Axiomization of Mathematics - Easter Egg

An axiom (ak-see-uhm) is a noun and is defined as the following:

Much work has been done concerning the production of a full-set axioms that provide for a foundation for all mathematical treatments.
The following brief web-clip discusses some of the widely-accepted and well-known work of nineteenth- and twentieth-century mathematicians, such as Gottlob Frege and Bertrand Russell.

It should suffice in saying that mathematics, albeit ancient, still is highly-immature and unformed in many aspects. And, much might be done in developing a unifying foundation built of axioms which support the entire field of mathematics. Intuition would suggest that one first unite the notions of an implement, its aggregations, and uses with that of containers such as sets and a system of logic. Such would address the most fundamental and foundational units found among the branches of modern mathematics.

Also, described in the web-clip above, Russel’s paradox is much like Zeno’s. It baffles, bewilders, and befuddles, at first; however, it is not intellectually tortuous and might easily be addressed. With the latter, one must accept that every step is of a minimum given size, an atomic distance. In the case of the former, one must admit that the field of set theory by its nature must permit the presence of sets which hold various categories of exception for any given set and its rules of construction. And, in terms of the members of a exceptional set, they might only have transient membership in the set under consideration, such as the set S of all sets which do not contain themselves. This set S cannot be a member of itself. Yet, when, it is not; it should be. So, its membership is dynamic alternating between inclusion and exclusion in S. So, it might be placed in a set of dynamic exceptions called S’ and dealt with accordingly.

Whether, such an observation would be sufficient for supporting the claims of logicism is a matter of investigation.