[Lingtyp] types of quantification

[Martin Haspelmath]

There are of course various ways in which "quantifier" can be defined 
and in which one could set up subgroups.

For general-comparative linguistics, it's probably not so useful to have 
a logic-based "(generalized) quantifier" concept where most (or many) 
NPs are quantifiers. I think we want to have primarily these two types 
of quantifiers:

– adnominal quantifiers (many, all, two, etc.)
– adverbial quantifiers (often, always, twice, etc.)

And if we want to follow (or take into account) earlier authoritative 
terminology, then I would take inspiration from these three works:

Gil, David. 2001. Quantifiers. In Haspelmath, Martin & König, Ekkehard & 
Oesterreicher, Wulf & Raible, Wolfgang (eds.), /Language typology and 
language universals: An international handbook (Volume 2)/, 1275–1294. 
Berlin: de Gruyter.
Keenan, Edward L. & Paperno, Denis (eds.). 2012. /Handbook of 
quantifiers in natural language/. Dordrecht: Springer.
Paperno, Denis & Keenan, Edward L. (eds.). 2017. /Handbook of 
quantifiers in natural language: Volume II/. Cham: Springer.

I find Gil's paper particularly accessible and sensitive to what the 
languages around the world do. The handbooks edited by Keenan and 
Paperno give rich exemplification, but the terminology of the general 
papers is strongly inspired by the logic-based tradition and thus not so 
transparent for ordinary working linguists.

Incidentally, I did a Twitter poll last year on whether cardinal 
numerals are considered a subtype on quantifiers, and two thirds thought 
so: https://twitter.com/haspelmath/status/1429061465332457478

Best,
Martin

Am 04.03.22 um 14:00 schrieb Östen Dahl:
>
> I think the answer to the question depends on what you want your 
> general-comparative linguistic semantics to look like, in particular 
> on how much you want it to reflect how quantifiers are grouped in 
> individual languages.
>
> Östen
>
> *Från:*Christian Lehmann <christian.lehmann at uni-erfurt.de>
> *Skickat:* den 4 mars 2022 13:02
> *Till:* Östen Dahl <oesten at ling.su.se>; lingtyp at listserv.linguistlist.org
> *Ämne:* Re: Sv: [Lingtyp] types of quantification
>
> Östen, what you mention is apparently a classification from a logical 
> point of view. Accepted.
>
> Is it useful from the point of view of (general-comparative) 
> linguistic semantics to take the "classical" quantifiers of predicate 
> logic out and to group numerals together with "inexact cardinality 
> measures"? (Note that this is a neutral, not a rhetorical question.)
>
> ----------------------------------------------------------
>
> Am 04.03.2022 um 12:53 schrieb Östen Dahl:
>
>     These should all fall under the notion of “generalized
>     quantifiers” discussed by logicians and formal semanticists, where
>     quantifiers are regarded as denoting sets of sets. See e.g.
>     https://plato.stanford.edu/entries/generalized-quantifiers/.
>
>     The classification follows naturally from the logical properties
>     of the different quantifiers. (2a) and (2b) are the “classical”
>     quantifiers of predicate logic. (1) indicate exact cardinality
>     measures; (2c) inexact cardinality measures.
>
>      1. Östen
>
>     *Från:*Lingtyp <lingtyp-bounces at listserv.linguistlist.org>
>     <mailto:lingtyp-bounces at listserv.linguistlist.org> *För *Christian
>     Lehmann
>     *Skickat:* den 4 mars 2022 12:35
>     *Till:* lingtyp at listserv.linguistlist.org
>     *Ämne:* [Lingtyp] types of quantification
>
>     In some languages, numerals have the same distribution as
>     quantifiers like 'some' or 'many'. From a functional point of
>     view, too, for instance in view of the approximative numerals
>     discussed last week, it makes sense to subsume the use of numerals
>     under quantification. Then one might subdivide the field of
>     quantification roughly as follows:
>
>      1. Numeral quantification: 'one', 'two' ...
>      2. Non-numeral quantification
>
>          1. Universal: 'all', 'every'
>          2. Existential: 'some'
>          3. Sizing: 'many', 'several', '(a) few', ....
>
>     Two questions:
>
>      1. Has anything concerning such a classification been published
>         which I should know?
>      2. To the extent that the above is reasonable: Any suggestions
>         for a better terminology?
>
>     -- 
>
>     Prof. em. Dr. Christian Lehmann
>     Rudolfstr. 4
>     99092 Erfurt
>     Deutschland
>
>     Tel.:
>
>     	
>
>     +49/361/2113417
>
>     E-Post:
>
>     	
>
>     christianw_lehmann at arcor.de
>
>     Web:
>
>     	
>
>     https://www.christianlehmann.eu
>
> -- 
>
> Prof. em. Dr. Christian Lehmann
> Rudolfstr. 4
> 99092 Erfurt
> Deutschland
>
> Tel.:
>
> 	
>
> +49/361/2113417
>
> E-Post:
>
> 	
>
> christianw_lehmann at arcor.de
>
> Web:
>
> 	
>
> https://www.christianlehmann.eu
>
>
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-- 
Martin Haspelmath
Max Planck Institute for Evolutionary Anthropology
Deutscher Platz 6
D-04103 Leipzig
https://www.eva.mpg.de/linguistic-and-cultural-evolution/staff/martin-haspelmath/
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