In case of failure, one could a priori choose between changing the formal rule of extrapolation, and changing one s coordinates. And indeed in practical applications, a first step in analysing data is often to attempt linear optimisations in different coordinates, and to see if any such descriptions are satisfactory. We see that one adapts one s language to the world in the attempt to preserve a rule of inductive inference. The relevance of this remark will become clearer in discussing our next example. Drawing on what we have learned in the previous example, we shall now look at an example that is even more realistic.
Every body remains in a state of uniform rectilinear motion unless compelled otherwise by forces.
Any two bodies attract each other by a force proportional to their masses and inversely proportional to the square of the distance between them. These laws are descriptions of regularities, and we can take them as rules fixing which regularities we are allowed to project. To be more precise, projectible regularities re fixed by these laws in the following sense. In order to make predictions, we first attempt to describe the observed data in terms of these laws, and if we succeed, we are then licensed to make predictions about the unobserved future or retrodictions about the unobserved past by projecting these observed regularities. This may be an extremely complex procedure.