I disagree with his assumption,that a type cannot have itself as a member of itself. Everything else is solid prepositional calculus ala G.E.B. and its ideas are very interesting, but it seems as if it needs to be a larger work. ( It extremely terse. ). The other thing is that type is mostly data except for the type code, which if used as data i.e self modifying code is completely evil.
I now am very interested in reading more of what he has to say, but it's very theoretical,and has immediate practical applications.
In set theory, a universal set has a proper subset of itself, which is a kind of paradox. If you seperat universal sets into those that have paradoxes and those that do not, then, You would assume that the universal Set without paradoxes is neither a proper subset of itself or that it is not universal, which is a paradox putting the universal set without paradoxes into the set of paradoxical universal sets. ( This is all just a small single line of prepositional calculus. )
Now I see that I assumed that you can cleave the universal set and wind up with a universal set which means it's a proper set of itself, but I am not sure You can cleave a non-paradoxal set from a universal set.