ABSTRACT
The principal measures are length or extension in space, time, angle, temperature and mass. There are also many other measures, example those for volume or capacity and electric charge. Every local authority has a department of weights and measures to ensure the correct standards, that is using the concept of one-to-one correspondence between the standard and each individual scales or measure. The measurement of time has very special problems and different scales, although with scientific advances the measurement has become more accurate. The cardinal numbers of axiomatic set theory are completely different. They are the numbers of collections of things, objects or members. Cardinal numbers are the numbers used for counting the individual members of a set, group, class or aggregate. The change from reality as a collection or aggregate or class of individuals to reality as one thing, one being, one object — the cosmos — entails a radical change in the conception of logic.
