  About 35 years ago Wheeler introduced the motto `law without law' to
highlight the possibility that (at least a part of) Physics may be understood
only following {\em regularity principles} and few relevant facts, rather than
relying on a treatment in terms of fundamental theories. Such a proposal can be
seen as part of a more general attempt (including the maximum entropy approach)
summarized by the slogan `it from bit', which privileges the information as the
basic ingredient. Apparently it seems that it is possible to obtain, without
the use of physical laws, some important results in an easy way, for instance,
the probability distribution of the canonical ensemble. In this paper we will
present a general discussion on those ideas of Wheeler's that originated the
motto `law without law'. In particular we will show how the claimed simplicity
is only apparent and it is rather easy to produce wrong results. We will show
that it is possible to obtain some of the results treated by Wheeler in the
realm of the statistical mechanics, using precise assumptions and nontrivial
results of probability theory, mainly concerning ergodicity and limit theorems.
