Abstract

1. Mr. Grünbaum says, "it is clearly meaningless to say that one object is larger than another unless there is a...common metrical framework to which...these bodies can be referred." But he also says, as one ought, that "sodium atoms separated by...light years...share the characteristics of sodium." Apparently he and I agree that sodium atoms, x and y, can share the characteristics of sodium without the need of an intermediary third term. Substitute "sodium similarity" for "share the characteristics of sodium" and we get "x and y have sodium similarity." Substitute "magnitude" for "sodium" and it then becomes evident that equal magnitudes can be members of two-termed relations. And since a larger body is a body, part of which has the same magnitude as the whole of another, unequal magnitudes can also, despite his denial, be related by two-termed relations. It would be foolish, of course, to deny that a metric introduces a third term. But must there not be something for the metric to measure? It was with this something my paper was concerned. I take it to be presupposed by the theory of relativity, and the theories which will follow it in the course of the history of science. Mr. Grünbaum, if I understand him, gets to his conclusion because he arbitrarily identifies "being" with "being known," "magnitude" with "measured size."