| Comment | I am fully aware that the two-word construction "can not" is often used where the opposite of "can" (=cannot) is intended. Despite the ubiquity of this usage, it is still an error.
Indeed there are differences! What we should use when we mean "are unable to" or "are not permitted to" is one word: cannot. This is the word that we contract when we write "can't." It is a common error to separate "can" and "not." The American Heritage Dictionary is quite clear on this point: cannot is the negative form of the word can.
Here's one example I use:
If I say "I cannot smoke," I mean that I am unable to or not permitted to smoke. If I say, "I can not smoke," not modifies smoke. My meaning is: "I am able to not smoke," i.e., I have the ability to avoid smoking, to prevent myself from smoking, or to stop smoking.
Another example:
If I am unable to go or am not permitted to go, I should write, "I cannot go." If I have a choice between going and not going, I may write, "I can go, or I can not go it is my choice."
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