Why are slippers with no toe and no heel called "mules"? Because they
are not quite shoes, as a mule is not quite a horse? I imagine there
is another, perhaps even sensible answer. Yes?

I've found this explanation which links mules (the animals) to mules
(the slippers):

"Backless shoes came to be called 'mules'...because like a stubborn
mule you couldn't go backwards while wearing them."

ThatHomeSite Forums
http://ths.gardenweb.com/forums/load/beauty/msg1015313614725.html

Unfortunately, although this explanation is cute, it's almost
certainly wrong. The actual origin of the term "mule" for a backless
shoe is unconnected with the animal.

"NOUN: A slipper or shoe that has no counter or strap to fit around
the heel.
ETYMOLOGY: Probably French, slipper, possibly from Middle Dutch muil,
ultimately from Latin mulleus (calceus), reddish-purple (ceremonial
shoe)."

Bartleby: American Heritage Dictionary
http://www.bartleby.com/61/98/M0469800.html

"Mule the 'slipper' is probably an adaptation of Latin mulleus, which
denoted a sort of red or purple shoe worn by high-ranking magistrates
in Rome. This was short for mulleus calceus 'red shoe,' and mulleus
itself appears to have been derived from mullus 'red mullet' (ultimate
source of English mullet), which in turn came from Greek mullos, a
relative of melas 'black."

Interracial Voice
http://www.webcom.com/~intvoice/liam5.html

"mule(2) - 'loose slipper,' 1562, from M.Fr., from L. mulleus calceus
'red high-soled shoe,' worn by Roman patricians, from mullus 'red'
(see mullet)."

Etymology Online
http://www.etymonline.com/m6etym.htm

The half-horse, half-donkey creature known as a mule takes its name
from a different Latin word:

"mule (1) - 'offspring of donkey and horse,' O.E. mul, O.Fr. mul (fem.
mule), both from L. mulus (fem. mula) 'a mule,' probably from a
pre-Latin Mediterranean language."

Etymology Online
http://www.etymonline.com/m6etym.htm

So, oddly enough, although the slippers called mules are unrelated to
the hee-haw farm animal, there is a relationship between mule slippers
and the mullet (the fish, not the Billy Ray Cyrus-style hairdo)!

Search terms used:

"mule(s)" + "etymology"
"called mules because"
"mules" + "slippers"
"mules" + "shoes"
"mulleus calceus"

Thanks for an interesting question. If anything I've said is unclear,
or if a link does not function, please request clarification; I'll be
glad to offer further assistance before you rate my answer.

Best wishes,
pinkfreud

Thanks! A fascinating albeit unexpected answer: they wore fish on
their feet! (NO-- I know--I'm kidding, sorry.) One of those loony,
middle-of-a-long-trip questions, and now I have an answer. Thanks
much.

Bata Shoe Museum:
http://www.batashoemuseum.ca/collectindex.html

Many thanks for the five-star rating and the nice tip!

~pinkfreud