Incommensurability then and now

Summary

The incommensurability of scientific theories is not the only famous incommensurability issue in the history of western philosophy. The commensurability of all magnitudes (things) by means of ratios of integers (arithmetical ratios) wasthe thesis of Pythagoreanism. The diagonal and side of a square, however, are not commensurable, thus the Pythagorean thesis is refuted. Most philosophers ancient and contemporary would agree that Pythagoreanism was refuted by the counter-example and the concommitant argument or proof. The incommensurabilists were victorious. The present paper examines the prospects of the contemporary thesis of the incommensurability of scientific theories in the light of the history of the Pythagorean thesis. What factors were responsible for the rather clear-cut victory of theincommensurability side? How were they able to carry through a refutation? How likely is it that the contemporary dispute over the commensurability of scientific theories will be resolved in such a sharp manner? The paper concludes that it is not at all likely.