A law is any equation that describes the world accurately. Moore's original article about doubling capacities does not print an actual equation (and so does not propose a law), but it uses graphs from which equations can be inferred. The second graph shows a trend of log2 Ncomponents/die ? t . This was amended later, to reflect that the doubling period had shifted to every two years, when semiconductor technology matured.
The first graph is actually more interesting, as it shows a trough-shaped function of cost vs. integration at each process point: the lowest cost per transistor is not at the greatest possible level of integration, but the one that optimizes device yield against packaging and interconnection costs. This graph foretells multi-chip modules among other things.
The original article (in Electronics 38.8, April 1965) has some other interesting predictions:
"There is no fundamental obstacle to achieving device yields of 100%." Well....
His observations about linear (analog) circuits being less amenable to miniaturization because capacitance and inductance cannot be shrunk as much as gain elements, and the coming of monolithic differential amplifiers, are all very astute. The paper includes a great number of predictions, which have all (with the exception of 100% yields) been borne out.