Volition: willingness and intention will, shall, ‘ll
Willingness
This can be paraphrased by be willing to. Willingness is expressed in speech time, while the action predicated by the main verb either coincides with speech time or refers to a future event. Unwillingness is expressed by will not, more usually contracted to won’t:
Will you give a donation to the Wildlife Society?
Yes, I will. I’m sorry, I won’t.
Will may also be used with inanimate objects when they apparently respond badly to what is expected of them.
The car won’t start.
The meaning of willingness, realized by will, readily lends itself to various pragmatic uses. Will would be interpreted as a directive in Will you listen to me and stop interrupting? and as a polite offer followed by acceptance in Will you have another whisky? Yes, I will.
Interrogative shall is used in the 1st person to consult the addressee’s wishes or to ask for advice. This is the most widespread use of shall in present-day English:
Shall I carry those bags for you?
Shall we go home now?
Intention
This can be glossed by intend to. When a speaker expresses an intention, the intention naturally coincides with speech time, but the intended action is in the future:
We’ll pick you up outside your house at 9.
I shall /I’ll be back in a minute.
The speaker’s commitment in using these modals is as strong as in the epistemic meanings. For this reason, the modals of intention can have the force of either a promise or a threat, according to whether the action is beneficial to the addressee or otherwise. These interpretations are reinforced by the addition of such verbs as promise and warn.
They shall be paid tomorrow. (formal)
I shan’t overcharge you, I assure you. (formal)
I’ll bring you something back from Paris, I promise.
I warn you that if you keep talking in this way, I’ll hang up.
The full form shall /negative shan’t used with a 2nd or 3rd person subject counts as the speaker’s guarantee.