The World as Will and Idea was written by Arthur ____ (12)

I believe the answer is:

schopenhauer

(Other definitions for schopenhauer that I've seen before include "Arthur -, nineteenth century German philosopher" , "Arthur -, pessimistic philosopher" , "Philosopher -- punches a hero (anag.)" , "19th century German philosopher" , "Cheer up on ash (anag) - German philosopher. d. 1860" .)

I've seen this clue in The Times.

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