Physicist Max Tegmark is widely known for proposing that there is a multiverse where mathematical structures would exist as real and actual universes (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)
He has suggested that his mathematical structures would be completely consistent. He uses Hilbert's definition of mathematical existence (Which basically says that as long as a mathematical structure is consistent, it will exist)
But he published a relatively recent paper (https://arxiv.org/pdf/0704.0646.pdf) where he says:
I hypothesize that only computable and decidable (in Gödel’s sense) structures exist
This confused me a lot since Gödel's incompleteness theorems deduce that undecidability implies consistency, and decidability implies inconsistency.
So what is happening here? Is he proposing inconsistent mathematical structures as existent now? Did he change his mind?
This confusion gets worse at the end of the article, where he said:
According to the CUH, the mathematical structure that is our universe is computable and hence well-defined in the strong sense that all its relations can be computed. There are thus no physical aspects of our universe that are uncomputable/undecidable, eliminating the above mentioned concern that Gödel’s work makes it somehow incomplete or inconsistent.
This seems to contradict Gödel's theorems: If a universe would be completely decidable defined and complete, wouldn't that mean that it would be inconsistent?