José Félix Costa (Lisbon)
We suggest that the Turing machine is a good model of a scientist,
both in the task of monitoring (let us say) measurement experiments in
Physics and in the task of establishing physical laws from those
measurements, providing mathematical support of concepts in the
philosophy of science.
Is the physical law computable or rather non-computable? We show that, in our model, once the observed phenomenon departs from pure randomness, a law of physics can be Turing machine computed from observations, regardless the computable or non-computable character of the observed phenomenon. Then we suggest that the price of such derivations is the disunity of science, a generic non-unification theorem.
To state and prove the above mentioned results, we have included in our previous model of a scientist conducting an experiment in Physics some concepts of computational learning theory, generalising the known computational EXplanatory classes EX, EXn and Behaviourally Correct classes BC and BCn to non-computable functions.
Then we revisit Popper and Kuhn theses in the new PREDictive PRED-identification paradigm and prove our formulation to be sound with respect to a notorious case study in the history of science.