Incomputability at the foundations of physics (A study in the philosophy of science)

摘要

In this article, we show that once we assume that there is some uniformity in Nature, empirical laws and theories involving the concepts of Physics can be learned by the scientists. We develop a mathematical framework to explain learnability of empirical relations. Then we classify the degree of learnability according to the degree of predictability by means of timescales. We also use the same mathematical framework to make formal the claim that learnability evolves according not only with the number of observations done, but also with the precision of measurements.