1.

Ex:

Let's (let us) go,

Let him speak

Let's rock,

ets

I can't find an answer. Why is the Verb (go, speak rock) without "to"?

2.

And should I say? Is it correct?

"Let's (to) walk quickly and (to) go home".

TIA
1 2
Some modals require the verb they subordinate to have 'to' before it while others do not. Let is one that does not.

Have, need, want, like, ought, be+going, be+willing, be+able are examples of modals that require 'to'.

Must, shall, will, should, could, let, may, might are examples that do not require 'to'.

With some like 'dare' you can use 'to' or not use it.
Linian_U1.
Ex:
Let's (let us) go,
Let him speak
Let's rock,
ets
I can't find an answer. Why is the Verb (go, speak rock) without "to"?
2.
And should I say? Is it correct?
"Let's (to) walk quickly and (to) go home".
These sentences are called 'imperatives' - they use the base form of the verb without "to". Although let-imperatives are a little unusual in the special use of the verb "let" (it doesn't mean "allow"), they are like any other imperative in not requiring "to", for example "Bring your own food", "Don't move", "Please pass the salt", and so on.

BillJ
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BillJ
Linian_U1.Ex:Let's (let us) go,Let him speakLet's rock,etsI can't find an answer. Why is the Verb (go, speak rock) without "to"?2.And should I say? Is it correct?"Let's (to) walk quickly and (to) go home".
These sentences are called 'imperatives' - they use the base form of the verb without "to". Although let-imperatives are a little unusual in the special use of the verb "let" (it doesn't mean "allow"), they are like any other imperative in not requiring "to", for example "Bring your own food", "Don't move", "Please pass the salt", and so on.

BillJ
That's not correct Bill. These examples are not all in the imperative mood.

"Let's go" is the cohortative mood. It's purpose is to mutually encourage something. The speaker is encouraging himself and at least one other person to do something (in this example, 'go').

"Let him speak" is the hortative mood but could also be the imperative mood if emphasis were provided (which it may be). The hortative is used to encourage someone (other than the speaker) to do something. If given as a command, this would also be imperative.

"Let's rock" is no different from "Let's go" and is thus cohortative.

The mood expressed has nothing to do with whether the following verb takes 'to' or not. That is determined by a structural effect of the modal used to expressed mood. In these examples the modal is 'let'. Let never requires 'to'.
drew.wardThat's not correct Bill. These examples are not all in the imperative mood
I didn't say they were. If you'd read my post carefully, you'd have noticed that I didn't use the word 'mood', but simply 'imperative' (as in 'imperative construction' - not 'imperative mood').The examples quoted are, in fact, unquestionably imperatives. With the exception of "Let him speak", these clauses all belong to a distinct subtype of imperative construction understood as '1st person plural', which is marked by a specialised use of the verb "let" (differing from the verb "let" meaning "allow").
drew.wardThe mood expressed has nothing to do with whether the following verb takes 'to' or not
I was referring to the fact that here the verb "let" itself is a so-called 'bare infinitive' (i.e. not "to let"). Clearly the non-finite complement that follows is a bare infinitival clause. The analysis of, for example, "Let us go for a walk", is "Let (catenative verb) - "us" ( NP object) - "go for a walk" (bare infinitival clause as second complement) with an interpretation that includes the addressee(s) in the reference along with the speaker, thus "Let us go for a walk" proposes that you and I go for a walk, not that I go with some third person.

"Let" can, however, be a modal (a lexical modal to be precise) expressing deontic possibility, permission (i.e. give permission) but it's also used more generally in a causative sense similar to 'enable', as in "The good weather let us finish the job early". But that's a genuine modal use. It has nothing to do with the OP's imperative examples.

English no longer has a mood system marked by inflection, such as 'indicative', 'subjunctive', 'imperative' etc., as used in such languages as Latin, French and German. As far as English is concerned, historical change has more or less eliminated mood from the inflectional system with irrealis mood confined to 1st/3rd person singular "were", which is moreover usually replaceable by the ordinary preterite form "was". The main mood system, therefore, is analytic rather than inflectional, marked by the presence or absence of special words, the modal auxiliaries.

BillJ
Imperative is a mood. But I understand what you mean when you say imperative form. However none of these are using the imperative form. By definition the imperative form is simply a special structure which signifies the imperative mood. In English that structure is formed by omitting the subject, omitting the aspectual auxiliary (for affirmative imperatives but keeping it for negative ones), moving the 'idea verb' to first position and keeping it in the form required by the omitted non-durational aspectual auxiliary 'do' which is the 'bare infinitive', (any further details such as the object of the verb (if not understood), and prepositions (and prepositional phrases), adverbs, and clauses that further qualify the verb (when, how, under what conditions) go next if desired) and an exclamation mark is placed at the end.

Go!

Get out!

Leave me alone!

Shut that dog up before I do it!

These are all imperatives which use that imperative form to express the imperative mood.

Let's go (Let us go).

Let him speak.

Let's rock.

Are not in that imperative form. Even if they had exclamation marks instead of periods (full stops), that would still not signify the imperative mood but rather the exclamatory mood which doesn't have near the same meaning.

LET+US is a special form which when used as a unit like it is in these examples acts as a modal expressing the cohortative mood (think of the word 'cohort' -- you want someone to do something with you). LET+US is only used in unperfected, non-durational ('simple') aspect affirmative statements in the present or future tenses in which the subject consists of at least two people, one of which must be the speaker and one of which must be the person to whom the sentence is directed (the listener or reader).

"Let's go" and "Let's rock" use 'let' as described above. In those examples, 'let' is not in the 'bare infinitive' form that would be used in an imperative structure. It is actually agreeing with 'us' for subject and number (1st person singular), a form which is identical to the 'bare infinitive' in English.

"Let him speak," also uses 'let' as a modal auxiliary. In this case it expresses a hortative mood (it's a family of moods which encourage or discourage to varying degrees) which is the same family of moods as the cohortative expressed in the other two examples. In this case the expressed mood is the adhortative. Like the cohortative, the adhortative is used to encourage or urge someone to do something. The primary difference is that the cohortative requires that the subject include the speaker while the rest of hortatives (including this, the adhortative) do not. As used in this example, 'let' can also be interpreted to express the permissive mood (allowing something). Just as different modals may be used to express the same mood (for instance 'may' also can express the permissive mood), one modal can express more than one mood, and sometimes (as in this example) can express multiple moods at once (in this case adhortative and permissive -- meaning that the speaker is urging the person to whom he is speaking to allow a person 'him' to speak). 'Let' when used as a modal auxiliary (aside from its use in the special LET+US modal form) is a whole verb, meaning that it may be used in every combination of tense, aspect, mood, and perfection as a verb used as a vector (idea verb) even though it occupies the first verbal position.

In such constructions, the subject (which is also the person or people the speaker is addressing) 'you' is omitted as "understood" when 'let' is used to express a hortative mood (even if other moods are also expressed by 'let' at the same time). The use of 'let' for expressing the hortative moods (excluding the cohortative) is limited to unperfected, non-durational aspect statements in the present and future tenses but unlike with the cohortative, those statements may be affirmative or negative. When the statement is affirmative the mood expressed is adhortative while when the statement is negative, it is the dehortative (which discourages the subject or urges him against doing something). When used to express a hortative mood, in addition to omitting the subject (you), the aspectual auxiliary 'do' is usually omitted as well for affirmative (adhortative) statements but may not be omitted for negative (dehortative) statements. Consider the following:

"Let him speak." (adhortative with 'do' omitted)

"Do let him speak." (adhortative with 'do' not omitted and vocal stress added to it to express the suprahortative which is used to strongly encourage or strongly urge)

Don't let him speak. (dehortative -- 'Do not let him speak' is equivalent. Vocal emphasis added to "don't", "do", "not", or "do not" would further strengthen the urging against to express the inhortative mood).

------------------------------------------------------------

For 'let' to express one of these hortative moods, the subject of the sentence must always be the person to which the speaker is directing the statement which means it is always 'you' (singular or plural).

Not all sentences in which 'let' is used as a modal auxiliary that have 'you' as the subject express hortative moods. The person the speaker is addressing (still 'you') can also be the subject of a sentence in which 'let' is used to express the permissive mood. For example: "Your children are very young. Do you let them walk to school alone?"

In all other modal uses aside from the hortative ones discussed above, 'let' may take on any combination of tense, aspect, mood, perfection, and negation. It may also be used for questions as well as statements. Again the example above:

Do you let them walk to school?

Do you not let them walk to school?

Don't you let them walk to school with their friends anymore?

Did you let them walk to school?

Will you let them walk to school tomorrow?

Should you let them walk to school?

Would you let them walk to school if I walk with them?

Couldn't you let them walk to school if they take their phone?

Are you letting them walk to school in the mornings?

Were you letting them walk to school when the weather was so bad last week?

Will you be letting them walk to school everyday next year?

Have you let them walk to school before?

Had you let them walk to school before this semester?

Should you have let them walk to school all by themselves?

Should you have really been letting them walk to school all this time knowing that so many criminals are out there?

In all of these variations, 'let' is used as a modal auxiliary expressing the permissive mood. Even in forms where that modal auxiliary has more than one component, it is still treated as a single unit.

Color Code:

Subject = Black

Object = Grey

Modal Auxiliary 'let' = Red (with everything modifying the modal auxiliary in underlined red)

Vector 'walk' = blue (with everything modifying the vector in underlined blue)

-------------------------------------------------------------

As you can see, 'let' as a modal auxiliary used for the permissive mood is also not in 'bare infinitive' form and can in fact take on quite complex forms. But either way, they're by no means imperative structures.

That said, the original example "Let him go," could be used as an imperative IF it were to have an exclamation point at the end. However, it could only be such an imperative in that one form and as its negative equivalent, but in no other (so not if a subject other than 'understood you' is used, not in the past tense, not as a question, etc.).
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drew.wardImperative is a mood
Imperative is actually a clause type, to be precise. The others are declarative, interrogative, and exclamative. They are differentiated by their internal structure.
drew.wardLET+US is a special form
All the properties of, say, "let us pray" suggest it is a special idiomatic imperative clause. For example, it cannot have a subject, and it is negated with a fixed "don't" that is understood inside the clause: "Don't let's get all bent out of shape" means "Let's not get all bent out of shape". There is of course an ordinary imperative reading for "let us pray", where it means "Please permit us to engage in prayer"; but the meaning is different: the idiomatic "Let's pray" can ONLY mean "Let's you and me pray, or "Let's all pray, you included"; it cannot mean what the ordinary imperative means, which typically would be "Please go about your business and permit me and him to engage in prayer: stop interfering with us".

drew.ward"...In this case it expresses a hortative mood
There is of course no hortative mood in English grammar. You are just being silly.

BillJ
Linian_ULet's (let us) go,
Let him speak
Let's rock,
ets
I can't find an answer. Why is the Verb (go, speak rock) without "to"?
It's without "to" because it follows the verb "let". let, make, have, and help all follow the same pattern.

They won't let me see it.

Please try to make him stop doing that.

I always have them arrive at 8.

Helen helped us carry this table.

help can also take "to": Helen helped us to carry this table.

You need this:

Let's walk quickly and go home. No "to"s.

CJ
@Billj So as not to continue down a pointless track, all I can say is that last post of yours is pretty much totally wrong in every way. You are obviously a very intelligent guy but you've been given some horribly incorrect information. I would be glad to discuss it with you in a proper forum but this not the place. But really, your entire understanding of the concepts discussed in this thread is so absolutely incorrect that I don't even know how to properly respond.

CalifJim
Linian_ULet's (let us) go,Let him speakLet's rock,etsI can't find an answer. Why is the Verb (go, speak rock) without "to"?
It's without "to" because it follows the verb "let". let, make, have, and help all follow the same pattern.
Let when used as a modal does not require its subordinate to have 'to'.

Have, when used as in your example below does not require 'to' but have as a modal auxiliary used to express obligation or necessity does require 'to' (I have to go to school - I have to buy groceries).

CalifJimThey won't let me see it.
Please try to make him stop doing that.
I always have them arrive at 8.
Helen helped us carry this table.
The examples you've provided above have nothing to do with the OP's question because none of the verbs (in boldface) are modals. They are in fact the 'main verb' in the first, third, and fourth sentences and the object of the second. The auxiliary for the first sentence is 'will', while 'let' is the 'main verb' meaning allow, 'me see it' is the direct object (what the subject 'they' will not allow). Because it's a completely different usage of the word 'let' than the example in the OP's post, it really has no bearing here.

Drew
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