By who? The west? They appropriated it for themselves in the middle ages while at the SAME time alienating and separating from themselves the current/contemporary Greeks (the Byzantines) as something nothing like them. Despite those same medieval Greeks continuing their traditions going back to those "ancient" times in a unbroken chain.
"the west" can't have it both ways. "the west" borrowed from and applied "some" aspects of Greek civilization, which they claim to be their founder when it suits them only.
Greek civilization was in its beginning, middle AND modern period all a "Near Eastern" civilization. Not western.