Associate Professor, Department of Philosophy, Lewis & Clark College

# Kuhn on Incommensurability

Traditionally, we think of successive scientific theories in a given domain as accumulating more and more truths about nature; we continually build on what we already know. For example, many have argued that Newton’s classical mechanics is just a special case of Einstein’s theory of special relativity. In classic mechanics, momentum is given by p = mv whereas it is given by p = mv [(1 − (v/c)^2] in special relativity. When v << c, then p mv. Newton’s theory is a special case of Einstein’s. Thomas Kuhn denies that Einstein’s theory merely accumulates the truths of Newton’s and provides additional ones because the two theories are incommensurable. Here is Kuhn in his own words.
Can Newtonian dynamics really be derived from relativistic dynamics? What would such a derivation look like? Imagine a set of statements, E_1, E_2,…, E_n, which together embody the laws of relativity theory. These statements contain variables and parameters representing spatial position, time, rest mass, etc. From them, together with the apparatus of logic and mathematics, is deducible a whole set of further statements including some that can be checked by observation. To prove the adequacy of Newtonian dynamics as a special case, we must add to the E_i’s additional statements, like (v/c)^2 << 1, restricting the range of the parameters and variables. This enlarged set of statements is then manipulated to yield a new set, N_1, N_2,…, N_m, which is identical in form with Newton’s laws of motion, the law of gravity, and so on. Apparently Newtonian dynamics has been derived from Einsteinian, subject to a few limiting conditions. Yet the derivation is spurious, at least to this point. Though the N_i’s are a special case of the laws of relativistic mechanics, they are not Newton’s Laws. Or at least they are not unless those laws are reinterpreted in a way that would have been impossible until after Einstein’s work. The variables and parameters that in the Einsteinian Ei’s represented spatial position, time, mass, etc., still occur in the N_i’s; and they there still represent Einsteinian space, time, and mass. But  the physical referents of these Einsteinian concepts are by no means identical with those of the Newtonian concepts that bear the same name. (Newtonian mass is conserved; Einsteinian is convertible with energy. Only at low relative velocities may the two be measured in the same way, and even then they must not be conceived to be the same.) (1962/1970a, 102)

Questions: For Kuhn, why are these two theories incommensurable?