When should one use “shall” and "will”?
'Sure, I __________ come.'
Which word - "shall" or "will" - should be used in the blank?
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In today's English, will is always correct and shall is always problematic in one way or another -- except in specific idioms, quotations and set phrases with an established wording, e.g. "What shall we do with a drunken sailor?".
Will and shall were once two ordinary full verbs that had the same meaning as their German cognates wollen and sollen. For will, the old sense (volition, what you want to do) has survived in the noun will (last will and testament) and in would [like]. For shall, the old sense (obligation, what you are supposed to do) has survived in should.
For some reason, these and similar verbs have gone through a series of weird changes of meanings. (Not just in English. The Dutch cognates willen and zullen have gone through a similar but different process. Among the three major West-Germanic languages, only German has preserved the original meanings.)
Proto-Germanic did not have a future tense; futurity was expressed using the present tense together with words such as tomorrow. (English still does this with present progressive, though not in the same generality.)
Even with their original meanings, will and shall could sometimes be used to express futurity:
Tomorrow I shall (= am obliged to) go to the office.
Tomorrow you will (= want to) celebrate your birthday.
Tomorrow he will (= wants to) celebrate his birthday.
Through overuse this led to a system in which shall could be used also to express pure futurity in the first person, and will could be used to express pure futurity in the second and third person. Initially the original volition/obligation senses survived as shades of meaning that were active only in certain situations. Also, one could still make the non-standard choice when expressing futurity shaded by volition or obligation:
Tomorrow I will (= want to) go home.
Tomorrow you shall (= are obliged to) see me in my office.
Tomorrow he shall (= is obliged to) see me in my office.
But later these distinctions were lost and in some cases even reversed. (I would really like to know how that happened.) More recently, the auxiliary used for pure futurity was standardised to will in all persons.
As a result of the partial reversal of the volition/obligation connotations of will/shall, now that all of them have become mostly obsolete, it is generally unsafe to rely on them at all. For instance, most people don't seem to be aware that "What shall we do with a drunken sailor?" once carried a connotation of "What are we supposed to do with a drunken sailor?" rather than "What do we want to do with a drunken sailor?".
Therefore it is best not to use shall to express futurity at all.
The Longman English Grammar says: The simple future tense is formed with will in all person forms. The auxiliary shall can be used with I and we as a variant. Unfortunately the grammar does not give a hint how learners should handle the use of shall for future.
I would say forget the shall-future. It is a system that is vanishing. All the same you find it in written English by some authors. Today shall has a touch of elevated style.
What was the cause for the use of shall for future of the first person (I and we)? "will" originally is a verb that expresses volition. If you will (intend) to do something then the normal consequence is that you will (future) do it. In this way "will" was adopted as auxiliary for future tense.
But in the first person (I, we) "will" is ambiguous. It can express volition or future. That's why "shall" was used in the first person. By the way, "shall" is the normal auxiliary for future in Dutsch ( zullan). Today the use of "shall" for future is becoming a bit old-fashioned or formal.
Shall has 4 possible occurrences. Yet it will be always a verb.
Shall I/you/he/she/they/we go?
Should we go?
They each mean the same thing, but the first sentence is just simply... eloquent.
None shall pass
The sentence above has a regal tone to it, a lot of expressed power. Yet it can also be used to demand that something succeeds.
You shall win the lottery.
Saying this would give someone the impression that you have the power over the lottery. Then again, it can also be said for good wishes.
We shall succeed
I/You/He/She/They/We shall see.
This use of shall is used to suggest that something will happen, but it's more demanding, and full of egotism.
They will eat cake tomorrow
They shall eat cake tomorrow.
Both sentences mean the same thing, but the one with sha'll suggests that the speaker/writer has the power to allow them to eat the cake.
We will leave tomorrow
We shall leave tomorrow
Again, the shall sentence is just a bit more demanding, in an eloquent way. It's as if the word itself is telling everyone to be prepared, that there isn't a choice.
Although use of shall is increasingly rare, it is perfectly legitimate to use it in the example sentence, particularly if you wish to emphasize certainty. To my mind, shall is predictive and does not carry the same connotations of intent that can attach to will.
(Others may disagree. My opinion is formed by my experience as an engineer used to authoring requirements documents. Many engineering organisations, including NASA, explicitly differentiate between the meanings of shall and will in their documentation. See Wikipedia)