Solomonoff induction is uncomputable because it requires knowing the set of all programs that compute a given set of data. If you just have two hypotheses in front of you, “Solomonoff induction” is not quite the term, as strictly understood it is a method for extrapolating a given sequence of data, rather than choosing between two programs that would generate the data seen so far. But understanding it as referring to the general idea of assigning probabilities to programs by their length, these are still uncomputable if one considers only programs that are of minimal length in their equivalence class. And when you don’t make that requirement, the concepts of algorithmic complexity have little to say about the example.
Solomonoff induction is uncomputable because it requires knowing the set of all programs that compute a given set of data. If you just have two hypotheses in front of you, “Solomonoff induction” is not quite the term, as strictly understood it is a method for extrapolating a given sequence of data, rather than choosing between two programs that would generate the data seen so far. But understanding it as referring to the general idea of assigning probabilities to programs by their length, these are still uncomputable if one considers only programs that are of minimal length in their equivalence class. And when you don’t make that requirement, the concepts of algorithmic complexity have little to say about the example.