Did Wheeler really believe that physics was undecidable? John Archibald Wheeler was a famous physicist

It has been stated that he thought that there was a strong connection between undecidability and quantum physics 


  This idea was given an early formulation by Wheeler
  himself: in unpublished notes to a discussion held with,
  among others, Roger Penrose and Simon Kochen, he
  identifies the point of origin of the ‘quantum principle’
  as the undecidable propositions of mathematical logic


(https://arxiv.org/pdf/1805.10668.pdf)

But then, this same physicist proposed that the universe was similar to a computer and that reality emerged as digital informational processes in form of bits (It from Bit): https://en.wikipedia.org/wiki/Digital_physics

As far as I know, digital physics models cannot be undecidable. They must be decidable (If not, we could never construct an algorithm which would get a correct answer to a yes/no question)

So, what is happening here? Did Wheeler change of mind?
The inference "the universe would be completely computable, so no undecidable/uncomputable things could exist" is invalid.

In the effective topos, where everything is computable, there are many undecidable phenomena. For example, all real numbers are computable, but equality of real numbers is undecidable (and computable).

To give you an idea how this happens: equality of reals is a map $\mathbb{R} \times \mathbb{R} \to \Sigma$ which is implemented by a Turing machine that takes (Turing machines that compute) reals $x$ and $y$ and returns a non-boolean truth value represented by a Turing machine which terminates if, and only if, $x \neq y$.

In contrast, equality of natural numbers is decidable. It is a map $\mathbb{N} \times \mathbb{N} \to \{0,1\}$ which takes two natural numbers and outputs either $0$ or $1$, depending on whether they are equal.

As far as physcists are concerned, I would be careful about learning computability theory from them. I wouldn't want anyone to learn physics from me.