Since concepts, in the field of cognition, perform a function similar to that
of numbers in the field of mathematics, the function of a proposition is
similar to that of an equation: it applies conceptual abstractions to a
specific problem.
A proposition, however, can perform this function only if the concepts of which
it is composed have precisely defined meanings. If, in the field of
mathematics, numbers had no fixed, firm values, if they were mere
approximations determined by the mood of their users—so that “5,” for
instance, could mean five in some calculations, but six-and-a-half or
four-and-three-quarters in others, according to the users’ “convenience”—there
would be no such thing as the science of mathematics.