All participants are not professional.

[Matthew Wai]

(1) All participants are not professional.
(2) All apples are not red.

Am I right in thinking that (1) is ambiguous, while (2) is unambiguous?

 

[teechar]

No. They mean what they say.
If you mean something else, consider:
1- Not all (the) participants are professional.
2- Not all apples are red.

 

[Matthew Wai]

(3) All that glitters is not gold.

Does the above sentence mean "Not all that glitters is gold"?

 

[5jj]

It does, though it could also mean that everything that glitters is something other than gold.

 

[emsr2d2]

(3) All that glitters is not gold.

Does the above sentence mean "Not all that glitters is gold"?

Although almost everyone now uses "glitters", note that the original quote by Shakespeare is "All that glisters is not gold".

 

[Annabel Lee]

(1) All participants are not professional.
(2) All apples are not red.

Am I right in thinking that (1) is ambiguous, while (2) is unambiguous?

Both are ambiguous. It has to do with scope. Besides the "no"-reading ("All participants are [not professional]" --> "No participants are professional"; "All apples are [not red]" --> "No apples are red"), there is the reading on which the corresponding positive assertions are being denied. To deny that all apples are red is not to assert that all apples are non-red, i.e., that there are no red apples; it is only to assert that redness is not to be predicated of all apples (the "not all" reading).

 

[jutfrank]

I'm going to take this as a question about logic rather than about what counts as good effective communication. Yes, both are ambiguous, due to the logical form, and the different kinds of negation that it allows.

The form is:

all X are not Y (All participants are not professional)

This can be logically equivalent to both of the following:

not all X are Y (Not all participants are professional)
no X are Y (No participants are professional)

 

[Annabel Lee]

Yes, both are ambiguous, due to the logical form . . . .

The ambiguity is observable in the grammar, too, as we can see by using tag questions. If a native speaker had to add a tag question to the sentence All apples aren't red, the tag are they? would be much more natural than aren't they? :

All apples aren't red, are they?​

The tag question is elliptical, as all tag questions technically are. It stands for the following:

Are they red? ​

= Are [all apples] red?​

The sentence All apples aren't red can thus be a negative answer to the question Are all apples red? We're given the "Not All" reading, just by looking at the grammar. Now, aren't they? is also a possible (though unnatural) tag question here:

All apples aren't red, aren't they?​

As before, the tag questions is elliptical. This time it stands for:

Aren't they not red? ​

= Aren't [all apples] not red?​

The sentence All apples aren't red can thus alternatively be an affirmative answer to the question Aren't all apples not red? This gives us the "No" reading, and we haven't ventured beyond grammar into the domain of pure logic. Note: The second tag question was for illustrative purposes only. I'd much more naturally say, "No apples are red, are they?"

 

[jutfrank]

... and we haven't ventured beyond grammar into the domain of pure logic.

Yes, very nice, thank you. Grammar and logic don't always match and I think this is a nice case in point.

I think this could be called a case of 'scope-shifting', since the negation practically broadens in its interpretation. To me, the fact that the sentence All apples are not red can be interpreted to mean Not all apples are red, where the scope of negation is shifted from operating only on the predicate red to operating on the whole sentence, shows some evidence to me at least that scope is ultimately resolved by pragmatics. The interpretation of 'not' may be on a higher level logically than it is syntactically, with this mismatch giving rise to the ambiguity.

 

[SoothingDave]

I would just note that "all that glitters is not gold" is a fixed expression and people understand what is meant.

With a unique sentence, the logical ambiguity is possible.

 

[Annabel Lee]

It may seem counterintuitive, but, from a strictly grammatical standpoint, the "not all" interpretation is perfectly straightforward!

A: Are all of you ready?​

B: No.​

​

What does "No" mean? "Not all," of course. But how do we add sentential-negation "not" to the sentence "All of us are ready"? We put it after "are"! The same story can be told about all the examples of "All [NPs] are not [Adj]" in this thread without exception. When we add sentential negation, we don't place it before the subject! We place it after the auxiliary.

The dogs are hungry.​

The dogs are not hungry. (*Not the dogs are hungry.)​

​

All the dogs are hungry. (Are they really?)​

All the dogs are not hungry. (No.)​

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