In this section, we examine the lexical status of French cardinals.2
Following Fradin (2003: 102), we distinguish two types of atomic units in the lexicon:
lexemes and grammemes. Lexemes are typically nouns, verbs, adjectives, adverbs, while grammemes are grammatical units such as prepositions, determiners, conjunctions. Fra-din identifies the following characteristic properties of lexemes:
(1) a. It is an abstract unit to which word-forms are related; this unit captures the variations across word-forms.
b. It possesses a phonological representation which gives it prosodic autonomy.
c. Its meaning is stable and unique.
d. It belongs to a category and can have an argument structure.
e. It belongs to an open-ended set and can serve as output and input of derivational morphology.
Whatever the analysis of French complex cardinals such asvingt-et-un‘21’, simple car-dinals likevingtorunare underived and therefore have to be listed in the lexicon. In what follows, we argue that simple cardinals in French pattern with lexemes rather than grammemes.
In French, the simple cardinals are the elements listed in (2) that serve as cardinals and as building blocks for complex cardinals.3
(2) un‘1’,deux‘2’,trois‘3’,quatre‘4’,cinq‘5’,six‘6’,sept‘7’,huit‘8’,neuf ‘9’, dix‘10’,onze‘11’,douze‘12’,treize‘13’,quatorze‘14’,quinze‘15’,seize‘16’,
1This does not mean that all determiners are lexemes but rather that cardinals have to be treated as an exception.
2For complex cardinals, see Section 3.
3The elementsmillionandmilliardare not simple cardinals in French; their respective values are realized asun million(‘one million’) andun milliard(‘one billion’). They semantically belong to the quantity noun series in-aine(see Table 2, p. 23)
vingt‘20’,trente‘30’,quarante‘40’,cinquante‘50’,soixante‘60’, cent‘100’,mille‘1,000’
Simple cardinals have the properties (1b–c). They can be used as single word answers, meaning they have an autonomous phonological representation. They have straightfor-ward semantics, denoting counting values.
2.1 Form variation abstraction
As for property (1a), whileun‘1’ is the only simple cardinal varying in gender (m: [œ̃]
un, f: [yn]une), many simple cardinals are subject toliaison(linking), a morphosyntactic phenomenon whereby French words can change in form depending on the phonological properties of the following word. For example, in (3), the adjective bon agrees in gender and number with the following noun, in both cases masculine and singular. But in a liaison context such as prenominally, the form bɔ̃ appears in (3a) in front of a word starting with a consonant (not a liaison trigger:⊖) and the form bɔn appears in (3b) in front of a vowel-initial word (a liaison trigger:⊕). Outside liaison context (⊘), adjectives assume the same form as in liaison context without trigger (⊘=⊖).4
(3) a. un
Unlike adjectives, cardinals can have three different forms for the three contexts above.5 For example,six‘6’ has different realizations (si, siz, sis) for the three contexts:
(4) a. in liaison context without a liaison trigger⇒si⊖ six
si⊖
souris suʁi
‘six mice’
b. in liaison context with a liaison trigger⇒siz⊕ six
4For more details about the morpho-syntactic aspects of liaison see Bonami et al. (2004).
5See Plénat (2008), Plénat & Plénat (2011) and the citations therein for a detailed description.
Not all cardinals have different forms in all three contexts. Table 1 gives the five different patterns of syncretism found with the simple cardinals. Type A cardinals are not sensi-tive to liaison and thus display only one form; in type B the⊖ and the⊘are identical and the⊕has an additional consonant at the end, while in type C all three forms are distinct. In type D,⊖is overabundant with a long form and a short form, and the long form is also used in the two other contexts. Type E is a variant of type B where instead of having an additional consonant for⊕, the final fricative alternates between voiceless f and its voiced counterpart v.6
Table 1: Type of simple cardinal variation according to liaison
Type Example ⊖ ⊕ ⊘ Cardinals
A 4 katʁ katʁ katʁ 4, 7, 11, 12, 13, 14, 15, 16, 30, 40, 50, 60, 1000
B 2 dø døz dø 1, 2, 3, 20, 100
C 6 si siz sis 6, 10
D 5 sɛ̃/sɛ̃k sɛ̃k sɛ̃k 5, 8
E 9 nœf nœv nœf 9
The simple cardinals in (2) have an associated form paradigm for liaison, which fit Fradin’s property (1a). This property is part of the conceptual definition of lexeme; it is neither required nor sufficient by itself. Definite determiners which have form paradigms in French and German are not considered lexemes, while English adjectives are lexemes even though their forms do not vary.
We turn now to the two remaining properties (1d–e): belonging to an open-ended category and participating as the output and potentially the input of derivational mor-phology.
2.2 Morphological input
In French, simple cardinals clearly serve as input for several morphological derivations as summarised in Table 2 below (see Saulnier 2008, Fradin & Saulnier 2009, Saulnier 2010 for a detailed discussion).7
As bases for the ordinals, simple cardinals are part of a morphological category in terms of Van Marle (1985) namely the derivational domain of ordinals, but to satisfy (1d), simple cardinals have to belong to a unique morphosyntactic category.
6In the case of type E, there is also hesitation for the⊕form between nœv and nœf as they can both provide an onset for the following trigger unlike in type B.
7While belonging to the same series of nouns designating groups of approximate cardinality,millier (‘thou-sand’),million(‘million’),milliard(‘billion’) are derived frommillewith different suffixes (-ier,-ion,-iard).
Table 2: Some derivations on French cardinals (adapted from Fradin & Saulnier 2009: 201)
Suffix Derivation Category
-ième deux (2)⟶deuxième(‘second’ ordinal) Adj -ième cinq (5)⟶cinquième(‘fifth’ part) Adj/N -ain quatre (4)⟶quatrain(‘quatrain’) N -aine douze (12)⟶douzaine(‘dozen’) N -aire trente (30)⟶trentenaire(‘thirty-year-old’) Adj/N
2.3 Morphosyntactic category
Following Saulnier (2010), we consider simple cardinals to be a sub-category of indefinite determiners, CARD.
Saulnier (2010: 31–40) applies the discriminating contexts defined in Leeman (2004)’s work on French indefinite determiners. She shows that cardinals have the following distribution across the six diagnostic contexts.
(5) endislocation:+ ⟶il adeuxsolutions = il en adeux
‘he has 2 solutions = he has 2’
only alone before N:− ⟶mesdeuxlivres (*mesplusieurslivres)
‘my 2 books (*my several books)’
following the indefinite:− ⟶*undeuxlivres (uncertainlivre)
‘*a 2 books (a certain book)’
following the definite:+ ⟶lesdeuxlivres (*lescertainslivres)
‘the 2 books (*the certain books)’
followed by the definite:− ⟶*deuxles livres (tousles livres)
‘*2 the books (all the books)’
followed bydeNP:+ ⟶deuxde mes collègues
‘2 of my colleagues’
With these criteria in mind for the category CARD, it becomes clear that there are sim-ple cardinals that were not listed in (2) because they do not participate in the formation of complex cardinals.
Zéro‘0’, for example, is not a construction unit for complex cardinals but it behaves like a CARD in all the contexts in (5). Saulnier (2010: 38) consideredzéroto depart from the cardinals distribution because she could not find examples for the contexts in (6), expectingzéroto be singular.8
8In the same contexts, Saulnier does not examineunand the surprising plural number that arises when it follows a definite or a possessive. For example, inpour ses/sonunmois‘for his one month anniversary’, the masculine singular form of the possessivesonis far less common than the pluralses; the possessive can take its plural formsesdespite the presence of the cardinalun‘1’.
(6) Examples from the web (26/12/2016)
endislocation:+ ⟶Il a des tas d’contacts, des tonnes de numéros pour remplir son phone mais des vrais potes il en azéro.9
only alone before N:− ⟶Et il ne nous restera alors quenosplzéroeuros d’augmentation pour pouvoir demander un crédit.10
following the indefinite:− ⟶*unzérolivre/livres.11
following the definite:+ ⟶Je vote pourlesplzéroheures payées trente-cinq.12
followed bydeNP:+ ⟶Mais même les potes des autres viennent ici etzéro de mes potessont venus me voir.13
And contra Saulnier (2010),zéroalso appears inzéro+N subject NPs:
zéro+N subject:+ ⟶Pendant ce temps,zéropersonnesplsont mortes de surdoses de marijuana.14
In derivational morphology,zéroalso gives a corresponding ordinalzéroièmefollowing the pattern of other simple cardinals.
2.4 Morphological output
Apart from fixed value cardinals, French uses variable cardinals such asn‘n’ (pronounced [ɛn] ) orx‘x’ (pronounced [iks] ). Likezéro, these variable cardinals do not participate in complex cardinal formation but they appear in the contexts in (5) and allow a subset of the derivations for fixed value cardinals (e.g.énième‘nth’ pronounced [ɛnjɛm] and xième‘xth’ pronounced [iksjɛm] ).
(7) a. Une solution consiste à rechercher lesNmeilleures solutions pour chaque ville épelée.15
b. Donc l’installateur fait des bidouilles avec lesX paramètres qui en [soi] ne sont pas très clairs ou pas forcément adaptés aux diverses situations des clients…16
9‘He’s got many contacts, tons of numbers to fill his phone, but real mates, he’s got zero.’
https://genius.com/Enz-narcisse-and-cassandre-lyrics
10‘Then we will only have our 0 euros of raise to ask for a credit.’
http://psasochaux.reference-syndicale.fr/files/2015/04/Tract-avril-15.pdf
11‘*a zero book/books’
12‘I’m voting for the 0 hours being paid as 35.’
https://fr.toluna.com/opinions/762230/Etes-vous-pour-ou-contre-les-35-heures
13‘But while even the other guys’ pals come here, 0 of mine have come to see me.’
https://twitter.com/MisHyding/status/762360289329307649
14‘All this while, 0 persons have died of marijuana overdose.’
https://anarchocommunismelibertaire.wordpress.com/
15‘A solution would be to search for the N best possibilities for every city name.’
http://www.afcp-parole.org/spip.php?article152
16‘So the installer switches around the X parameters which are a bit obscure or not necessarily adapted to the various customer situations.’
https://www.bricozone.fr/t/reglage-chaudiere-viessman.11296/page-7
c. Aujourd’hui, je constate que pour laénièmefois, une voiture est garée devant mon entrée de garage, m’empêchant de sortir.17
These cardinals are obtained by converting letter names, usually French or Greek, to cardinals, making them the output of a morphological process and therefore fitting part of criterion (1e).
2.5 Open-ended set
In the general domain or in mathematical contexts this practice is limited to the con-version of a few letter names, but in computer programming names for integer-valued variables are created all the time and behave as simple cardinals , making CARD an open-ended category.18Even the derived ordinals appear in computer program descriptions.
(8) a. Lance le son à partir de lanbième[ɛnbejɛm] seconde.19
b. appFunc(NUM): Renvoie l’adresse de laNUMièmefonction de la page courante20
The preceding discussion shows that French simple cardinals are part of an open-ended set with the productive coinage of integer variables. As we have seen above, ordi-nal derivation takes simple cardiordi-nals as input and letter name conversion gives simple cardinals as output. These three observations indicate that French simple cardinals fit the property (1e).
2.6 Interim conclusion: the lexical status of simple cardinals
In this section, we have shown that simple cardinals in French have all the proper-ties deemed characteristic of lexemes by Fradin (2003). Like typical lexemes, elements of CARD are created by borrowing and arbitrary coining while grammemes emerge through diachronic phenomena. Considering simple cardinals to be lexemes might seem at odds with the fact that we have taken them to be a sub-category of determiners, usu-ally not regarded as a lexeme-based category. In the following section, we argue that CARD, in general, are a part of the syntactic category of determiners but constitute a morphological category of their own.
17‘Today, for the nth time, I see a car parked in front of my garage door, blocking my way.’
https://goo.gl/lOrTuo
18Note that the French complex cardinals are not an open-ended set but rather a large set containing one trillion elements, as French speakers can count from 0 to 999,999,999,999.
19‘Run the soundbite from the nbth second.’
http://www.forum-dessine.fr/index.php?id=06038
20‘Returns the address of the NUMth function in the current page.’
https://goo.gl/LHh46c