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We will make the convention that exact categories be skeletally small.

Is this construction (used in a mathematical context) correct? There is something that strikes me as odd in that "be". Should it be "are"? I know I've seen a similar way of using "be" like that, without conjugating the verb, but I'm not completely sure when it should be used.

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    That’s simply a present subjunctive. Nothing special going on here. – tchrist Apr 2 '14 at 18:55
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    @tchrist - why dont you present that as an a answer? subjunctive is not a common word.. – Argot Apr 2 '14 at 18:58
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    @tchrist: if you'd care to elaborate that into a full answer I'd be happy to upvote it. For what it's worth, my English has been mostly self-taught, so I'm really not aware of most grammar rules, I just go with what "seems right" to me. – Bruno Stonek Apr 2 '14 at 19:01
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    welcome to the "world of nitpicking" ...( could be stated as a manifesto for ell if such questions are in huge number ) – Argot Apr 2 '14 at 19:03
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    @Wierin: no, I think it's a verbose way of saying "We will consider exact categories to be skeletally small". There's a difference between saying "let the dogs be tame" and "we will consider all dogs to be tame". – Peter Shor Apr 3 '14 at 23:48
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I am not a linguist, so please understand that this is only the best I can do, and may be more long-winded than necessary.

Grammatical mood is the quality of a verb that conveys the writer's attitude toward a subject. Verb moods indicate a state of being or reality. Commonly known moods are indicative (states reality), interrogative (states questioning), imperative (states command), conditional (indicating a conditional state that will cause something else to happen), the now uncommon subjunctive mood (indicating a hypothetical state, a state contrary to reality, such as a wish, a desire, command, recommendation, or an imaginary situation, etc.) The conditional mood has largely replaced the subjunctive in English.

The subjunctive clause can be a mandative subjunctive which is a clause following a mandative word (expressing a demand, requirement, request, recommendation or suggestion) and usually, but not always, begins with 'that' and contains a bare infinitive.

Sometimes the bare infinitive can be hard to spot unless it stands out. With inflected verbs such as to be, it is easy, as the inflected forms are 'am, are, is', whereas the bare form is 'be'.

  • I suggest that you be careful.

With other verbs, sometimes the bare infinitive is apparent only in the third person singular.

  • It is important that he stay by your side.

The important word is the mandative word.

  • We demand that he refund our money immediately.
  • He insists that the Carrot Bisque be the first course for the celebration.

NB: that is not a necessary element in the mandative subjunctive, but the bare infinitive is:

It is important he stay by your side.
It is imperative he tell the truth. I suggest he depart immediately.

Your example:

  • We will make the convention (that) exact categories be skeletally small.

is a correct use of the subjunctive, which is very common in mathematics today. It can also be seen in poetry, and earlier writings before the conditional came to be used commonly, e.g. the Bible.

Edited to add: I had a lot of help in making this answer correct. I am very appreciative of this and just want to acknowledge that.

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    This is very useful and informative. Thank you very much for taking the time to explain it so carefully! – Bruno Stonek Apr 2 '14 at 20:27
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    Thank you both for your precision and willingness to help! – Bruno Stonek Apr 3 '14 at 22:30
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    Just a nitpick wrt "The conditional mood has largely replaced the subjunctive in English." Though true of English in general, it is somewhat less true for AmE than for BE, I think. In AmE, "if I were a schoolteacher" is perhaps more common than "if I was a schoolteacher." My impression is that BE rarely uses the subjunctive. – Drew Apr 4 '14 at 22:50
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Ever since I have been on English forums I have found that many forum participants have problems with the subjunctive present tense. In this subjunctive the third person singular has no -s and the verb to be has the form be.

To show that be is a subjunctive, and not the infinitive, I'll write "be*". The asterisk indicates the subjunctive. A look at German might be helpful so as to understand the difference between the infinitive and the subjunctive.

  • Infinitive: It must be wrong. - Es muß falsch sein.
  • Present tense indicative: That is not true.- Das ist nicht wahr.
  • Present tense subjunctive: Be* that as it may, I don't trust him.- Sei es wie es mag, ich trau ihm nicht*.

In German the infinitive is sein, the subjunctive is er sei*. In English the form be can be infinitive or subjunctive. So, in order to get a feeling for the subjunctive present tense a native speaker should know the sentence types where this subjunctive is used.

As far as I know, there is no comprehensive chapter in any English grammar book where all the sentence types are presented. The Longman English Grammar has the subjunctive in various paragraphs and in the register there is no differentiation between subjunctive present tense and subjunctive past tense. Consequently, a native speaker is forced to make his own list of sentence types with the subjunctive present tense. By the way it is cumbersome when writing about grammar to write the names of tenses in full. Normally I write Pr for present tense indicative and Pr* for present tense subjunctive.

We will make the convention that the values for A be* small.
The strikers demanded that their salaries be* raised.

After verbs expressing demands and the like, the subjunctive present tense is used in formal styles. Of course, a formula such as "we will make the convention" is also a form of wish/requirement/demand.

  • @Mari-Lou A Thanks for the editing. I wanted to ask you whether I have to replace my original post by the post edited by you but as it seems contact from my tablet is not possible. – rogermue Apr 4 '14 at 10:56
  • I should add that in AmE subjunctive sentences of the type "The workers demanded that the salaries be* raised" are frequent in newspapers, whereas in BrE such subjunctives are not so frequent and the normal construction is a that-clause with should. – rogermue Apr 4 '14 at 11:08
  • You can choose whether to "rollback" to the original post or make further edits to your post. It is your answer, the aim was to improve its presentation but if you disagree with any of the modifications, you're absolutely free to go back to the original version. – Mari-Lou A Apr 4 '14 at 16:59
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    It is absolutely all right. Your edit is an improvement, no question. I'm writing with a tablet. Obviously, formatting facilities such as oblique letters are not possible from a tablet. – rogermue Apr 4 '14 at 17:02
  • The subjunctive present tense and subjunctive past tense are now completely different constructions in English. And native speakers don't make lists ... they have learned how to use them without lists. – Peter Shor Jul 10 '15 at 0:04
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This construction is common in the mathematical context, where the bare "be" is a well understood abbreviation of the full phrase "will be defined as." It sounds odd in conversational English, because we expect "could be", "should be", "will be" or so forth.

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