Internet search recommends opening gconf-editor and going to apps->nautilus->desktop, then de-selecting volumes_visible. I have installed gconf-editor (sudo apt-get install gconf-editor), started it with “sudo gconf-editor”, but there are only two entries under “apps”: gconf-editor and gksu. I was unable to find any other solutions in the Internet, at ubuntu-mate.community or mate-desktop.org. Thank you in advance.
Gconf-editor has been replaced with dconf-editor and you almost never use any form of sudo with either.
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Thanks, that did the trick.
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It was also as simple as a checkbox in 
MATE Tweak:
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Very true Luke, but just nice for people to know about dconf 
So you get a like out of the deal 
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