So: I am not too worried about the universe being uncomputable.

On the race to superintelligence, there are more pressing things to worry about than such possibilities - and those interested in winning that race should prioritise their efforts - with things like this being at the bottom of the heap - otherwise they are more likely to fail.

I don't think that Solomonoff induction has a problem in this area - but it is a plauisble explanation of what the reference to "higher-order logic" referred to.