There are several traditional models of computation such as Church's lambda calculus, Herbrand-Gödel equational calculus and representability in formal systems of arithmetic, that appear unrelated to the general framework of physics. The extreme example in this context is Fenstad's axiomatization of computability. On the other hand, several models that are often more popular with theoretical computer scientists and complexity theorists such as Turing machines, register machines and cellular automata are physics-like in the sense that they are arguably realizable in any plausible model of physics. Of course, all these logical models are equivalent in a certain precise technical sense, but implementations of the latter class are far more direct and they avoid tedious coding issues. The question thus arises whether any insights into the nature of computability can be gained from a careful study of logical versus physical computation. As a case in point we consider discovered rather than constructed universal systems and the old problem of the epistemological status of intermediate recursively enumerable degrees.