Does this phrase have a name or something with which to search it up? When I try to, no authorized website shows up to provide a source in writing, except for purpose usages ''so as to'', which isn't what I wanted.
Some would say that this is a
result-clause construction, that is, a construction involving a result clause. In generative syntax, the grammar of these is very complex. I would never recommend that a learner explore the formal syntax of these, which is complicated even for native speakers who have studied formal syntax for many years!
It is far more important for learners to understand what these constructions mean and how they are put together and used. Nevertheless, I can appreciate the desire for a name. Recently, I read an article by a former professor of mine (which he co-authored with a professor at U.C. Berkeley) in which this type of construction is briefly discussed at the end (see pp. 17-19 at link 2 below). They use the umbrella term
"as"-comparatives.
1.
https://www.phon.ucl.ac.uk/home/PUB/WPL/97papers/white.pdf
2.
http://linguistics.berkeley.edu/~mikkelsen/papers/CP_complements.pdf
It should not bother you if you can't find sentences with constructions specifically resembling "so stupid as to believe his so-called claims" at the links above. If you understand the meaning of such constructions, then you understand that we are talking about the same
type of thing when we analyze constructions like "so stupid that she believed his so-called claims" or "too stupid to believe his so-called claims."
The basic syntactic point is that the result clause is intimately related to the degree word ("so," "as," "too," etc.). The result clause may be said to be the complement of the degree word. Incidentally "DegP" stands for "Degree Phrase."
