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You don't get that choice. Yeah, you can not show up, and you might have a flexible work environment, but there's still the social pressure of, 'My desk is sitting empty while everybody else's in the office.'” Source

Methinks the latter is correct. I cannot find anything with regards to using to after can not in any dictionary.

Is there any rule with regards to the usage of to with not after a modal verb? If so, does it apply in the same manner to can not and cannot or can't? With respect to the quoted sentence there would a semantic difference between can not show up and cannot show up, and this difference, in turn, makes me think that I should use to after can not.

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You cannot show up.

This means you won’t be able to show up, or that you shouldn’t show up.

You can not show up.

This means you can choose to be a no-show, and is what the article is saying.

You can learn to dance.
You can dance to music.
You can march to the beat of a different drummer.

These are all grammatically correct, and the “to” is following a verb. In the first sentence, the “to” is part of the infinitive “to dance”; in the following two sentences; the “to” is a preposition.

You can not to show up.

As others have said, this is not a grammatical sentence. The words “can not to” can be used in sequence, but the structure goes something like this:

Facebook will do whatever it can not to mess it up.

which could also be reworded as:

Facebook will do whatever it can to not mess it up.

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  • Would "Facebook will do whatever it can not mess it up" be incorrect then? In what structures would it be correct to use "can not to" or "can to not" and why? – Jerzy Brzóska Jun 30 '19 at 4:34
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    @JerzyB - No that is correct English. In fact, it was taken from a news article (link provided in my answer). – J.R. Jun 30 '19 at 13:05
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As you mentioned, after modal verbs (can, could, would should, ...) we are not allowed to use to. Instead, we need to use the simple tense of the verb. So, here using to after can is incorrect and "Can not show up" is correct.

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  • Is then the rule(with regards to using "to") for "can not" the same as "cannot". Here the author appears to be saying that the can (not to show up at work), not that he cannot. If one were to read this sentence it would sound exactly the same as the following, "Yeah, you cannot show up, and you might..". Would you elaborate on the semantic differences in meaning between "cannot" and "can not" in this context? – Jerzy Brzóska Jun 29 '19 at 5:27
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    @JerzyBrzóska Cannot means being unable to do something; can not means being capable of not doing something—but also possibly capable of doing it too. – Jason Bassford Jun 29 '19 at 18:39
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"Can not show up" is correct here.

In fact "Can not to" would not be correct, unless the syntax was different; for example:

They are doing everything they can not to alienate their users.

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