Is “can not” unambiguous?

Question

I always try to remember to use "cannot" when applicable as in "I cannot take an umbrella" (because I do not have one).

I also thought that the problem with "I can not take an umbrella" was that it was ambiguous: it could also mean that I could decide not to take an umbrella. Trying to write unambiguously most of the time, I would therefore never use it.

Now I see it claimed that it is in fact not ambiguous, and only carries the second meaning. Usually I would accept such advice at face value and start using "can not" when the second meaning is unambiguously meant, but this comes from a style guide I have other reasons not to respect very much.

Does "can not" have a single unambiguous meaning?

(I have read http://english.stackexchange.com/questions/4510/why-is-cannot-spelled-as-one-word but my question is more about current usage. The length of the answer to that question does confirm my prejudice a bit, though)

Answer 1

"Can not" is ambiguous and should be avoided. If you write "I can not take an umbrella" you can be interpreted in two opposite ways:

1. That you cannot take an umbrella (because you forgot to buy one, for example).

2. That you can not take an umbrella (meaning, for example, that you are allowed to go without an umbrella).

---

Note that according to Common Errors in English Language,

These two spellings [cannot and can not] are largely interchangeable, but by far the more common is “cannot” and you should probably use it except when you want to be emphatic: “No, you can not wash the dog in the Maytag.”

Answer 2

Cannot is not the same as "can not".

I cannot go

Means you are unable to go.

I can not go

Means you are able to not-go, that is, you CAN avoid going.

Probably you should always use cannot and never try to make sentences with the "can not" sense.