THERE seems to be little agreement as to the importance of the so-called 'problem of simplicity'. Weyl said, not long ago, that 'the problem of simplicity is of central importance for the epistemology of the natural sciences'.1 Yet it seems that interest in the problem has lately declined; perhaps because, especially after Weyl's penetrating analysis, there seemed to be so little chance of solving it.
Until quite recently the idea of simplicity has been used uncritically, as though it were quite obvious what simplicity is, and why it should be valuable. Not a few philosophers of science have given the concept of simplicity a place of crucial importance in their theories, without even noticing the difficulties to which it gives rise. For example, the followers of Mach, Kirchhoff, and Avenarius have tried to replace the idea of a causal explanation by that of the 'simplest description'. Without the adjective 'simplest' or a similar word this doctrine would say nothing. As it is supposed to explain why we prefer a description of the world with the help of theories to one with the help of singular statements, it seems to presuppose that theories are simpler than singular statements. Yet few have ever attempted to explain why they should be simpler, or what is meant, more precisely, by simplicity.
If, moreover, we assume that theories are to be used for the sake of simplicity then, clearly, we should use the simplest theories. This is how Poincaré, for whom the choice of theories is a matter of convention, comes to formulate his principle for the selection of theories: he chooses the simplest of the possible conventions. But which are the simplest?____________________