Scientific epistemology has a distinction between realism and instrumentalism. According to realism, a theory tells you what kind of entities do and do not exist. According to instrumentalism, a theory is restricted to predicting observations. If a theory is empirically adequate, if it makes only correct predictions within its domain, that’s good enough for instrumentalists. But the realist is faced with the problem that multiple theories can make good predictions, yet imply different ontologies, and one ontology can be ultimately correct, so some criterion beyond empirical adequacy is needed.
On the face of it, Solomonoff Inductors contain computer programmes, not explanations, not hypotheses and not descriptions. (I am grouping explanations, hypotheses and beliefs as things which have a semantic interpretation, which say something about reality . In particular, physics has a semantic interpretation in a way that maths does not.)
The Yukdowskian version of Solomonoff switches from talking about programs to talking about hypotheses as if they are obviously equivalent. Is it obvious? There’s a vague and loose sense in which physical theories “are” maths, and computer programs “are” maths, and so on. But there are many difficulties in the details. Not all maths is computable. Neither mathematical equations not computer programmes contain straightforward ontological assertions like “electrons exist”. The question of how to interpret physical equations is difficult and vexed. And a Solomonoff inductor contains programmes, not typical physics equations. whatever problems there are in interpreting maths ontologically are compounded when you have the additional stage of inferring maths from programmes.
In physics, the meanings of the symbols are taught to students, rather than being discovered in the maths. Students are taught that the “f” in f=ma, f is force,”m* is mass and “a” is acceleration. The equation itself , as pure maths, does not determine the meaning. For instance it has the same mathematical form as P=IV, which “means” something different. Physics and maths are not the same subject, and the fact that physics has a real-world semantics is one of the differences.
Similarly, the instructions in a programme have semantics related to programme operations, but not to the outside world. Machine code instructions do things like “Add 1 to register A”. You would have to look at thousands or millions of such low level instructions to infer what kind of kind high level maths—vector spaces , or non Euclidean geometry—the programme is executing.
It’s how science works: You focus on simple hypotheses and discard/reweight them according to Bayesian reasoning
It’s not how science works, because science doesn’t generate hypotheses mechanically, and doesn’t attempt to brute-force-search them.
Versus: it only predicts.
Scientific epistemology has a distinction between realism and instrumentalism. According to realism, a theory tells you what kind of entities do and do not exist. According to instrumentalism, a theory is restricted to predicting observations. If a theory is empirically adequate, if it makes only correct predictions within its domain, that’s good enough for instrumentalists. But the realist is faced with the problem that multiple theories can make good predictions, yet imply different ontologies, and one ontology can be ultimately correct, so some criterion beyond empirical adequacy is needed.
On the face of it, Solomonoff Inductors contain computer programmes, not explanations, not hypotheses and not descriptions. (I am grouping explanations, hypotheses and beliefs as things which have a semantic interpretation, which say something about reality . In particular, physics has a semantic interpretation in a way that maths does not.)
The Yukdowskian version of Solomonoff switches from talking about programs to talking about hypotheses as if they are obviously equivalent. Is it obvious? There’s a vague and loose sense in which physical theories “are” maths, and computer programs “are” maths, and so on. But there are many difficulties in the details. Not all maths is computable. Neither mathematical equations not computer programmes contain straightforward ontological assertions like “electrons exist”. The question of how to interpret physical equations is difficult and vexed. And a Solomonoff inductor contains programmes, not typical physics equations. whatever problems there are in interpreting maths ontologically are compounded when you have the additional stage of inferring maths from programmes.
In physics, the meanings of the symbols are taught to students, rather than being discovered in the maths. Students are taught that the “f” in f=ma, f is force,”m* is mass and “a” is acceleration. The equation itself , as pure maths, does not determine the meaning. For instance it has the same mathematical form as P=IV, which “means” something different. Physics and maths are not the same subject, and the fact that physics has a real-world semantics is one of the differences.
Similarly, the instructions in a programme have semantics related to programme operations, but not to the outside world. Machine code instructions do things like “Add 1 to register A”. You would have to look at thousands or millions of such low level instructions to infer what kind of kind high level maths—vector spaces , or non Euclidean geometry—the programme is executing.
It’s not how science works, because science doesn’t generate hypotheses mechanically, and doesn’t attempt to brute-force-search them.