There is no/not?

Interesting question. I DON'T HAVE ANY absolute answers, but I HAVE SOMEcomments. I also HAVE NO absolute answer.

First, we can say "There isn't any/a", but we cannot say "There is no any/a". "Any/a" can be used with countable nouns, but we can't with "no" (ex. "There is no restaurants here."). Compare this with "There aren't any restaurants here." This is where these two forms meet. We have to change "is" to "are" ("There are no restaurants here" and "There aren't any restaurants here.")

To me, using "There is no" has a more concrete aspect to it ("There is no school today"). "There isn't any school today" sounds like there could be several schools, but we don't have to go to any of them today. In reality, we probably only go to one school, so even though "school" is countable it holds a quasi-noncountable quality to it.

Let's look at it the other way around. "There is no milk in the fridge". In this case, and in English books, I have only seen chapters where they try to get students to say "There isn't/aren't any". 

However, in certain cases, I think "There is no" would be perfectly fine. If both people are aware of what is being talked about, like with definite articles, then "There is no" would have more relevance.

A: Can you get that milk we bought yesterday out of the fridge?
B: Ok. I am looking, but there is no milk.

If one of the speakers doesn't know, "There isn't any" would have more relevance.

A: I am thirsty, can I have something to drink?
B: Ok. There is some orange juice and apple juice in the fridge, but there isn't any milk."

In conversation though, we treat them the same with a few exceptions.

"There is no turning back" / "There isn't any turning back(???)"
"There is no place like home" / "There isn't any place like home (???)"
"There are no cats" (???) / "There aren't any cats" - If the number is zero, then you only need to state there isn't 1, and logically "There are no cats" could just convey "There aren't 2 cats or more". It doesn't preclude there being 1, even though we usually assume it's zero.
"There are no tires in the trunk" / "There aren't any tires in the trunk" - This is the same as the school example. We would only have one tire, so as the cat example isn't clear enough, "There aren't any" goes too far conveying "There isn't the spare tire we would normally find, and there isn't another one either which we would never account for".


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