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On Discovering Scientific Laws
José Félix Costa

We review how inductive methods operate on recursive data to uncover empirical laws as those of Physics, as well as the research programme of weakening learning criteria aiming at identifying the class of recursive functions.We think that this work should be better known, namely as of applications to understand large scale limitations of scientific discovery. Methods of recursion theoretic learning theory are also revised to cope with difficulties in the cases of infinite self-reference of identification theory.

There are two main concerns in this paper. The first is to convince the reader that the set of recursive relations is a good model of the universe of potential empiric laws. The second is to make the point that any such law can potentially be discovered by an unconventional scientist that accepts to weaken the criteria of what is “to know a law”.

This paper can be read by any patient reader with some experience in programming.

Keywords: Empirical science, Ex- and Bc-identification, infinitary self-reference, learning empirical laws, limits of algorithmic learning, recursiontheoretic machine learning

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