Is it true that both the following lines are identical in English?

  1. All dogs are animals. All animals are not dogs.
  2. All dogs are animals. Not all animals are dogs.

In some other languages, (1) and (2) are not the same. In those languages, (1) means "none of any animal is a dog" and is different from (2). But in English, are (1) and (2) identical? (although, some people may prefer writing (2)?)

This comes up in a computer programming book, with the word "promise" meaning one particular thing, and a "thenable" meaning also some particular thing, and that line is, "all promises are thenables, but all thenables are not promises". From this context, it seems like the second part of that line means "not all thenables are promises".

Is this true in a specific situation, such as:

a. I have a bag of shapes in the bag. All triangles are blue. All blue shapes are not triangles.
b. I have a bag of shapes in the bag. All triangles are blue. Not all blue shapes are triangles.

Again, is (a) and (b) identical in English? There are people who actually say as a standalone sentence, "All blue shapes are not triangle" or "All answers are not good answers" -- and I usually take it to be "none of the blue shape is a triangle", or "none of the answer is a good answer" -- so sometimes this may cause confusion to me. But sometimes I do hear somebody saying an assertive statement such as "All of these oranges are not good." Is that also the same as "Not all of these oranges are good"?

  • 1
    "All animals are not dogs" is ambiguous. It can be used to express the idea that you are making a claim about every animal, that each of them is not a dog (factually incorrect) or it can mean simply, "It is not the case that all animals existing are dogs." On the other hand, "Not all animals are dogs" simply means that there is at least one animal that is not a dog. (Some might also think the speaker has implied that at least one animal is a dog, in casual speech.) Commented Dec 24, 2019 at 18:50
  • This is not a question about English, per se. It's logic. And this: "All dogs are animals. All animals are not dogs." would usually be expressed as: All dogs are animals. But not all animals are dogs.
    – Lambie
    Commented Dec 24, 2019 at 18:53
  • Related: tag negative-raising as well as 1, 2, 3, 4, 5
    – tchrist
    Commented Dec 24, 2019 at 19:08
  • 1
    Does this answer your question? "Everybody is not" vs "Not everybody is" Commented Dec 24, 2019 at 19:18
  • The man who wrote "All that glisters is not gold" evidently thought (1) and (2) meant the same thing.
    – user370390
    Commented Dec 25, 2019 at 16:01

1 Answer 1


To answer the presenting question first,
No, the two constructions are not always the same in meaning. There are several reasons for this.

The most important one is the point made in the comments, that logic (and computer languages) are not the same as natural language; and, while logical statements can usually be put into English, any English sentence containing quantifiers (especially if it also contains modals or negatives of any kind) is multiply ambiguous.

Logic is a stick-figure representation of linguistic meaning, and like stick figures, it leaves out a lot and expects you to fill it in from your imagination (or presuppositions, to the extent there's any difference). Logic assumes that quantifiers (like all, each, every, some, and most) modify nouns (all the men, each man, etc.)

But in fact quantifiers can "float". Some, but not all, of them can appear in adverbial position, before the main verb or after the first auxiliary verb. This doesn't change the meaning, but it does change the grammar. Especially with negatives.

  • All the men read the book. ==> The men all read the book.
  • Each man read the book. ==> The men each read the book.
  • Every man read the book, but not *The men every read the book.

When there is a negative morpheme in the sentence, the relative order of the negative and the quantifier can produce meaning problems.

  • Not all the men read the book. ≠ All the men didn't read the book.
    (the first says some didn't read it, but the second is ambiguous)
  • The men didn't all read the book. (same as Not all the men...)

The real problem here is that there are rules in logic for order of operators (modals, negative, and quantifiers) in propositions:

  • (∀x: Man(x)) (Read (x, Book)) is unambiguous, and so is
  • ¬(∀x: Man(x)) (Read (x, Book)), and
  • (∀x: Man(x)) ¬(Read (x, Book))

The first one says for every man, that man read the book. The second says that the first one is not true (for whatever reason) of every man. The third one says that for every man, that man did not read the book. The first and the third are contradictory, and the second one can report multiple situations.

That's logic.
Syntax requires modifiers to have certain positions in the sentence, whatever the math rules of logic require.

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