I want to take my idea of a coding invariance principle further (see my earlier post defining the philosophical principle).

What do we mean when we say "The law of gravity is true"? We could mean that the law of gravity matches all the available data. We could even require that it matches all true statements about the universe (or does so to within some degree of approximation). But more might be required. We might ask that there is no other simpler theory that matches the world as well or better.

What if there are two theories explaining different physics (like quantum mechanics and relativity) and a third simpler theory comes along that explains both areas (the very small and the very large) better than either theory. This third theory might be simpler than the combination of quantum mechanics and relativity. But in this case would it make sense to say quantum physics is true or even the best theory for the very small anymore?

Clearly its conceivable that a theory explains a narrow domain well but is superseaded by a theory which is little better on this domain but explains a much wider domain and therefore is a better theory overall. A theory could also be better at explaining that narrow domain than our original theory in which case you would also say that it was a better theory.

A significant question is then "Is there a best theory to explain any domain of our universe?". It is consistent that the answer is no and that for any theory there is another theory which is either more elegant (explains more with little additional complexity) or explains the same data with a higher degree of accuracy.

This isn't to say that in such a universe science could not progress and make better predictions over time. However, it does draw into question whether it is meaningful to talk about a theory giving a truthful description of the universe.

There are various bizarre possibilities in such a universe:

For instance the best available theory may keep changing its opinions on matters such as:

1) Whether the universe had a beginning

2) What exactly happened in the past

3) Whether the universe is infinite

4) The number of dimensions the universe has

A universe that has many partial descriptions matching 1,2,3,4 would be a strange beast indeed but it would certainly be an interesting place to reside!

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