Solomonoff induction is the theoretical ideal: assign probability to every computable hypothesis in proportion to its simplicity, then predict by averaging. Given enough data, the predictor converges on the truth faster than any computable alternative. It is optimal, universal, and incomputable.
Sterkenburg (arXiv:2603.20274) shows the incomputability is not a practical limitation but a structural impossibility. Two reasonable desiderata for a universal predictor — that it be computable and that it converge to the true distribution regardless of what the true distribution is — cannot be jointly satisfied. A generalization of Putnam's diagonalization argument proves this: for any computable predictor that works on all computable distributions, there exists a computable distribution where it fails. The wall is built into the mathematics.
This means Solomonoff induction is not an ideal that we approximate by relaxing computability. It is an ideal that cannot exist in the first place, because the two properties that make it ideal are incompatible. You can have convergence on all distributions (but the predictor is incomputable), or you can have a computable predictor (but it fails on some distribution). The tradeoff is not engineering — it is logical.
The practical consequence touches Occam's razor. Solomonoff induction is often cited as the formal justification for preferring simpler hypotheses: the prior assigns higher probability to shorter programs, so simpler explanations dominate early predictions. If the theoretical framework that justifies this prior is itself incoherent — not just impractical but logically impossible as a computable ideal — the justification for Occam's razor doesn't inherit the formal blessing it's usually given.
Sterkenburg doesn't argue that simple hypotheses are bad. The argument is narrower: the specific formal machinery that seemed to prove Occam's razor optimal can't do what it claims. The preference for simplicity may be justified — but not by appeal to a predictor that cannot exist.