## ABSTRACT

Numerosity is just one dimension along which quantities can be compared. Others are length, area, volume, and mass. Similarly, counting is just one of a class of procedures for comparing quantities. Indeed, both discrete and continuous quantities can be compared without any reference to number. For example, two collections of discrete objects can be precisely compared by putting elements of the two collections into one-to-one correspondence until all the elements of one collection have been exhausted and then determining whether any elements of the other remain unpaired. Two lengths can be precisely compared by placing them side by side in order to determine whether either one extends past the end of the other, or by using an intermediary such as a stick, and comparing how far along the stick each of the lengths extends. Volumes can be compared by placing two quantities into identical containers (or placing each volume in succession in the same container) and observing whether they rise to the same height.