Consider these sentences:

  1. I like movies that are not long and boring.
  2. I like dishes that are not sweet and flavorful
  3. He is not humble and arrogant.

According to chapter-7 of forall x: Calgary An Introduction to Formal Logic, these types of sentences can have two different types of interpretation.

  • First is something like '... both: not ... and ...'. For instance, sentence (3) has the general interpretation 'He is both: not humble and arrogant'.

  • Second is something like '... not both: ... and ...' or '... either not ... or not ...' (both are same). Quoting from the textbook:

One common source of structural ambiguity in English arises from its lack of parentheses. For instance, if I say ‘I like movies that are not long and boring’, you will most likely think that what I dislike are movies that are long and boring. A less likely, but possible, interpretation is that I like movies that are both (a) not long and (b) boring. The first reading is more likely because who likes boring movies? But what about ‘I like dishes that are not sweet and flavorful’. Here, the more likely interpretation is that I like savory, flavorful dishes. (Of course, I could have said that better, e.g., ‘I like dishes that are not sweet, yet flavorful’.)

Essentially, the author is saying that the general interpretation of sentence (2) is 'I like movies that are not both: long and boring' or 'I like movies that are either not long or not boring' (both are same), which feels wrong to me. In fact, This Google search shows that 'not long and boring ' is mostly being used for 'neither long nor boring' on the web. So, the general interpretation seems 'I like movies that are neither long nor boring' to me. So, what should be the general interpretation here?

Also, I am not able to find a single example where a sentence like '... not ... and ...' have that second type of interpretation. So, Do you know such an example? Or sentences like these don't have such interpretations and the author made a mistake?


Your third alternative would not be a customary reading of "not A and B". It is possible that someone writing casually about Avengers: Endgame this way might mean not long and not boring.

That possibility is not really relevant in the context you quote. Those paragraphs refer explicitly to the ambiguity implicit in "not A and B" which with the parentheses required in formal logic would be written as "(not A) and B" or "not (A and B)".

In formal logic "not (A and B)" is never "(not A) and (not B)". De Morgan's laws tell you it's "(not A) or (not B)".

  • Thanks, but I don't see how it is not relevant. Those paragraphs refer to the ambiguity of sentences of the form '... not ... and ...'.These are sentences in English. We are transcribing these sentences into formal Logic, so we need to know all of the interpretations those sentences can have.
    – Navneet
    Jun 10 at 6:39
  • I know that in formal Logic 'not(A and B)' and 'notA and notB' are different sentences, what I want to know is can sentences of the form '... not ... and...' have that third interpretation so, I may transcribe them into 'notA and notB' (when context allows).
    – Navneet
    Jun 10 at 6:53

If someone asked about cucumbers and the reply was "They are long and green".

And then they asked about strawberries and was told "They are not long and green!"

What does this tell you about strawberries? Logically I see two interpretations, "Not long and/or Not green", or "Not long, and green"

You will note that we don't even have an unambiguous word in English for the "inclusive or" (and nor do most other languages). Pragmatically a you would probably understand that strawberries are neither long nor green.

This is because if the person asked about bananas, the reply could be "they are long, but they are not green". It would be ridiculous for someone to describe (long, yellow) bananas as "not long and green" in comparison to cucumbers, even though it is logically correct

So logically "not long and green" can mean not long and/or not green. Which may contextually be understood as not long and not green.

In the case of "long and boring" my understanding would be that the film may be long in absolute length (relative to other movies) is not too long since if it were too long it would be boring. So you see the meaning of a sentence depends on the interactions between the individual words.

  • Not "Not long and/or not green" is one interpretation. It uses the "inclusive or "A or B or Both" The second interpretation is "Is not long, and is green"
    – James K
    Jun 10 at 18:29
  • Well that seems an interesting way to mention inclusive or.
    – Navneet
    Jun 11 at 6:16

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