When should I use the subjunctive mood?

In which cases should I use the subjunctive mood?

I suggest that every applicant fill out the form carefully.

If she were rich, she would live on Long Island.

What is called the "subjunctive" or the "present subjunctive" is in fact just a simple untensed variant of normally tensed that-complement clauses.

Unlike real subjunctive systems in languages like German or Spanish, this construction appears
- only in subordinate complement clauses,
  never in main clauses, or other kinds of subordinate clauses;
- only in one variety of subordinate clause (that-complements);
- only with one variety of predicate (impositives).
It's what you call extremely limited in distribution.

Complement clauses are governed by their predicates. Which predicate you use controls what kind(s) of complement can be used with it, or whether it can have a complement at all. With impositive predicates (see lists below), that-complements must have a subject noun phrase (i.e, the subject NP can't be deleted), but in these that-clauses the verb form is infinitive, not present or past; i.e, the verb does not agree with its subject NP.

Since this construction is governed by the predicates it can occur with, and the predicates are all impositive -- i.e, they are predicates indicating that the speaker is imposing their will on the addressee -- the construction is associated with that concept, and traditionally "subjunctive" verbs were sposta "express" this "mandative" notion. Actually, of course, that's expressed by the predicate, and only emphasized by the use of this construction with it.

There are four patterns, with four different kinds of complement-taking impositive predicates:

1) Transitive impositive communication verbs:
insist, suggest, demand, prefer, propose, suggest, recommend, demand, ask, mandate, prefer, request, ask, desire, advise, urge, specify, instruct, order, demand, insist, require, rule, necessitate, suffice, advocate, vote, would rather, and move (in the parliamentary sense).

Pattern: NPVolit Verb that [NP + Infinitive VP]
They asked that he remove his shoes.
They prefer that she arrive ten minutes early.

2) Transitive impositive emotive predicate adjective: adamant

Pattern: NPVolit be Adj that [NP + Inf VP]
They were adamant that he remove his shoes/that she arrive ten minutes early.

3) Intransitive impositive predicate adjectives (normally with Extraposition):
necessary, desirable, imperative, important, necessary, preferable, optional, permissible, acceptable, okay, all right, satisfactory, desirable, advisable, sufficient, necessary, mandatory, urgent, vital, crucial, essential, fitting, right, appropriate, better, expedient, and legitimate

Pattern: That [NP + Inf VP] be Adj = Extraposition => It be Adj that [NP + Inf VP]
That he remove his shoes is desirable = Ext => It is desirable that he remove his shoes.
That she leave early is preferred = Ext => It is preferred that she leave early

4) Picture nouns derived from impositive predicates:
recommendation, necessity, insistence, proposal, preference, request, desire, advice, suggestion, option, alternative, recommendation, demand, requirement, necessity, imperative, condition, mandate, specification, rule, ruling, edict, instruction, principle, prerequisite, order, qualification, ultimatum, vote, and motion (in the parliamentary sense).

Pattern: [PictureN that [NP + Inf VP]] (not a clause, but an NP with a complement clause)
I heard about [the request that he remove his shoes].
[The request that she arrive ten minutes early] is highly improper.

There are other predicates, but if one learns these lists, one comes to recognize the semantic characteristics of impositive predicates, and thus to decide whether to use this construction with them, or others, or not. That's it for the "present subjunctive".

The "past subjunctive" -- which I will not deal with here -- is a different set of constructions altogether, completely distinct from the "present subjunctive" constructions, expressing nothing like their sense, and behaving in completely different ways.

The reason why they're both called "subjunctive" is because Latin had a subjunctive mood that was used in many ways, and these constructions reminded classically-educated grammarians of certain uses of the Latin subjunctive mood.

But in English they're just a couple more mildly idiomatic constructions, out of thousands. That's why obsessing about the English "subjunctive mood" is a waste of time and effort, and always ends up in confusion.

In general, the subjunctive mood should be used in "a statement contrary to fact, a wish, a mandative statement" (from this guide). I think "statement contrary to fact" could also often be considered a hypothetical, so I will refer to it as that.

In your first example, you are expressing a wish or possibly a mandative statement, "I suggest" and so it follows with a subjunctive: "every applicant fill".

In your second example, you have constructed a hypothetical, thus you use the subjunctive mood ("she were"). When you see "if" or "whether" used in a hypothetical way, it is a good bet that you want to use the subjunctive mood.

And another example:

I demand that you be on time at work.

Then we are using the subjunctive mood ("you be") because this is a mandative statement (note that the imperative is something else, grammatically).

In any discussion of the subjunctive mood in English, it is worth noting that this particular grammatical construction is often morphologically identical to the normal indicative, showing up only with "be" and in constructions involving third person (historically, this was not the case). Perhaps as a result, the subjunctive mood as something with overt morphological markings is disappearing from English. (That is not to say that the subjunctive mood would cease to exist if the distinguishing morphology disappeared — it would still be there whether it looks different from other constructions or not.)

Because the overt subjunctive is disappearing, you often see it looking like normal past tense: "if I was ten years younger". At the moment, this remains nonstandard, but common.

Well, the above answer is very close. I mean, to be all honest, the subjunctive isn't dead in Modern English. You probably say it all of the time and don't know it. Technically, in all honesty, when one says something like, "If he only knew what I had done, he would kill me", the verb "knew" in "he knew" is technically 3rd person singular past subjunctive of the verb "to know", but it looks the same as the past indicative in Modern English. Another example:

"If I had had more time, I would have done it."

The above "I had had" is the past perfect subjunctive, but it looks just like the past perfect indicative so the subjunctive is there; its just hard to see these days. Although, if one were to say (future subjunctive) something like, "If I were king of England, I would cut taxes", he would be using a subjunctive conjugation with a morphological inflection that differs from the past indicative "I was".

Technically, we used to use the morphological present subjunctive in Modern English after conjunctions like "if, whether, unless, until, before, although, though, lest, etc.", but, nowadays, this is rarely seen or heard and many consider it pretentious to use it, but it's still correct. Here's an example:

"If music be the food of love, play on." (Shakespeare)

We can see this in "if truth be told", "whether it be", "until death do us part", and so on wherein the verb is in the subjunctive form. These above statement are still said in English. Below, I shall show the indicative/subjunctive conjugations in English for the verbs "to be" and "to speak":

Present Ind./Subj. He is/He be He speaks/He speak

Past Ind./Subj. He was/He were He spoke/He spoke

Future Ind./Subj. He will be/He were to be He will speak/He were to speak

Past Perfect Ind./Subj. He had been/He had been He had spoken/He had spoken

Present Perfect Ind./Subj. He has been/He have been He has spoken/He have spoken

There are more conjugations, but these are the most common ones. I'm not going to go into how to use them in detail per se because that has already been shown to you in the original answer. Here are the conjugations, though. I hope this might help.

I'll just quote the Encarta encyclopedia, since I believe the rule it mentions is different from what the answers mention.

Specifically, note the part that says "however remote", which I did not seem to see in the other answers. (This is different from how the subjunctive is used in languages such as French, where it is merely used to express doubt.)

Subjunctive Mood

The subjunctive mood is a characteristic of a verb that expresses a wish or a condition contrary to fact. The subjunctive is now rarely used except in the following instances.

If, As If, and As Though Clauses

Use the subjunctive in clauses that begin with if, as if, and as though if the wish or condition expressed could never come to pass. If there is a possibility, however remote, that the wish or condition could become fact, use the indicative instead.

Subjunctive:

If I were a fire-breathing monster, …

Indicative:

If I was promoted, …

That Clauses

Use the subjunctive in clauses that begin with the word that and include verbs that express commands, requests, or requirements.

The prisoner insisted that his demands be met.

Because the subjunctive is heard infrequently in speech, such constructions may seem overly formal in some contexts. For a more informal tone, rephrase the sentence with a verb in the indicative mood.

The prisoner insisted that they meet his demands.

Expressions with the Subjunctive

Some common expressions make use of the subjunctive mood, including:

as it were
be that as it may
come what may
far be it from me
so be it

Subjunctive Forms

Some verbs have different endings or spellings in the subjunctive than in the indicative mood. Most often confused are the subjunctive and indicative forms in the present tense, active voice, and third person.

Indicative:

he, she, it sees

Subjunctive:

he, she, it see

Be careful also when choosing the proper subjunctive form of the irregular verb be, particularly in the present and past tenses.

Present active:

Indicative: I am; you are; he, she, it is; we are; you are; they are
Subjunctive: I be; you be; he, she, it be; we be; you be; they be

Past active:

Indicative: I was; you were; he, she, it was; we were; you were; they were

Subjunctive:

I were; you were; he, she, it were; we were; you were; they were

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