I don’t know exactly what it’s called. Phenomenology, empirio-criticism, Machism — these are closely related currents. Rationality according to Yudkowsky will be closer. The formalization of this theory is called AIXI.
Ideologically similar to the scientific method, but a little wider. I did not come up with it, I just systematize a little and go through the objections I know.
To some extent, this approach is an alternative to the philosophical currents of materialism and idealism, and in addition, it underlies one of the theories of AI.
A bit of background
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* Your approach is based on axioms, just like the approach of such and such. You just believe in some other stuff.
- The above approach is based on prior probabilities, not axioms. The difference is that the prior probabilities are primary assumptions, and they will definitely change as we go. We use the mathematical apparatus, and therefore the axioms of probability theory, to measure accuracy. This does not mean that we are at the mercy of initial assumptions - it means that we use the language of matstat to express our thoughts. It can be used to describe almost any rule by which the quality of a model is judged.