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I'm having a difficult time determining if a certain math problem should be classified as using Formal or Informal Logic. Here it is:
1. ALL except 2 of my pets are dogs.
2. ALL except 2 of my pets are cats.
3. ALL except 2 of my pets are birds.
Q: How many pets do I own?
A: 2 or 3
So, while it's obvious why the answer could be 3, it's not obvious how it could be 2 as well. The reason why is because the phrase "All" could be zero, which would represent an empty set. And, of course, I could own pets other than the ones mentioned (fish / lizards). So, knowing that, we can substitute that example back into the original problem as follows: I own two, pets, which are both fish. All except 2 of my pets are dogs, which in this case, is equal to zero. So, the set of dogs can possibly be an empty set.
So, anyways, I was wanting to know if the puzzle itself could be considered "formal", or is it informal because most people would mean "All" to at least equal one, and we add that assumption in there?

### I read you as asking this:

I interpret you as asking this: Why do we find it puzzling or counterintuitive that statements 1–3 are true in the case in which you own exactly two pets, neither of which is a dog, a cat, or a bird? Is it because we assume that "all" implies "at least one"?
Those are empirical, psychological questions whose answers I don't know. But I do think it's worth distinguishing between what "all" logically implies and what "all" conversationally implies. (You might have a look at the SEP entry on implicature .)
On the one hand, the statement "All intelligent extraterrestrials are extraterrestrials" had better be true, and its truth had better not depend on the existence of intelligent extraterrestrials. So I think there's good reason to deny that "all" logically implies "at least one."
On the other hand, someone who owns no dogs and who says "All my dogs have their shots" has said something odd or misleading, even if true. So I think there's good reason to say that, at least sometimes, "all"...

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