ReL "I have evidence that he plagiarized."
 
Good question!  The description that best approximates the function of
"that he plagiarized" -- though I know it doesn't hit it on the head --
is that it is an appositive in apposition to "evidence."
 
Donald Emery, in a pamphlet called *Sentence Analysis* gives this example
of an appositive noun clause:
 
"The announcement that taxes would be lowered was happily received."
 
"That taxes would be lowered" seems more closely in apposition to
"announcement", perhaps, than "that he plagiarized" is to "evidence<' but
not so very much closer, it seems to me.
 
If this description won't work, how about calling "that he plagiarized"
an appositive of an elliptical "fact" in an elliptical prepositional
phrase: "of the fact>"
 
We use a similar concept to describe a relative clause that refers to a
whole idea as antecedent, as in (Donald Emery's example again) "I arrived
quite late, which annoyed my hostess" -- which Emery reads as  "I arrived
quite late, [a fact] which annoyed my hostess."
 
So we could read "I hasve evidence [of the fact] that he plagiarized<" in
which case "that he plagiarized" is an appositie of "fact."
 
Michael Kischner