of the universe", but I agree that is not precisely correct language within the scheme you have defined. Nevertheless, it carries the spirit much better than the awful "the universe is a model of the theory", which is really what I was objecting to, and indeed which remains the core of my objection to MWI-- I see MWI in exactly that light, people really think the theory is the truth and the universe is some kind of model of that theory. It's right out of Plato. Maybe Plato was right after all, but I see that as turning the scientific clock back thousands of years. Anyone who does not think that will certainly disagree with my assessment, I'll admit I'm being staunchly anti-Platonic.

But we can ask if a particular the universe is a model of a theory (under a chosen interpretation).

Did you really mean "a particular universe"? This is exactly my point-- imagining hypothetical universes to place "model theory" into a larger conceptual context is a mathematical device that can be pedagogically useful to science, but it is quite separate from the process of testing theories on the one universe we can demonstrate a connection with, and on whose back science is built.

Incidentally, I note the Wikipedia page on the meaning of the word that you're using (i.e. not the model-theoretic kind) explicity states that models have ontologies.

I admit that the word "ontology" can be taken to mean "pretending something exists in order to help visualize a model". As I've said many times now, if that's all people are doing when they talk about "many worlds", I have no objection at all. But a simple googling of "many worlds interpretation" generates immediate hits that put the lie to the claim that this is all it is being used for, and I listed them earlier. Furthermore, the same person on that other thread you allude to, who at one point distinguished between "real" ontologies and these more "pretend" flavor of ontologies, is also the person who clearly felt it was intellectually "lazy" to not use ontologies in the real sense of the word.