However, if reformulate the hypothesis as “the cause of patients symptoms is cancer”, it can be treated by SI. Reductionism says that “the patient has cancer” can be translated to a statement about physical laws and elementary particles. There are problems with such a reduction, but they are of practical nature. In order to apply SI, everything must be reduced to the basic terms. So human-identified, macro-scale patterns like “cancer” must be reduced to biochemical patterns, which in turn must be reduced to molecular dynamics, which in turn must be reduced to quantum mechanics. Doing these reductions is not possible in practice due to computational limitations—even if we did know all the laws for reduction. But in theory they are fine.
A problem of more theoretical nature: whatever evidence we get in the real-world is probabilistic. SI supposes that our observations are always 100% correct.
On the other hand, it’s intuitively obvious that if we treat some high-level concepts as irreductible entitities, then a form of Solomonoff induction can be applied directly. E.g. it can be used to a priori prefer “the cause of the symptoms A, B and C is cancer” over “”there are three unrelated causes a, b, and c to the three symptoms A, B, and C”.
It seems to me, however, that SI is not very useful if there are other reliable methods of determining the probabilities. For example, “the single cause of the two patient’s symptoms is bubonic plague” in the modern world is a hypothesis of low probability even if it is the shortest one, as the empirically-determined a priori probability of having bubonic plague is tiny.
A good point!
However, if reformulate the hypothesis as “the cause of patients symptoms is cancer”, it can be treated by SI. Reductionism says that “the patient has cancer” can be translated to a statement about physical laws and elementary particles. There are problems with such a reduction, but they are of practical nature. In order to apply SI, everything must be reduced to the basic terms. So human-identified, macro-scale patterns like “cancer” must be reduced to biochemical patterns, which in turn must be reduced to molecular dynamics, which in turn must be reduced to quantum mechanics. Doing these reductions is not possible in practice due to computational limitations—even if we did know all the laws for reduction. But in theory they are fine.
A problem of more theoretical nature: whatever evidence we get in the real-world is probabilistic. SI supposes that our observations are always 100% correct.
On the other hand, it’s intuitively obvious that if we treat some high-level concepts as irreductible entitities, then a form of Solomonoff induction can be applied directly. E.g. it can be used to a priori prefer “the cause of the symptoms A, B and C is cancer” over “”there are three unrelated causes a, b, and c to the three symptoms A, B, and C”.
It seems to me, however, that SI is not very useful if there are other reliable methods of determining the probabilities. For example, “the single cause of the two patient’s symptoms is bubonic plague” in the modern world is a hypothesis of low probability even if it is the shortest one, as the empirically-determined a priori probability of having bubonic plague is tiny.