Which of the following is right?
I am reading a paper (math) where it says:
Demanding that A is a Lorentz scalar, ...
But I feel like it should be
Demanding that A be a Lorentz scalar, ...
I'd be grateful for help and would appreciate if someone could point out what kind of grammatical construction this actually is.
You are right, though I would use a completely different verb than "Demanding". E.g. "Without loss of generality, take A to be ..." or "If we take A to be ...", Demanding that something is is hardly a mathematically rigorous method of proof.
In academic papers the sunjunctive is preferred. Passive constructions are also preferred. I'd be okay with the indicative if the mood was conditional "assuming A is ... then..." or "if A is ... then ..." or that a quality has been already established "as A is ..." but not when positing something.
The following are all perfectly acceptable English sentences (well, beginnings of sentences), and they all mean the same thing:
[1] i Demanding that A be a Lorentz scalar...
ii Demanding that A should be a Lorentz scalar...
iii Demanding that A is a Lorentz scalar...
These are three types of mandative construction. In [1], i is a subjunctive construction, while ii and iii are tensed constructions. In the terminology of CGEL, ii is a should-mandative, while iii is a covert mandative.
Discussion
First, here is a bit of what CGEL says about the subjunctive construction (p. 90):
Subjunctives
These exclude auxiliary do, and are usually subordinate: subjunctive main clauses are restricted to fixed phrases (So be it!. Be that as it may, etc.) or frames (Long live... !, Far be it from me to..., etc.). In other respects, however, they are more like tensed clauses than non-finites. In the first place the subject is an obligatory element. Secondly, the most productive use of the subjunctive construction takes the same subordinator as is found with tensed declaratives, that, as in the earlier We demand that he be reinstated, etc. And, thirdly, except in more or less fixed expressions, the subjunctive alternates with a tensed construction:
[38] i It is important [that she be reinstated immediately]. [subjunctive]
ii It is important [that she is/should be reinstated immediately]. [tensed]
And about the mandative construction in general (pp. 996-1000):
7.1.1 The mandative construction
Mandative clauses characteristically occur in construction with various verbs, nouns, and adjectives, such as demand and mandatory (to cite the two that contain the element mand on which the term 'mandative' is based).
[5] i They demanded [that access to the park remain free].
ii It is mandatory [that all pools be properly fenced].We will apply the term mandative not only to the subordinate clauses but also to the verb, noun, or adjective which licenses or governs them—for example, we will say that as used in [5] demand is a mandative verb and mandatory a mandative adjective.
■ Three types of mandative clause
On the basis of their internal structure we distinguish three types of mandative clause:
[6] i They demand(ed) [that the park remain open]. [subjunctive mandative]
ii They demand(ed) [that the park should remain open]. [should-mandative]
iii They demand [that the park remains open]. [covert mandative]
iv They demanded [that the park remained open] [covert mandative]Those with the form of a subjunctive construction we refer to as subjunctive mandatives, those containing the specialised use of should as should-mandatives, and those with the form of an ordinary declarative content clause as covert mandatives. There is nothing in the internal structure of the bracketed clauses in [iii-iv] to distinguish them from the non-mandative content clauses in I know [that the park remains open] or He said [that the park remained open]—the mandative meaning derives entirely from the governing verb demand. Covert mandatives contain a present tense verb, or else a backshifted preterite, as in [iv]: we can't have an ordinary, past-time preterite (*They demand that the park remained open).
Clear cases of the covert construction are fairly rare, and indeed in AmE are of somewhat marginal acceptability. In AmE the subjunctive is strongly favoured over the should construction, while BrE shows the opposite preference.
■ Semantic contrast between mandative and non-mandative clauses
A content clause in construction with demand or mandatory—or require, stipulate, essential, necessary, etc.—is always mandative, but others items such as insist, suggest, important can select either a mandative or a non-mandative clause as complement:
[7] i a. She insisted [that he tell her the whole story]. [mandative]
b. I suggest [you go and see a doctor]. [mandative]
c. It's important [that he should take us into his confidence]. [mandative]
ii a. She insisted [that he had been lying]. [non-mandative]
b. I suggest [she doesn't like us very much]. [non-mandative]
c. It's not important [that the gift won't be a surprise]. [non-mandative]The difference in meaning is comparable to that between imperative and declarative clauses.[It has indeed been suggested that mandatives should be analysed syntactically as subordinate imperatives; we have argued against that view in Ch. 10, §9.8.] With mandatives it is a matter of bringing about the situation expressed in the content clause. As with imperatives, we can invoke the concept of 'compliance': in [ia] she insisted on compliance, in [ib] I'm advocating compliance in a relatively tentative way, and in [ic] compliance is said to be important. With the non-mandatives, by contrast, it is a matter of the truth of the proposition expressed in the content clause.
In [iia] she insisted on the truth of the proposition, in [iib] I put the proposition forward as something that may well be true, and in [iic] the truth of the proposition is taken for granted, presupposed: it is treated as a fact, a fact that is said to be not important.
■ Ambiguity between mandative and non-mandative clauses
With the items that allow both mandative and non-mandative complements there may be ambiguity between them. Compare:
[8] i She insists [that he take the eight o'clock train]. [mandative]
ii She insists [that he took the eight o'clock train]. [non-mandative]
iii She insists [that he takes/they take the eight o'clock train]. [ambiguous]Example [i] is distinctively subjunctive. By contrast, [ii] is non-subjunctive and cannot be taken as a covert mandative because took is an ordinary past-time preterite, not a backshifted one: the time of his taking the train is earlier than that of her insisting. Both versions of [iii] are ambiguous. With he takes it can be a covert mandative equivalent to subjunctive [i]: the meaning is that she insists on his taking this train, either on some particular future occasion or habitually. But the more likely interpretation is non-mandative, that she emphatically asserts it to be the case that he takes this train—most probably a matter of his habitually doing so, but it could be a single future occurrence with a futurate interpretation ("She emphatically maintains that he is scheduled to take the eight o'clock train"). The version with they take has the same ambiguity, but on the mandative reading it is also syntactically indeterminate between the subjunctive and covert constructions.
■ Mandatives and modality
The mandative construction falls within the broad area of meaning that is known as modality. In our discussion of modality as expressed by the modal auxiliaries (Ch. 3, §9), we distinguished various dimensions of modal meaning, including 'kind' and 'strength'. Two of the main kinds of modality are deontic and epistemic: deontic modality is concerned with obligation and permission (as in You must leave at once or You may leave as soon as you've finished), while epistemic modality is primarily concerned with one's level of assurance about the truth of the proposition expressed (as in He must/may have missed the train). On the dimension of strength, must is strong and may weak, while ought is somewhere in between, of medium strength. Within this framework, mandatives clearly involve deontic modality: It is necessary that you leave at once is comparable to the above You must leave at once, with the deontic use of must.[Note that the adjective necessary, unlike the verb must or the adverb necessarily, is restricted to the deontic kind of modality, so that it takes mandative but not non-mandative clauses: we can say He wasn't necessarily referring to you, but not, equivalently, *It isn't necessary that he was referring to you.] As for the dimension of strength, mandatives show variation here, with demand, insist, necessary, for example, stronger than advise, recommend, desirable. In general, however, they occupy an area on the scale of deontic strength higher than that represented by permission: mandatives are rare with allow (He won't allow that she attend the meeting), questionable with permit, and quite impossible with let—verbs of permission generally take infinitival complements (He won't allow/permit her to attend the meeting).
Blurring of semantic contrast between mandative and non-mandative
Verbs expressing deontic modality (whether auxiliaries or lexical verbs) may of course appear in content clauses, and this may lead to a loss of the sharp distinction between mandative and non-mandative illustrated in [7i] vs [7ii]. Consider:
[9] i She insisted [that he must/had to wear a hat when he went out].
ii I suggested [that we might invite the Smiths at the same time].There are grounds for saying that the bracketed clauses here are non-mandative. The modals must and might do not have plain forms and hence cannot occur in subjunctive or should mandatives; have is not morphologically restricted in this way, but had could not here be replaced by have (or should have), so we cannot plausibly argue that these clauses are covert mandatives. Note, moreover, that we could replace insisted and suggested by, for example, said and added, verbs that do not take mandative complements. Nevertheless, the meanings are very similar to the mandative She insisted that he wear a hat when he went out and I suggested that we invite the Smiths at the same time. This phenomenon is similar to that found with main clauses. You must/have to wear a hat when you go out and We might invite the Smiths at the same time are declarative clauses, not imperatives, and yet they are most likely to be interpreted in context as directives, as having much the same force as the imperatives Wear a hat when you go out and Let's invite the Smiths at the same time (cf. the discussion of declarative directives in Ch. 10, §9.6.2). This strengthens the analogy we have drawn between mandatives and imperatives on the one hand, non-mandatives and declaratives on the other. Mandatives and imperatives are inherently deontic; non-mandatives and declaratives are not, but when they incidentally contain deontic modal expressions their interpretation may come to merge with that of mandatives and imperatives respectively.
Modal harmony between mandative governor and its complement
One consequence of the resemblance between a modalised non-mandative and a mandative is that such items as stipulate, essential, requirement, which (unlike insist and suggest) normally allow only mandative complements, may nevertheless appear with a non-mandative that contains an appropriate deontic modal:
[10] i The agreement stipulates [that an election must be held next year].
ii These criteria must be satisfied within the overriding requirement [that work
assessed must show literary merit].
iii It is essential [that the radiochemical procedure for the assay of lead-210 shall
provide for a high degree of decontamination from major fission products].We will say that a non-mandative is allowed with such items if it is modally harmonic 'ith them: the strong deontic modals must and shall here match the modality expressed by stipulate, requirement, and essential. (For further discussion of modal harmony, see Ch. 3, §9.2.3.)
■ Should-mandatives
In main clauses should expresses medium strength modality (like ought): You should inform he police countenances that you may not do so—I could add but I don't suppose you will, which would not be possible with strong must. Consider now its use in:
[11] i They demanded [that he should be freed]. [should-mandative]
ii She insists [that I should have told her]. [non-mandative]
iii They insisted [that all murderers should be hanged]. [ambiguous]
iv They suggested/recommended [that we should engage a consultant].Example [i] is clearly not a case of modal harmony, for demand is stronger than should is in its main clause uses: cf. the discussion of [2ic] above. It is for this reason that we recognise a specialised use of should as a grammatical marker of a distinct should-mandative construction, equivalent in meaning to the subjunctive. Insist in [11ii] is also strong, but here should is the ordinary medium-strength one that we have in the main clause I should have told her. Moreover, insist cannot here be being used mandatively, for the past time expressed by have rules out a mandative interpretation. The example is like [7iia], meaning approximately "She maintains that I should have told her". Example [11iii] can be interpreted in either way. As a should-mandative it is equivalent to subjunctive They insisted that all murderers be hanged, "They insisted on having all murderers hanged" (which implicates that they were in a position of power); in the non-mandative reading they forcefully expressed their view as to the right punishment for murderers (and hence may have been ordinary citizens).
More problematic is [11iv]: suggest and recommend are of medium strength and hence potentially harmonic with the ordinary should. This time, therefore, We should engage a consultant does accurately express the content of their suggestion/recommendation. We probably need to accept that the distinction between a should-mandative and a modally harmonic non-mandative is here neutralised; such examples are much more frequent than the clear cases of modal harmony like [10], but they are also considerably more frequent, especially in AmE and AusE, than strong should-mandatives like [11i].
■ Distribution of mandative clauses
In the most straightforward cases the mandative clause functions as (internal) complement to the governing mandative word or else, with nouns and certain adjectives, as subject or (much more likely) extraposed subject in the clause in which the governing item heads the predicative complement:
[12] i the requirement that it be signed by a director [complement]
ii That it be signed by a director is no longer a requirement. [subject]
iii It is no longer a requirement that it be signed by a director. [extraposed subject]The syntactic relation between the mandative clause and the governing word may, however, be less direct:
[13] i The main recommendation was that an outside consultant be engaged.
ii It seemed the most important thing in my life at this moment that she should
know the real truth about me.
iii One of the qualities demanded of a politician by other politicians is that he or
she always keep a confidence.In [i] recommendation is head of the subject while the mandative clause is complement of be: this is the specifying use of be, where properties of the variable (here the subject) carry over to the value (here the predicative complement). In [ii] the mandative property of important percolates up, as it were, so that it applies to the NP in which important is modifier. And [iii] combines these two extensions of the relationship: the main clause contains specifying be and the subject is mandative by virtue of demand, which heads the non-finite clause modifying qualities.
A sample of mandative verbs, adjectives, and nouns
We give here examples of items from these three categories that license mandative clauses. The annotation '†' signifies that the item readily takes ordinary, non-mandative, content clauses too (as illustrated for insist, suggest, and important in [7i-ii]).
[14] advise/advice† agree/•ment† allow† arrange/•ment
ask beg command/- decide/decision†
decree/- demand/- desire/- determine/•ation†
enjoin entreat/•y insist/•ence† instruct/•ion
intend/intention move/motion ordain order/-
pledge/- prefer/•ence propose/•al† recommend/•ation
request/- require/•ment resolve/-† rule/•ing†
stipulate/•ation suggest/•ion† urge/•ing† vote/-[15] i advisable appropriate† compulsory crucial† desirable
essential fitting† imperative important† necessary
obligatory preferable proper urgent vital
ii anxious eager insistent† keen willingList [14] gives verbs together, where applicable, with the corresponding nouns; the notation '-' indicates that the noun has the same lexical base as the verb.[The final e of the verb base is deleted before a suffix beginning with a vowel, as in determination, etc. (see Ch. 19 §5.15). With wish, mandatives are commonly found with the noun (It is her wish that the matter be resolved quickly), but are hardly possible with the verb, which takes, rather, a modal preterite (He wishes he had told them). Similarly mandatives are licensed by the noun regulation but not normally by the verb regulate. Besides ruling, there is a noun rule which takes only a mandative complement: the rule that ties be worn.] The items in [15] are adjectives: with those in [15i] the mandative characteristically appears as subject or extraposed subject (It's vital that she be kept informed), while with those in [ii] it is normally complement within the AdjP (I'm anxious that it should be settled quickly). A few of these provide the base for de-adjectival nouns: importance, necessity, eagerness, etc. It should be emphasised, however, that there can be no question of giving a definitive list of mandative items: in spite of suggestions that have been frequently made that the subjunctive is dying out in English, this construction is very much alive, with attested examples like I would stress that people just be aware of the danger suggesting that its distribution is increasing.
References
R. Huddleston and G. K. Pullum, The Cambridge Grammar of the English Language (Cambridge University Press, Cambridge, UK, 2002).
