In modern German (and in other contexts) the noun "der Übergriff" is
but the literal meaning of the compound noun that is built from "über" and "Griff" comes from its components:
über (adjective, adverb)
der Griff (noun)
The noun "der Übergriff" as used in your text is much more related to the verb übergreifen than it is in modern German.
- übergreifen (verb)
- to encroach
- to grab over
- to overlap
- to flash over (fire)
Note, that there is a very similar German noun, that would also fit into the text instead of "Übergriff":
(der Begriff = term, concept; begreifen = to understand, to realize, but also to grasp. So "der Begriff" is the thing that you understand, and it comes from "the thing that you can grasp, touch and feel")
All in all, in this context I would translate Übergriff simply as
the umbrella term
This does not match exactly the intended meaning, but is very close.
Also note, that the author makes excessive usage of nominalization. This means here, that he uses terms as nouns, that in everyday speech would only be used as adjectives. You can do this in German, but it's rare and makes the text hard to read. You can find this stile often in old academic texts. (The intention of the authors was to deliberately make the text harder to understand, because they hoped, that the readers believe, that the author must be a genius if he is able to express himself this way.)
You have to translate the text together with the context and the intention of the writer:
- Man scheut sich, dem Logischen oder der Idee den Übergriff über das Reale einzuräumen.
- People are (one is) afraid to grant logicnoun and idea to stand above the real.
- Es gibt Denker, die das Ideale und das Reale wenigstes im Gleichgewicht halten möchten.
- There are thinkers (philosophers), who want to keep the ideal and the real on the same level. (literal: in balance)
- Aber wenn man dennoch das Persönliche will, so sollte man bedenken, daß die Persönlichkeit, ihrem Wesen nach, ein über das Real-Natürliche Übergreifendes ist und auf einem Geltendmachen der Idee beruht.
- But if you still want the personalnoun, so you should reflect, that personality by nature is something that covers the real-naturalnoun and is based on an assertion (enforcement) of the idea.
(Literal: "... personality by nature is an over the real-natural spanning" where "over the real-natural spanning" has to be handled as one term (think of it as one multi-word noun)
- Ferner (sollte man bedenken), daß dieser Übergriff eben nur dann als ein Berechtigter erscheint, wenn das Real-Natürliche selbst an sich als von der Idee gesetzt und als ein von ihr zu Übergreifendes betrachtet wird.
- (You should reflect) furthermore, that this coverage just only in this case appears as a beneficiary (legitimatednoun), if the real-naturalnoun itself will be seen as being stated by the idea, and something to be covered by it.