(Some debate about the last example: Hofweber 2005, Jackson & Penka 2017, Moltmann 2013,2017.)
# Bare Numerals in Japanese
Bare numerals in Japanese can be used as names of number concepts.
# Counting Modifiers without Classifiers
Modifiers like hotondo ほとんど
'most' and suuhyaku 数百
'hundreds' are born as modifiers, so they don't need classifiers.
According to this view, whether a classifier is necessary for a given counting modifier is determined by the semnatics of the modifier (not by the noun).
Some supporting evidence:
- Bale & Coon's (2014) observations
- Exceptional numerals in Japanese
- Exceptional numerals in Korean
# Partly Classifier Languages: Bale & Coon
Bale & Coon's (2014) observations
- In Mi'gmaq (Eastern Algonquian), 1-5 do not appear with classifiers, 6- must.
- In Chol (Mayan), native numerlas (e.g. ux 'three', waxäk 'eight') require classifiers, while Spanish-based numerals (e.g. ses 'six', nuebe 'nine') are incompatible with classifiers.
(Though it is not entirely clear if these languages have the same type of classifiers as Japanese)
# Partly Classifier Languages: Japanese
In Japanese too, certain numerals do not require classifiers:
'There are about 1500 volcanoes on Earth'
: For which numerals are classifiers optional? (Numbers expressed cannot be small)
# Partly Classifier Languages: Korean
In Korean, native numerals (1-9) often do not require classifiers (especially low numerals with animate nouns).
Also, hana 하나
'one' often appears without a classifier post-nominally.
(based on Linda Yoon Jae Shin's 2017 UCL BA thesis)
Open question: These might be compounds?
# Further Directions: Slavic Numerals
Slavic languages have several types of numerals (Kim 2009, Dočekal, Grimm & Ziková 2014)
. E.g. Czech:
- Normal numerals
- Aggregate numerals
): used with pluralia tantum, collective nouns (e.g. sirky
- Taxonomic numerals
) are used to count sub-kinds.
- Group numerals
) are used to count members of a group. E.g. dv-ojice mužů
'a group of two men'.
: These suffixes are similar to classifiers in Japanese.
The Number Asymmetry Hypothesis
- Count nouns always have countable denotations.
- Mass nouns might (fake) or might not (pure).
Nouns in Japanese are grammatically mass nouns.
Classifiers are not for nouns.
In classifier languages like Japanese:
- Numerals are always referential;
- Classifiers turn such referential expressions into modifiers/predicates.
class: center, middle
# Appendix: Details
# Numerals and Classifiers
Numerals are names for (abstract) entities (of type n) (Rothstein 2013)
⟦yon⟧w,c = ⟦four⟧w,c = 4
⟦kyuu⟧w,c = ⟦nine⟧w,c = 9
Classifiers take abstract entities and turn them into predicates
⟦-rin⟧w,c = λn.λx: x consists of flowers in w. x measures n in w wrt a salient way of counting (individual) flowers in c
⟦-tsui⟧w,c = λn.λx. x consists of n pairs in w wrt a salient way of pairing things in c
NB: classifiers refer to contextually salient ways of counting (cf. Zucchi & White 2011, Rothstein 2010)
# Modificational and Predicative Uses
NUM+CL will be of type (e,t).
= λx: x consists of people in w
. x measures 3 in w wrt a salient way of counting (individual) people in c
It can modify an NP intersectively.
Being of type (e,t) it can also function as predicates:
(lit.) 'My students are three.'
'The number of students I have is three.'
# Type-Shifting Back
NUM+CL in Japanese have a referring use:
'The number of students is three.'
Idea: the property denoted by NUM+CL has a type-n counterpart (cf. Chierchia 1984, Chierchia & Turner 1987, Scontras 2014, 2017)
⟦san-nin⟧w,c = λx: x consists of people in w. x measures 3 in w wrt a salient way of counting (individual) people in c
⦅san-nin⦆c ⇝ three-people-ness (in c)
# Optional Classifiers
Expressions like suuhyaku 数百
are born as modifiers:
⟦suuhyaku⟧w,c = λx. x measures hundreds in w wrt some way of counting
(This predicate is vague wrt how to count)
This property can also type-shift to type n, which in turn can combine with a classifer.
# Non-Classifier Languages
No classifiers in English. Modificational use is acheved by type-shifting (which is blocked in classifier languages):
⟦four⟧w,c ⇝ λP.λx. x measures 4 wrt a contextually salient way of counting P-entities in c
Note that it's necessary to refer to the intension of the NP (P), because counting is relative to a property (and context).
E.g. If you are counting letters, there are six. If you are counting logos, there's only one.
# Predicative Numerals in English
Predicative uses of numerals in English are very limited.
# My laptops are three.
(intended: I have three laptops.)
If type-shifting is only from type n to type ((s,et),et), the predicative use will not be allowed.
Acceptable cases of predicative numerals (incl. age-interpretations) are all conventionalized?
We will soon be three.
My niece is five. (age interpretation)
Numerals in all languages have referring uses (type n).
Numerals in classifier languages cannot be type-shifted but classifiers convert them to predicates of type (e,t).
⟦yon-rin⟧w,c = λx: x consists of flowers in w. x measures 4 in w wrt a salient way of counting (individual) flowers in c
NUM+CL have type-n counterparts (similar to the Scontras degrees)
Numerals in non-classifier languages can be type-shifted to modifiers of type ((s,et),et)?
## Selected References
- Bale & Barner (2009) The interpretation of functional heads. J. of Semantics, 26.
- Bale & Coon (2014) Classifiers are for numerals, not nouns. LI, 45.
- Barner & Sndeker (2005) Quantity judgments and individuation. Cognition, 97.
- Chierchia (1998b) Referent to kinds across languages. Nat. Lang. Sem, 6.
- Chierchia & Turner (1987) Semantics and property theory. Ling & Phil, 11.
- Inagaki & Barner (2009) Countability in absence of count syntax. In Studies in Language Sciences 8.
- Rothstein (2010) Counting and the mass/count distinction J. of Semantics.
- Rothstein (2013) A Fregean semantics for number words. In Ams. Colloq. 19.
- Scontras (2017) A new kind of degree. Ling & Phil, 40.