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While we normally use both our feet to walk, why is it grammatically acceptable to say "on foot" not "on feet"?

Mohammad Nazar
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    For the same reason that we say 'by rail', when in fact there are always two rails involved; and 'shoe store', when in fact nobody buys only one shoe there. I.e, why mention the obvious? – John Lawler May 04 '14 at 16:59
  • There's also "Please, give me a hand", and "She bent his ear with all the gossip she had collected in town." :) – F.E. May 04 '14 at 17:02
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    But on "shoe store" I guess there is a grammar rule. Because shoe is used as an adjective, it cannot be made plural. – Mohammad Nazar May 04 '14 at 17:16
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    Yes, and when you walk on foot there is a grammar rule that says it's not "on feet". Grammar rules are not something passed onto us by some high committee. Grammar "rules" are really just descriptions of what we already do anyway, long before we go to school to learn that grammar even exists. Adjectives can be plural alright, in many many languages. There is no rule that we cannot do that in English. There is merely an observation that right now we don't. Likewise, another observation is that we do not go by feet or by cars. – RegDwigнt May 04 '14 at 18:00
  • I love how John Lawler makes the insightful point that there is a reason, albeit doesn't actually share that he knows what that reason is. –  May 04 '14 at 21:16
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    To echo John Lawler's point, why is it toothbrush, and not teethbrush? (As a child I always asked myself that question!) – Mari-Lou A May 04 '14 at 21:29
  • Mari-Lou, it makes linguistic sense to name something by its simplest function. You can always use a toothbrush on one tooth, then another, then another, until all the teeth are cleaned, but, strictly speaking, you could not use a teethbrush on one tooth (if you only had one tooth to clean). The simpler form is desired. –  May 04 '14 at 21:36
  • It is not grammar, it's an idiomatic expression you find in the dictionary, all the same the question is justfied. What do you say in your language? I'm just wondering whether such a formula wasn't already in use in Latin. But I have to search. – rogermue May 04 '14 at 22:23
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    Can I throw in * on horsesbacks ? By trains ? – Edwin Ashworth May 04 '14 at 22:48
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    Regarding what Mari-Lou A mentioned, there are plural forms as well, of course. E.g., a savings account, a goods train, the outpatients department, and the sales department.In some other cases even both singular and plural can work. E.g., an antique(s) shop, the drug(s) problem, the arrival(s) hall. – Mohammad Nazar May 05 '14 at 12:26
  • @Mari-LouA - There’s an old joke that goes, “How do you know that the toothbrush was invented in West Virginia? Because anywhere else it would have been a teethbrush...” – Jim May 11 '18 at 05:45

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The funny thing is in German this expression is also used in singular: on foot - zu Fuß. I've just had a look into a Latin and Greek dictionary though I have no big standard dictionaries. It seems in Latin pedibus, ablative plural, with feet, was used but also pedem ferre, accusative singular, an idiomatic expression for to go or to come. Maybe the singular was a kind of artistic literary device of variation by using the singular instead of the plural and this poetic use gained general acceptance.

rogermue
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Both are used:

He stands on feet of clay.

and

I will follow you on foot.

Gary's Student
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The process of physiology in human locomotion (walking) requires one foot in front of the other but the locomotive action of using both feet necessitates hopping or jumping

Third News
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We use on foot to describe a person who goes to another place without using any transportation.

Example

Majedo goes to school on foot everyday.

But We use on feet to describe a person who stands for 2 hours or more to complete his work.

Example

He stands for 3 hours on feet.

Radi'a AL Saadi
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    "He stands for 3 hours on feet" is not good English, but "He was on his feet for 3 hours" is. It means he--whoever "he" was--was standing or perhaps walking about for three hours. A surgeon might stand at an operating table doing his job for hours at a time. A cook might stand at the stove or the kitchen table for a similar length of time. – tautophile May 11 '18 at 03:58
  • If I am standing, I am already on my feet, there's no need to add "on feet" to your example sentence. It is like saying: "He dances three hours on feet" Redundant and frankly quite odd, but you can say "*light-footed", and ["light on your feet*"](https://www.ldoceonline.com/dictionary/be-light-on-your-feet). – Mari-Lou A May 11 '18 at 05:54