This, and your links to Lob's theory, is one of the most fear inducing piece of writing that I have ever read. Now I want to know if I have understand this properly. I found that the best way to do it is to first explain what I understand to myself, and then to other people. My explanation is below:

I suppose that rationalist would have some simple, intuitive and obvious presumptions a foundation (e.g. most of the time, my sensory organs reflect the world accurately). But apparently, it put its foundation on a very specific set of statement, the most powerful, wild and dangerous of them all: self-referential statement:

*Rationalist presume Occam's razor because it proof itself *Rationalist presume Induction razor because it proof itself *etc.

And a collection of these self-referential statement (if you collect the right elements) would reinforce one another. Upon this collection, the whole field of rationality is built.

To the best of my understanding, this train of thought is nearly identical to the Presuppositionalism school of Reformed Christian Apologetics.

The reformed / Presbyterian understanding of the Judeo-Christian God (from here on simply referred to as God), is that God is a self-referential entity, owing to their interpretation of the famous Tetragrammaton. They believe that God is true for many reasons, but chief among all, is that it attest itself to be the truth.

Now I am not making any statement about rationality or presuppositionalism, but it seems to me that there is a logical veil that we cannot get to the bottom of and it is called self-reference.

The best that we can do is to get a non-contradicting collection of self-referential statement that covers the epistemology and axiology and by that point, everyone is rational.