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Background

Below are cited from pp. 14-15 of Introduction to Mathematical Thinking by Keith Devlin:

You often see the following notice posted in elevators:

IN CASE OF FIRE, DO NOT USE ELEVATOR.

Obviously this notice is intended to mean:

  • If there is a fire, do not use a elevator.

But the writer of the book insisted that if the notice is interpreted literally, there are more than 1 possible interpretations. He didn't write them out in the book.

My question

I could come up with the following interpretetions of the notice. Are each of my sentences legitimate literal interpretations? Is there other possible interpretation?

  • In a box of fire, do not use a elevator.
  • If you got dismissed, do not use a elevator.
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    No: why would you want to come up with some other (wrong) interpretations? You can't 'case fire' and "fire", as in being dismissed from one's job, is not expressed that way.
    – BillJ
    Apr 12, 2021 at 9:20
  • 23
    Mathematicians are known for their very precise and highly non-idiomatic use of language. I suspect that most active users here are unfamiliar with a mode of thinking that, e.g., suggests the interpretation "if you are holding a burning torch, don't use the elevator". (I always explain math studies as a kind of brainwashing.)
    – Stephan Kolassa
    Apr 12, 2021 at 12:28
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    @StephanKolassa - Indeed - I once saw a cartoon in which a mathematician had crossed out the word "Area" in a "No Smoking Area" sign and replaced it with "Volume"; that seemed to say it all, really.
    – Spratty
    Apr 12, 2021 at 14:42
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    It could also mean "In case there is a fire, do not use the elevator", meaning "never use the elevator just in case there's a fire". That's what I thought it meant for years when I was younger :p
    – Radvylf Programs
    Apr 12, 2021 at 14:49
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    A mathematician goes to the store. His wife tells him: "Bring a bottle of milk, and if they have eggs, bring a dozen." The mathematician comes back with a dozen bottles of milk and says: "They had eggs." – I believe that joke says all you need to know about what happens when mathematical thinking and natural language meet.
    – Jörg W Mittag
    Apr 12, 2021 at 18:25

11 Answers 11

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At my grandmother's apartment, someone had changed the sign so that it reads:

IN CASE OF FIRE DO NOT USE ELEVATOR
USE WATER

That is, they're making a joke that plays on a possible alternate reading of the unaltered sign: in the event of a fire, do not use the elevator to extinguish it.

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    This is the answer. It demonstrates the concept that In case of fire there are many things that should happen, not all of which are limited to the evacuation of the building. The usual contextual interpretation of the phrase is - If there is a fire, do not use the elevator [to evacuate the building], as opposed to - If there is a fire, do not use the elevator [to extinguish the fire].
    – EllieK
    Apr 12, 2021 at 16:34
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    Unless the fire is at the bottom of the elevator shaft, in which case, a falling elevator may actually smother it out.
    – pacoverflow
    Apr 13, 2021 at 5:43
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    @Mari-LouA The deletion was my fault, I asked for the discussion of the lack of explanation to be cleaned up now that the answer had been edited. I think your comment about the edit was collateral damage. The joke is easily understood, how it answers the question should be explained.
    – ColleenV
    Apr 13, 2021 at 11:08
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    This is a pretty common joke.
    – benrg
    Apr 13, 2021 at 17:07
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    Similar to the “Get a loaf of bread. If they have eggs, get a dozen” joke. (The mathematician comes back from the store with 12 loaves of bread because they had eggs.)
    – Todd Wilcox
    Apr 14, 2021 at 6:11
27

One other possible meaning is:

Do not use the elevator, in case it causes a fire.

(That one seems pretty obvious to me, so I'm surprised not to see it amongst all the other ingenious meanings already listed here :-)  I guess it shows how flexible English can be, especially when you start leaving words out.)

And to answer a request for elaboration:

Grammatically, I think it's just a simple re-ordering.  For example, you might say:

“Don't eat spoiled meat, in case it makes you sick.”

You could reverse the order of phrases to tweak the emphasis without changing the meaning:

“In case it makes you sick, don't eat spoiled meat.”

Alternatively, for brevity (such as on a sign) you might contract it to:

“Don't eat spoiled meat, in case of sickness.”

And reversing that gives you:

“In case of sickness, don't eat spoiled meat.”

— which is now ambiguous but could still have the original meaning, AIUI.

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    I can't see how this would work grammatically. Would you mind elaborating?
    – 2br-2b
    Apr 12, 2021 at 19:22
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    I don’t see it. We don’t bury the lede with safety warnings or say “In case of car accident, look both ways.” The ambiguous part is the “use”, not the “in case of”.
    – ColleenV
    Apr 12, 2021 at 19:22
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    Yes, this. Saying "In case of fire, do not light a BBQ outdoors on a hot day" is not assuming a fire has already started. My immediate idea of what the mathematician's contrived alternative meaning might be was "In case of fire, do no use the elevator ... it is faulty and might catch fire if used."
    – traktor
    Apr 13, 2021 at 8:38
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    @gidds traktor I don't really see it, but apparently everyone else can, so I guess I'm just wrong :-)
    – 2br-2b
    Apr 13, 2021 at 18:44
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    @2br-2b No, you're not wrong. That is now how "in case of" is used
    – Kevin
    Apr 13, 2021 at 22:07
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In a box of fire, do not use a[n] elevator.

This could be a literal interpretation of the sentence, but it would make very little semantic sense in context. What is a box of fire, and how are you inside of it?

If you got dismissed, do not use a[n] elevator.

I don't see how that interpretation can make sense. You cannot put an infinitive verb after "in case of" like that. It would be ungrammatical. The preposition "of" takes a noun or noun phrase, not a verb. If you wanted to put a verb there, you would need to use a gerund instead of an infinitive ("in case of firing").

Another possible interpretation: Don't use the elevator, because ("in case," sense 1) a fire could happen.

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    The "because a fire could happen" interpretation is how I, a native English speaker, interpreted those signs as a child. I was always confused why they would even put elevators there if we weren't supposed to use them. And why we were always so concerned about fires starting spontaneously.
    – Daniel
    Apr 12, 2021 at 13:35
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    You can't put an infinitive verb after "in case of", but "fire" could be a noun meaning "gunfire" - another meaning to add to the collection.
    – alephzero
    Apr 12, 2021 at 13:37
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    As a native speaker, I find, "Don't use the elevator, because ("in case") a fire could happen." to be the most convincing misinterpretation. While it semantically it makes no sense (why are there elevators at all!?", syntactically it works as well as the intended interpretation. That's the kind of interpretation that would cause an AI to fail a Winograd Schema Challenge, despite not being a traditional WSC (i.e., traditional WSCs require AI to resolve ambiguous pronouns, which isn't quite what goes wrong, here) .
    – Brian
    Apr 12, 2021 at 20:33
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    @EllieK: The sentence omits any determiner for "elevator," so my interpretation is that it is abbreviated and does not use articles or determiners. Otherwise, there is no grammatically valid interpretation.
    – Kevin
    Apr 13, 2021 at 15:26
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    @EllieK: You are not reading my comments. There is no determiner in front of "elevator," and the English language does not allow such omission in any interpretation. Therefore, the only way to salvage the sentence is to assume it's something like headlinese where determiners are systematically omitted.
    – Kevin
    Apr 13, 2021 at 15:30
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I think your writer's claim is a bit of a stretch. There's no risk of confusion and it's quite hard to see what other meanings could be reasonably construed.

The best I can think of is this:

Do not use the elevator [ever], because there might be a fire [that you don't know about].

Although the phrase "IN CASE OF FIRE" clearly means "if there is a fire", in general, we can say "[just] in case" to refer to an event that may already be the case, but where we don't know for sure.

For instance: someone in your household brings a guest to dinner and you don't know their dietary needs. You might say:

In case you're vegan/coeliac/observe kosher/halal, I prepared a plant-based gluten-free lentil dish.

In the same sense:

In case a fire might be happening that you don't know about, you shouldn't use the elevator.

or, for short,

IN CASE OF FIRE, DO NOT USE ELEVATOR.

It's a totally unreasonable interpretation for an Earthling to make, but it is at least logically and grammatically plausible.

Edit Owen's comment below explains it very clearly. Often, "in case of X" means "because X might happen", not "if X should happen".

For instance:

"Don't eat honey outdoors on a hot day, in case of wasps!"

That doesn't mean:

"If there are wasps, you shouldn't eat honey outdoors on hot days."

It means:

"You should never eat honey outdoors on hot days, because wasps might attack."

Because we are familiar with the expression

"In case of fire, do not use elevator"

we know that it means

"Don't use the elevator if there is a fire"

but if we were seeing the phrase for the first time, we would probably take it to mean

"Do not ever use the elevator because there might be a fire".

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    I think the strong part here for an English-Language-Learner is how "in case of X" usually doesn't mean "when X happens", it means "because X could happen". I also feel like "in case of fire" is almost an idiom when you see in on a sign. It means "don't use the elevator during a fire" because we we were taught that special meaning.
    – Owen Reynolds
    Apr 12, 2021 at 17:37
  • That's a nice (and much shorter) way of explaining it!
    – tea-and-cake
    Apr 12, 2021 at 17:38
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    If you want to, you're allowed to edit, and comments are specifically "steal any of this if you find it useful". But very few people do. Feel free to ignore comments for any reason w/o offending the commenter.
    – Owen Reynolds
    Apr 12, 2021 at 17:46
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    I definitely had this exact interpretation as a kid (and the real meaning didn't even occur to me until I asked someone -- I had never seen that meaning of "in case of")
    – Tavian Barnes
    Apr 12, 2021 at 20:00
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"In case of fire" does not specify where or when the fire occured.

"Use" is ambiguous. The main use of elevators is to travel between floors of buildings, but they have other uses... You can hide in an elevator, or use it for holding a private conversation.

"Elevator" does this mean "this elevator, the one which the sign is attached to", or is it a general rule for any elevator.

(Moreover as you and another answer already has, a "case" can mean a container, and "in case" can be used as a warning of something that could happen")

The point, of course, is that normal language is always interpreted in context. But when thinking mathematically you don't use normal language. You don't use the normal way of understanding the meaning of words from their context.

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  • All the uses you state are intentionally prohibited by the sign, as are plenty of uses which don't occupy the elevator (as moving it or opening the doors helps fire to spread). Using it as an example in a discussion of semantics is probably safe though.
    – Pete Kirkham
    Apr 12, 2021 at 15:05
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    You can use an elevator as a spatial reference point, e.g. to find your current location on a floor map, relative to the stairs.
    – Tim Sparkles
    Apr 12, 2021 at 18:44
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+500

Captain obvious here, since nobody else is being obvious enough.

The mathematical text quoted is belabouring the point that in mathematics, precision matters. Even in such scenarios where the interpretation of a statement could be deemed as 'reasonably obvious', as in this scenario.

Therefore the point being made is NOT that any reasonable person would have trouble interpreting that sign. The point being made is that, if you've got your mathematician hat on, it is not precise enough, and as such it allows for a number of other interpretations, even though the main one is in theory reasonably clear enough from the context.

We could come up with alternate, fun interpretations which no reasonable person would think of before the main one, but in this trivial example, it would be a fun but otherwise pointless exercise. There are however very real problems in mathematics where the preciseness of the definition matters, and it matters a lot!

E.g. you are a mathematician / engineer, and you are tasked with coming up with rules that a robot could follow. You are given this sentence and are asked to design a rule for the robot. Even within the limits of the intended meaning, we still have a lot of ambiguity:

IN CASE OF FIRE, DO NOT USE ELEVATOR:

  • Does this mean that when there is no fire I should always use the elevator? Or is it optional? What defines my choice?

  • Which elevator. The left one? The right one? Any elevator? In all buildings? Only on this floor? Can I go one floor down in the floor that is not (yet) on fire, and use that elevator?

  • What constitutes a fire. If the robot sees someone smoking a cigarette, should it not use an elevator? If there was a fire last week, does the 'no elevator' rule still apply? Does fire involve an ACTUAL fire, or just a fire alarm?

  • Is this an absolute rule, or a relative suggestion? If there is an actual fire, but the stairs are blocked, and the elevator is the ONLY means of escape, is the robot still forbidden from using it as its only means of escape?

etc.

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    This is the answer. I think it’s a bit funny that you’ve called yourself “Captain Obvious” when the only thing that’s obvious is the well known “use water instead” joke sent most people down the wrong path trying to think of all the ways we could willfully misinterpret the meaning of the words instead of looking at the context of the sentence.
    – ColleenV
    Apr 14, 2021 at 2:28
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    @ColleenV to the mathematician many things are obvious which remain anything but obvious to others. Like how a coffee cup is the same as a bagel.
    – mdewey
    Apr 14, 2021 at 14:25
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    I’m an engineer and I have several good jokes about the differences between engineers and mathematicians, but today we are on the same page. :)
    – ColleenV
    Apr 14, 2021 at 14:27
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    @Mari-LouA “kinda the same but indirectly” is not “just as well as”. This explains it better in my opinion. You’re free to award a bounty to James when mine is over. This answer explains explicitly how different interpretations support the point being made by the author of the source text. What annoys me is that the two sentence retelling of an old joke has 5x the score of either of the better answers. I did upvote James’ answer too btw.
    – ColleenV
    Apr 15, 2021 at 11:06
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    @Mari-LouA for me it was the robot which swayed me in favour of up-voting this one because it clarified the thinking behind the phrase in a neat and memorable way.
    – mdewey
    Apr 15, 2021 at 13:34
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According to https://www.jj5.net/sixsigma/Math_Think

Q: You often see the following notice posted in elevators:

In case of fire, do not use elevator.

This one always amuses me. Comment on the two meanings and reformulate to avoid the unintended second reading. (Again, given the context for this notice, the ambiguity is not problematic.)

A: The notice is not suggesting that the elevator can be used to combat the fire.

If there is a fire do not travel using the elevator.

The (supposed) ambiguity would be that you could try to use the elevator to combat the fire. Honestly, this is a vast exaggeration, nobody in their sane mind would think that.

In a box of fire, do not use a elevator.

This does not match the original phrase. It would need to be "In a case..." to match.

If you got dismissed, do not use a elevator.

Likewise, does not match, it would need to be "In case of being fired", "In the case you are fired" or something similar.

So your ideas don't match because the grammar clearly excludes them. Only the (pretty much insane) proposition above matches grammatically, even if it doesn't make much sense!

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    There is also the meme of “In case of fire, take the stairs.” that shows a person running away from a burning building carrying some stairs. The willful misunderstanding of the sign is usually done to either make a joke or comment on ignoring context/taking things too literally.
    – ColleenV
    Apr 12, 2021 at 17:37
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  1. Do not use this elevator to exit the building when the building is on fire.

  2. Never use this elevator because of the risk of fire. ("In case of jay walkers, use caution.")

  3. Do not use this elevator to put out fire. ("In case of fire, use fire extinguisher")

  4. When inside a box made out of fire, do not use any elevators. ("In case of wood, lies golden treasure")

  5. When flying an airplane that catches on fire, do not use the flight control surfaces that change your pitch. ("In case of fire, cut fuel to engine")

All of those are some kind of reasonable English reading for something structured similarly.

"In case of X" can mean "when the case X occurs" or "because of the risk of X".

"Use" can mean many things. Here we are relying on "the typical use for the elevator" and not "the typical thing you do when there is a fire" (namely, put it out).

And "elevator" has at least 2 meanings in common use.

In theory, that would lead to up to 8 interpretations (2 times 2 times 2), of which the above are 5 of them.

As this is a sign on the elevator, interpreting it to be an airplane elevator is unlikely; unless the learner knows the other meaning, but not the "box on a cable" one.

Use being either "to deal with fire" or "as you would normally" is a big one. Only because the elevators are not something you'd consider putting a fire out would this be unlikely.

The final one, which of the two "in case of"s, relies on more context.

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  • "the typical thing you do when there is a fire" - in any environment in which this sign could be found, the most typical thing I'd do would be to escape, rather than attempt to put it out. An individual who is not a trained firefighter will usually not be terribly effective at fighting any fire larger than one caused by a cooking accident, and then only if they respond very quickly when it first begins.
    – Dan Henderson
    Apr 13, 2021 at 20:05
  • @danh I encounter far more cooking fires than building consuming blazes in my life (like, non zero vs zero)
    – Yakk
    Apr 13, 2021 at 23:09
  • or "because of the risk of X". No, it does not mean this
    – Kevin
    Apr 14, 2021 at 2:40
  • @kevin I have used it just above in a way that at least some dialects of English native speakers would understand it to mean that. Can you address the example and explain how I got it wrong?
    – Yakk
    Apr 14, 2021 at 3:40
  • @Yakk, "in case of x" is an expression with an idiomatic meaning, which is "in the event of x".
    – Kevin
    Apr 14, 2021 at 12:57
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The term "in case of fire" is too broad/unspecific. As such, having someone standing next to you lighting a cigarette would mean that you should not use the elevator - as there was (the lighter) and is (the burning cigarette) a fire.

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    this absolutely does not mean "in case of no fire, use the elevator"
    – user253751
    Apr 12, 2021 at 14:05
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    en.wikipedia.org/wiki/Affirming_the_consequent
    – wizzwizz4
    Apr 12, 2021 at 14:32
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    @user253751 Especially to a mathematician. They know that P->Q does not entail ~P->~Q
    – Barmar
    Apr 12, 2021 at 14:44
  • That is why I put "could interpret" - not "must interpret". Nevertheless, I removed the paragraph. Interesting though, the highest upvoted answer does not have anything to do with mathematical thinking either.
    – MSentis
    Apr 12, 2021 at 16:25
  • Sure you "could" interpret it that way, but it would be a wrong interpretation not logically implied at all by the words in the sentence. I would have added another downvote if that backwards logic hadn't already been removed, but since it has, this answer deserves an upvote instead.
    – Peter Cordes
    Apr 12, 2021 at 18:59
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If you got dismissed, do not use a elevator.

No - "fire" in this context is a verb so it would have to be, "in case of having been fired..." or "in case of a firing"

Perhaps they meant, "Detectives investigating arson may not use the elevator".

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Clearly, fire is in nominative case. So it means, "let me tell you this in nominative: do not use elevator." Although the intended meaning of the second part is "do not use elevator, use something else instead," one may think of interpreting it as "do not use elevator, do something else with it." Btw. arguing that "nobody in their sane mind would think that" is missing the point I think. Nobody in their sane mind would think of using the elevator in case of fire, still the warning is actually there for some reason. In case of insanity, probably.

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    Nobody in their sane mind would think of using the elevator in case of fire It's not insane to imagine someone trying to escape a burning building, several stories high, by using the fastest way possible, i.e. an elevator. It therefore makes perfect sense to remind (or warn) people that elevators are death traps in case of fire
    – Mari-Lou A
    Apr 13, 2021 at 10:58
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    BTW this contribution does not answer the original question.
    – Mari-Lou A
    Apr 13, 2021 at 11:00
  • "In case of" doesn't take a nominative noun.
    – Gred
    Apr 14, 2021 at 1:23

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