One of my followers on Twitter named Aaron Allbrooks tweeted, “Why does ‘let’s know when you arrive’ sound weird, but ‘let us know when you arrive' doesn’t?” It was a good question. I tweeted back at him, “And conversely, ‘Let us go to the mall’ sounds weird, but ‘Let’s go to the mall’ sounds fine.” Also, just imagine a group of prisoners begging their captor to set them free. Let us go makes sense; Let’s go doesn’t. What’s going on with let us and let’s? Let’s find out.
Traditional English-grammar doesn’t distinguish sentences like Let’s go and Let us know. It classifies them both as imperatives. The understood subject of each is You, and us is the direct object of let. But as Aaron noticed, the two kinds of sentences don’t behave the same way. Sometimes you can contract let us to let’s, and sometimes you can’t. In fact, as reported in the Cambridge Grammar of the English Language, this is only one of five differences between sentences beginning with let’s and let us.
At this point, we need to have a name to refer to the two kinds of let-sentences. The Cambridge Grammar of the English Language, or CGEL for short, refers to sentences like Let us know as “ordinary imperatives,” and to sentences like Let’s go as “first-person inclusive let-imperatives.” By first-person inclusive, the authors mean that if I say Let’s go, I’m not talking about me and some other people; I’m talking about me and you. They also use the term “open let-imperatives” to refer to very similar sentences that don’t involve us. These are sentences such as Let x be a rational number between zero and infinity, Let that be a lesson to you, or What God has joined together, let no one put asunder, or even sentences with dummy subjects, such as Let it snow and Let there be light. I’ll use the term special let-imperatives to refer to both kinds: first-person inclusive let-imperatives and open let-imperatives. Not only is this term more convenient, but also most of the differences we’re going to talk about apply to both kinds of special let-imperatives.