On 7/8/2013 7:07 PM, Shmuel (Seymour J.) Metz wrote: > In <S42dnXXbbOzYOETMnZ2dnUVZ_sadnZ2d@giganews.com>, on 07/07/2013 > at 12:28 PM, fom <fomJUNK@nyms.net> said: > >> Coming from one who slipped in a few references >> to New Foundations in other threads, this is surprising. > > NF is somewhat out of the mainstream, albeit interesting. I'm > wondering what the people who start from Category Theory do about > cardinals and ordinals. >
I have worked out many of my questions with respect to classical logic and set theory. It is probably time to tackle category theory.
In spite of its apparently simple formulations, its history arises out of algebraic topology. So, it will be a lot of work. It has been a while since I looked at that subject.
>> So, if one asks "What is a number?" > > I'd answer "Whatever it is productive to call a number." I certainly > don't take issue with the nomenclature "Cayley Number". >
That is an entirely different can of worms. :-)
I spent a great deal of time trying to understand the origin of "undefined language primitives". Part of that story is the introduction of arithmetical systems such as the complex numbers and the quaternions. It is the beginnings of universal algebra and model theory.