Topoi Chapter 2

I actually started in Chapter 4 to get context for the earlier chapters, then worked backward and I’m working my way back forward again. There are definitely some subtle hints this theory plays at least some part in the mathematical aspect of the CTMU. The first example that comes to mind is in section section 2.4 on “a pathology of abstraction“. Paraphrasing, Goldblatt talks about mathematics developing via a pathology of abstraction where the mathematician observes some set of structures and extracts some commonality they all share. Then after the abstraction the mathematician looks for new instances of the abstracted pattern. Note the obvious resemblance to conspansion when reality is identified a self-reifying theory (MP 4.6). Another interesting similarity is in the use of identity: In Category Theory an object is sometimes identified with it’s own identity function (Goldblatt 2.5), while Langan defines an identity as a self-dual intension | extension coupling (MP 6.6). Simply map intension to identity function and extension to object and these two are effectively the same (If you allow an object to be both the object and the identity rather than just one of them). This is even self-dual: If you swap object, identity, domain, and codomain you have the same object you started with.

Note: I haven’t uploaded all my pages, just a few to show effort.