Unit 8. Numerals II
Cantor illustrated the concept of infinity for his students by telling them that there was once a man who had a hotel with an infinite number of rooms, and the hotel was fully occupied. Then one more guest arrived. So the owner moved the guest in room number one into room number two; the guest in room number two into number three; the guest in three into room four, and so on. In that way room number one became vacant for the new guest. What delights me about this story is that everyone involved, the guests and the owner, accept it as perfectly in order to carry out an infinite number of operations so that one guest can have peace and quiet in a room of his own. That is a great tribute to solitude.
Cardinal, indefinite and weighting numerals
As we have seen in the previous unit, cardinal numerals (‘one, two’), as well as indefinite and weighting numerals used in the same way, work like adjectives. They form brackets or coordinations, including – especially the weighting numerals, as might be expected – partitive ones.
|sklÌxt trÌy. ⇔ trÌ sklÌxty.||rooms, three individuals (see bracket inversion for word order)||three rooms|
|room-acc1 three-acc-acc2. ⇔ three-acc1 room-acc-acc2.|
|trÌ sklÌxtyn.||three individuals from the set of rooms||three of the rooms|
|ìvd crÌi. ⇔ crÌ ìvdy.||guests (recipients of hosting), a few||few guests|
|host-dat1 1/4-acc-dat2. ⇔ 1/4-acc1 host-dat-acc2.|
|crÌ ìvdyn.||a few from the set of guests||a few of the guests|
|jnÌ sklÌxtyn.||everything from the set of rooms||all rooms|
The latter phrase is a partitive construction that describes all items from its set, a possibility left open by the partitive cases’ definition. The corresponding cumulative bracket would mean ‘all things, which are rooms’ or ‘everything, which is a room’, i.e. there are no other things than rooms.
Multiplicative numerals (‘once, twice’) work like adverbally used adjectives: they form factive brackets.
|ftràsk dwÌa.||sneezing, two individuals||She sneezes twice.|
As an individual need not be temporally connected, two individuals of a continuous action such as ‘eat’ or ‘sleep’ do not necessarily mean eating or sleeping twice in the sense of two temporally separate actions. But then, even in English we speak of sleeping twice if we are thinking of two nights, even if we wake up in the middle of the first night and then go to sleep again. It’s not a question of continuity but of what functions as an individual, as mentioned before.
Distributive numerals (‘one each, in pairs’) are another use of the indefinite numeral RÌ. ‘each’, this time with a cumulative bracket.
|RÌ ìvdy dwÌi.||Each [pair] is two guests.||pairs of guests, two guests each|
|each-acc1 host-dat-acc2 two-acc-dat3.|
To express ‘each of something’, we additionally need the partitive bracket we know from the reflexive constructions. Again, we normally use a compound derived from the partitive bracket.
|RÌ ivdÌn dìy sklÌxty rÌy.||Each of the guests is the recipient of giving one room.|
|each-acc1 host-dat-partacc2 give-dat-acc2 room-acc-acc3 one-acc-acc4.|
|⇔ dà RÌi ivdýn sklÌxty rÌy.||Someone gives each of the guests one room. (verbose)|
|give-fact1 each-acc-dat2 host-dat-partacc3 room-acc-acc2 one-acc-acc3.|
|dà ivdRiì sklÌxty rÌy.||Someone gives the guests – each of them – one room.||Each of the guests gets one room. The guests get one room each.|
|give-fact1 host-dat-each-dat-dat2 room-acc-acc2 one-acc-acc3.|
|dà ivdì sklÌxty rÌy.||The guests are the addressees and one room is the content of giving.||The guests get one room [together].|
|give-fact1 host-dat-dat2 room-acc-acc2 one-acc-acc3.|
Adjectives of possession containing a numeral (‘two-windowed, four-legged’) need the same kind of construction, as sklÌxt jmÙxty dwÌy. room-acc1 window-ben-acc2 two-acc-acc3. would be read as ‘one (or several) rooms with two windows altogether’. The same is true of related nouns and such.
|sklyxtRÌ jmÙxty dwÌy.||Each of the rooms is the beneficiary of making two windows.||two-windowed room(s)|
|room-acc-each-acc1 window-ben-acc2 two-acc-acc3.|
|dnyRÌ gwÌqu.||Each of the walkers has four means of walking, i.e. legs (tool noun).||four-legged; quadruped(s)|
|qmyRÌ qÌfi.||Each of the groups is made of seven individuals.||group(s) of seven|
|kRà djiltRÌoR.||Each of the days is an episode of working. (inverted in comparison to the previous examples)||days’ work|
‘day’ defines a certain quantity and is therefore multiplied with ‘each’ by an epenthetic consecutive; see Measuring in unit 12 and Units of measurement in the appendix for more on this.
Recall that pnà. ‘make five individuals’ implies making them one after the other. Consequently, ‘the fifth’ is the temporal or spatial end point of making five: either the egressive (iR, closing time, temporal end point) or the illative (ir, spatial end point) case is appropriate here.
|pnìR.||the temporal end point of making five individuals||the fifth|
|pnìr.||the spatial end point of making five individuals|
|mìR ynjÌ pnÌny.||(mà.-desorption)||the twenty-first|
|make-egr1 16-partacc-acc2 five-partacc-acc2.|
‘the fifth room’ is the end point of making five rooms. We know from the cardinal numerals that the rooms in the phrase ‘five rooms’ are the accusative object of ‘five’, i.e. they are the content of making five individuals. As with multiplicative numerals, we can use this kind of construction with verbs that have an inner factive.
An illative or egressive bracket has a quite different meaning.
|pnìr sklÌxty.||the fifth room|
|pnìr sklÌxtyn.||the fifth of the rooms|
|dwìR sràjy.||the second meeting||They met for the second time|
|pnìr sklÌxtir.||the fifth thing, a room|
|rìR rOsàciR jmÌxi.||the first thing, the making of ice crystals||At first, ice crystals form.|
|one-egr1 crystal-fact-egr2 ice-acc-dat3.|
Repetitive ordinal numerals (‘every sixth’) are ordinals built into the kind of construction we used for the distributive numeral in ‘two guests each’.
|RÌ swÌhy. ⇔ swìrh RÌy.||six each ⇔ every sixth|
|each-acc1 six-acc-acc2. ⇔ six-ill1 each-acc-acc2.|
To translate numerals describing composition (‘twofold/double/binary, threefold/triple/ternary’), a cardinal numeral (a bracket or coordination) will often suffice.
|hlÌg dwÌy.||a twofold/double wall, two walls|
|ftràsk dwÌa.||a twofold/double sneeze. She sneezes twice.|
To highlight the integritive (twofold, i.e. one thing in two parts) or the composite aspect (double/binary, i.e. two parts forming a whole), we use a compound of a grouping numeral with different inner cases.
|krÌj dwÌi. ⇔ dwÌ krìjy. ⇒ krijdwÌ.||an ensemble of two [things]|
|ensemble-acc1 two-acc-dat2. ⇔ two-acc1 ensemble-dat-acc2. ⇒ ensemble-dat-two-acc1.|
|hlÌg krijdwÌy.||a wall, an ensemble of two||a twofold wall|
|hlÌg krijdwìy.||walls, forming an ensemble of two; walls, two ensembled ones||a double wall|
‘two/three sorts/kinds/types of’ is translated with the grouping numeral ‘sort’. The things which are sorted into a number of kinds of course want the dative.
|mÌh swyhÌ snÌwi. ⇔ swÌh mÌhy snÌwi. ⇒ myhswÌh snÌwi.||six sorts of snow|
|sort-acc1 six-acc-acc2 snow-acc-dat2. ⇔ six-acc1 sort-acc-acc2 snow-acc-dat3. ⇒ sort-acc-six-acc1 snow-acc-dat2.|
In counting, we use the inner factive.
|rà. dwà. trà. —||making one individual, making two individuals, making three individuals, …||one, two, three, …|
|one-fact1. two-fact1. three-fact1. …|
Room number eight is the room having an ‘8’, the one marked with an ‘8’; so what we need is an adjective of possession. To distinguish this from a room having eight things, we enclose the numeral in quotes.
|sklÌxt <8>Ùy.||the room with an ‘8’||room (number) eight|
For consecutively numbered rooms, ordinal numerals (‘the eighth room’) are an alternative.
Digit sequences such as numbers with many positions after the decimal point (including recurring ones) – or, say, credit card numbers – are also read as quoted digits.
|<1,A51A662530–>Ì.||1.A51A662530…hex = 1.644934066848…|
|rÌ. xÌk. dÌh. pnÌ. rÌ. dÌh. —|
|one-acc1. point-acc1. ten-acc1. five-acc1. one-acc1. ten-acc1. …|
We can get close to the idea of grammatical number (singular, plural, dual and others) by using a numeral as a compound modifier and thus downtoning it. Some examples of compounding have already been shown in the chapters above; to grasp the difference to uncompounded constructions, it may help to think of them as weaker forms of numerals, just as ‘a room’ is weaker than ‘one room’ with respect to the number ‘one’.
|sklÌxt rÌy. ⇔ rÌ sklÌxty. ⇒ sklyxtrÌ.||a/the room|
|room-acc1 one-acc-acc2. ⇔ one-acc1 room-acc-acc2. ⇒ room-acc-one-acc1.|
Don’t be tempted to translate grammatical number like this on principle; in most situations, the number of things is irrelevant.
Compounds with the grouping numeral krÌj. ensemble-acc1. as head form collective nouns.
|krÌj kRÌqi. ⇔ kRÌq krìjy. ⇒ krijkRÌq.||an ensemble of tones, of musical notes||melody|
|ensemble-acc1 tone-acc-dat2. ⇔ tone-acc1 ensemble-dat-acc2. ⇒ ensemble-dat-tone-acc1.|
This compound loses the tones’ inner case, which is fine here. It can, however, cause problems with an ensemble of gifts-acc (as opposed to an ensemble of givers-nom) or an ensemble of hosts-nom (as opposed to an ensemble of guests-dat); those should not be compounded.
Switching head and modifier to give a construction parallel to the ones in the previous chapter is not a good idea: objects of the compound would then refer to the tones, not the melody, so adding an adjective would not yield ‘a beautiful melody’ but ‘a melody of beautiful tones’
Other collective nouns include ‘team, flock, mankind, lexicon (vocabulary)’.
Strengthening, weakening and opposition
Adjectival verbs generally denote properties that are on the ‘positive’ side of some scale. For example, pràj. is on the positive side of a beauty scale, màv. is on the positive side of a wisdom scale, and fàt. is on the positive side of a speed scale. Compounds with the weighting numerals 5⁄8, 3⁄4 and 7⁄8 can be used to convey a more specific positive meaning, and 3⁄8, 1⁄4 and 1⁄8 indicate the less positive meanings ‘of little beauty or wisdom’, ‘slow’, and the like. These compounds work exactly like negated adjectives: they have an inner consecutive or factive case, depending on whether the underlying abstract nouns decribe consequences (‘beauty’) or actions (‘wisdom, speed’). Thus, priljdmÌ. beautiful-cons-3/4-acc1. means ‘very beautiful’, mavxpÌj. wise-fact-7/8-acc1. describes an extremely wise deed, and mavxpèj. wise-fact-7/8-nom1. an extremely wise person (while mevxpèj. wise-nom-7/8-nom1. means ‘almost all the wise ones’).
The nonexistence negator nÌ. marks the zero point, and the opposition negator kÌ. is on the negative side: priljnÌ. beautiful-cons-not-acc1. ‘not beautiful’ is definitely more impolite than priljcrÌ. beautiful-cons-1/4-acc1., and priljkÌ. beautiful-cons-opposition-acc1. is downright rude. And xacgnè. light-fact-not-nom1. means ‘dark, not giving out any light’. The weighting numeral rÌw. amount-acc1. marks an arbitrary point on the scale, which we will need in unit 11.
Uncompounded adjectives are another issue handled by pragmatics: literally, fèt. fast-nom1. just describes someone who is moving, speaking or otherwise acting, however slowly, but is usually taken to mean someone acting at a speed relevant to the context; lÌxw. green-acc1. is usually understood as something that is completely or predominantly green, and not just a bit greenish. This issue can also be understood as leaving out the weighting numeral if the weight is clear from context.
There is no generally applicable definition of the ‘positive’ side of an adjective; it is part of its lexical meaning. For example, there is no compelling reason why rÌc. ‘right’ is expressed by an uncompounded word and rilckÌ. ‘left’ is its opposition, and not the other way round. (See unit 12, Temporal and spatial verbs.)
Adjectives are not the only words that can be strengthened or weakened. The transition to nouns is smooth.
|dmà prìljy. ⇒ priljdmÌ.||the beauty (abstract noun) is much||a real beauty (concrete noun)|
|3/4-fact1 beautiful-cons-acc2. ⇒ beautiful-cons-3/4-acc1.|
|crà wìlgwy. ⇒ wilgwcrÌ.||the dog-ness (the consequence of dog-making) is a bit||a bit of a dog|
|1/4-fact1 dog-cons-acc2. ⇒ dog-cons-1/4-acc1.|
|jnà anày. ⇒ anajnÌ.||the secrecy (the ‘making secret’) is complete||a complete secret|
|1/1-fact1 secret-fact-acc2. ⇒ secret-fact-1/1-acc1.|
Weighted actions often, but not necessarily, have an epenthetic factive.
|jnà làxty. ⇒ laxtjnà.||want at all costs|
|1/1-fact1 want-fact-acc2. ⇒ want-fact-1/1-fact1.|
|crà wàxy. ⇒ waxcrà.||speak a bit|
|1/4-fact1 speak-fact-acc2. ⇒ speak-fact-1/4-fact1.|
|càwb Ràjgy. ⇒ Rajgcèwb.||hardly alive|
|1/8-fact1 live-fact-acc2. ⇒ live-fact-1/8-nom1.|
|nà Ràjgy. ⇒ Rajgnè.||dead|
|not-fact1 live-fact-acc2. ⇒ live-fact-not-nom1.|
|àv jnÌy. ⇔ jnà Ìvy. ⇒ yvjnà.||eat all||eat up|
|eat-fact1 1/1-acc-acc2. ⇔ 1/1-fact1 eat-acc-acc2. ⇒ eat-acc-1/1-fact1.|
‘He eats a lot (= a large amount)’ has the weighting numeral in the accusative, ‘He eats a lot (= He does a lot of eating)’ in the factive.
A grammatical form expressing strengthening is generally called augmentative or intensive, one expressing weakening is called diminutive. ‘eat up’, expressing a completed action, is the Lemizh equivalent of the completive aspect.
The sentence ‘She doesn’t eat it because of the vitamins’, with stress on the vitamins, is usually understood as ‘She eats it, but not because of the vitamins’. The seemingly obvious translation avnà crURÌjgOl. eat-fact-not-fact1 vitamin-acc-psu2. negates the whole sentence and consequently does not claim anything about the eating. Rather, it says ‘It is not true that she eats it because of the vitamins’, effectively meaning ‘She might eat it, but if so, it’s not because of the vitamins’. Instead, we need to negate the vitamins, yielding nà crURÌjgy. ⇒ crURyjgnÌ. not-fact1 vitamin-acc-acc2. ⇒ vitamin-acc-not-acc1. ‘something that is not vitamins; non-vitamins’. Again, an epenthetic consecutive would be an alternative, but this time the concrete accusative seems more appropriate.
And for the sake of completeness: nà avÌ crURÌjgOl. not-fact1 eat-fact-acc2 vitamin-acc-psu2., with the vitamins as an object of the negator, means ‘She doesn’t eat it, because of the vitamins’.
|àv crURyjg-nÌOl.||She eats it because of something that is not vitamins / because of non-vitamins.||She doesn’t eat it because of the vitamins.|
|àv crURyjgÒl djmynÌOl.||(coordination)||She eats it because of the vitamins, not the taste.|
|eat-fact1 vitamin-acc-psu2 taste-acc-not-acc-psu2.|
|Other modifiers and epenthetic cases also occur:|
|àv crURaRjg-RÌbvOl.||The times of vitamin-making are 3⁄8, i.e. she eats it because of something that is sometimes vitamins.||She sometimes eats it because of the vitamins.|
She eats it, sometimes because of the vitamins.
The same type of construction, but with outer cases other than the persuasive, is found in the following sentences:
- ‘He didn’t give it to his brother [but to someone else].’ (compound with nà. ‘not’, dat)
- ‘They aren’t talking to themselves [but to each other].’ (nà., dat – see reciprocity in unit 6)
- ‘I won’t come today [but maybe tomorrow].’ (nà., temp)
- ‘She came without the mechanic.’ (nà., com)
- ‘I’m not paying you to ask questions.’ (nà., fin)
- ‘I can manage with just the tiniest bit of help.’ (càwb. ‘1⁄8’, ins)
- ‘Not many arrows hit the target.’ (crà. ‘1⁄4’, acc – don’t use a negation of dmà. ‘3⁄4’)
Likewise, ‘someone/something else’ and ‘different’ are negations of the definite pronoun, not of the whole sentence.
|dà tynÌi.||He gave it not to this one.||He gave it to someone else.|
|nàgw gwalpÌer tynÌy.||She is drinking from a different cup.|
|drink-fact1 cup-acc-ela2 this-acc-not-acc-acc3.|
Objects can also be modified with modal verbs and adverbs (‘She should eat it because of the vitamins’, ‘Maybe she eats it because of the vitamins’, unit 13) or ‘that’-clauses (‘They say that she eats it because of the vitamins’, unit 15).
Modified objects vs. partitive
Modified objects cannot express that she eats it partly because of the vitamins, as this is the domain of the inner partitive. We can use the partitive alone or combine it with weighting numerals for specification (‘mostly, marginally’). These constructions incidentally illustrate the subtleties of cumulative vs. partitive brackets with weighting numerals.
|àv crURynjgÒl djmÌnOl.||She partly eats it because of the vitamins, partly because of the taste.|
She eats it because of the vitamins and the taste.
|eat-fact1 vitamin-partacc-psu2 taste-partacc-psu2.|
|àv dmÌnOl crURÌjgy.||Much of the reason for eating is vitamins.||She mostly eats it because of the vitamins.|
She eats it, mostly because of the vitamins.
|eat-fact1 3/4-partacc-psu2 vitamin-acc-acc3.|
The second example might look like it would mean ‘She eats it because of many vitamins, among other things’. However, the inner partitive indicates that the weighting numeral is taken from the set of reasons for eating, and the cumulative bracket with the vitamins equates ‘much from the reason for eating’ with the vitamins.
Other examples of such partitive constructions include:
- ‘I wasn’t speaking about you for the most part’ (crà. ‘1⁄4’, acc)
- ‘He is mostly eating fish’ (dmà. ‘3⁄4’, acc)
As you know, an object in an outer partitive case indicates a part of something in the sense of one or some of a set of things. But what about a fraction of a whole, as in ‘I see part of the hotel’? While what I see is not taken from a set of hotels, it is taken from a set of things (walls, doors and windows, roofs, chimneys) that, taken together, form a hotel. So we have to use qmì vxÌzdy. group-dat1 hotel-acc-acc2. ‘things grouped to form a hotel’, the outer accusative equating the hotel with the group (as opposed to the grouped things). We can also compound: inversion yields vxÌzd qmÌy. hotel-acc1 group-acc-acc2. ‘a hotel, which is a group’ ⇒ qmyvxìzd. group-acc-hotel-dat1.. This loses the hotel’s inner case, which, as with collective nouns, can cause ambiguity. Whether or not we compound, we need an outer partitive to specify that we are only talking about some of these grouped things.
|dmàt qmìen vxÌzdy.||I see some of the things grouped to form a hotel.||I see part of the hotel.|
|see-fact1 group-dat-partnom2 hotel-acc-acc3.|
|dmàt qmyvxìzden.||I see a hotel-part.|