I am a computer science professional. I am reading the book Natural Language Understanding by James Allen where he writes:
“Every boy didn’t run” which is ambiguous between the reading in which some boys didn’t run and some did and no boys ran.
As I am not a native English-language speaker, I couldn’t understand the ambiguity here. Please explain how the meaning can ever be some boys didn’t run and some did here.
The quote would be clearer if it spoke of the difference between the reading in which all boys didn’t run and (that in which) some did.
In the positive version “every boy ran”, there is no ambiguity: 100% of the boys ran.
Logically, “every boy didn’t run” follows the same pattern: for each boy x, the statement asserts that x didn’t run. That is, the negation in “didn’t” applies to the action “run”.
The problem is that in English, the form has also been used idiomatically to assert something different: that not all of the boys ran. That is, the negation in didn’t applies to the qualifier “every”.
Here is a classical example:
Wikipedia traces this (or variants) to a Latin quote dated to the 12th century or earlier, and popularised by Shakespeare in The Merchant of Venice.
The article mentions a 1175 version by the French monk Alain de Lille: "Do not hold everything gold that shines like gold", where the logical meaning matches the literary intent. The version popularised by Shakespeare, however, sounds more catchy even though its logic is wonky.
As a result, the literary meaning of the form “all that (...) is/does not (...)” no longer matches its literal/logical meaning.
One might try to argue that the literary meaning should be deemed ‘incorrect’ or ‘inaccurate’, but it is precisely this kind of idiomatic usage of language that lies behind the ambiguity your quote highlights.
If "every" is in the scope of "not", it means "It is not the case that every boy ran," or, that is, "Some boy didn't run," or "Not every boy ran." That is the preferred interpretation if every is focused or emphasized: "Every boy didn't run" with rising intonation at the end.
If "not" is in the scope of "every", it means "For every boy it is true that that boy didn't run," or, that is, "No boy ran." For some English speakers, this is not a possible interpretation.
This stack is about usage. First, "every boy didn't run" is a very awkward usage, and would not be used without context. The context will decide which meaning is applicable.
”Your list of possible candidates was way off. The boys on your list didn't run for a student board position."
"Yeah, turns out most of them didn't run."
"No, every boy [on your list] didn't run. You could not have been more wrong."
In this case, the bolded phrase, a perfectly normal usage, sets up the "_______ didn't run" framing that the third speaker repeats. That is why she is using this otherwise awkward form.
Versus
"No, nobody stayed around to make statements. When the police came, everyone ran away."
"That's to be expected from the townies, but are you saying every boy from our school ran? Despite our teachings about morality?
"Well, every boy didn't run. Carl Heinz stayed, the Peterson brothers, Conrad Hamm, which you'd expect... A few others.
In these usages, the meaning pops right out. And this is the kind of usage where "every boy didn't run" is appropriate. It should not be used where it would create an ambiguity. If you do, the reader will infer from context which meaning is most likely, just as you did above.
A linguistic perspective might help here.
We (linguists) typically talk of movement - a word starts in one place in the sentence and moves to another before it is spoken. Ignoring the technical aspects of that (and ignoring that the verb has to change slightly depending on how the sentence is written), there are two possible starting sentences here:
Not every boy did run
Every boy did not run
In the first, we get some boys didn’t run and some did and in the second we get no boys ran. In both of these cases, it is possible for not to move to did and become didn't, leaving us with the reading "Every boy didn't run". The first is also rather stilted and sounds weird. As @GregLee pointed out, emphasis helps with clarifying which meaning is intended.
For these reasons, it's more common (in writing) to see the phrases
Not every boy ran
No boy ran
Because those are unambiguous.
I think it's meant to be ambiguous between
only true if 0% ran or not 100% ran (i.e. true if 50% ran).
Edit: I found the excerpt of the book in question - looks like I was right:
In addition, operators such as negation and tense are also scope sensitive. For example, the sentence Every boy didn't run is ambiguous between the reading in which some boys didn't run and some did, that is, (NOT (EVERY bl: (BOY1 bl) (RUN1 bl))) and the reading where no boys ran, that is, (EVERY bl : (BOY1 bl) (NOT (RUN 1 bl))) These two readings are captured by the single logical form
Of course "didn't" here is a contraction for "did not". It's ambiguous because it is not clear what "not" refers to.
If "not" refers to "run", then it's "(every boy) did (not run)". That is, every boy did this. What did they do? They did not run.
If "not" refers to "every", then it's "(not every boy) did (run)". That is, not every boy did this, so some of the boys did not do this. What is it that some of the boys did not do? Run.
I, and I think most English readers, would generally assume that the first meaning was meant.
A more clear way to say it if you meant that none of the boys ran would be to say, "None of the boys ran." If you meant to say that some ran and some didn't, you could say, "Not every boy ran".
Consider the following dialog where two people describe an incident:
"There was panic. Every boy ran for cover."
"Every boy didn't run."
It might be more "formally correct" if the second speaker had said "Not every boy ran," but the sentence he actually used emphasised the difference between the two speakers' descriptions - the second speaker is emphasising the difference in behaviour between running and not running, not the the number of boys who didn't run.
On the other hand, if you consider the sentence as a logical proposition and ignore the context in which it was spoken or written, "Every boy didn't run" is logically identical to "No boy ran".
“Every boy didn’t run”
is just not how you say anything. It's not grammatical. So it actually doesn't mean anything at all.
But an English speaker wants to squeeze some meaning out of it. What is called ambiguity is really the different ways one imagines the speaker intended but fouled up.
English (or human language) isn't formal logic, so the words don't apply necessarily in a strict order. So forcing one meaning on the phrase would be translated back into words as
Not every boy ran (there are some boys who did not run but some probably did, otherwise you would say 'no boy ran'),
or
No boy ran (For every boy, it is not the case that the boy ran)
as though 'every boy' is like a logical universal quantifier over all boys and the predicate says 'the boy did not run'.
It is problematic to say the sentence is ambiguous because it is not a pattern interpretable directly in English. So you have to guess what is meant, and in those collection of words, there are pretty much only two directions to go.
The way I understand it is that:
Every boy didn't run
could be read as the negation of:
Every boy did run
thus, the negated sentence is equivalent to:
It is not true that every boy did run
and the above statement is already true if even a single boy failed to run (even if all the other boys succesfully escaped).
But it may happen with “all” adjectives quoting totatility or infinite. The negative form shouldn’t exactly mean the negation of its affirmative sentence: “All the boys run” vs “all the boys didn’t run”; “Zero boys run” vs “zero boys didn’t run”; “Infinite number of stars covered the sky” vs “infinite number of stars didn’t cover the sky “ “Millions of drops fell down” vs “millions of drops didn’t fall down”, Etc...
Isn’t there ambiguity in all of these negative forms? There shouldn’t be any problem to interpret when speaking, but context or perifrasis to avoid confusion is needed when writing. That is happening with Spanish and in all Latin languages too, because negative form doesn’t negate the adjective, only the verb is negated. Anyway, I agree that the use of those negative forms is weird, not only in English. Actually, if we want to negate the adjective we have to say the adverb “not” before the adjective itself: “Not every/all/infinite, etc.”
¬(∀x∈B r(x))and∀x∈B ¬r(x).