[Lingtyp] types of quantification

Fri Mar 4 16:25:35 UTC 2022

Thanks, Juergen, for this perspective on quantifiers – which doesn't 
conflict at all with what I said.

Notice that I talked about definitions of terms (especially 
"quantifier"), not about "analyses" or "theoretical innovations". I see 
terminology as part of our methodology, and I have been suggesting that 
we might treat our grammatical terms somewhat like IPA characters (which 
are part of our common toolkit, or "meme pool", without having any 
theoretical status).

Outside of the formal semantics community, everyone thinks that "many" 
and "all" are typical quantifiers, and (it seems) a clear majority think 
that "two" is a quantifier. But no linguist who lacks special 
logical-semantic training thinks that all or most of the following are 
"quantifiers":

/everything, nothing, three books, the ten professors, John, John and 
Mary, only John, firemen, every, at least five, most, all but ten, less 
than half of the, John’s, some student’s, no…except Mary, more male than 
female, usually, never, each other/ (see 
https://plato.stanford.edu/entries/generalized-quantifiers/)

It's an interesting question how to analyze all of these, but the 
analyses may be different for different languages, and the questions are 
surely not settled. But just as phonologists of diverse orientations are 
able to agree on the IPA, we can perhaps discuss our terminology without 
necessarily getting into the details of formal analyses.

I had understood Christian Lehmann as asking for advice on the 
terminology, as he is writing a grammar and wants to use terms that are 
as clear and standard as possible.

Best,
Martin

Am 04.03.22 um 17:02 schrieb Juergen Bohnemeyer:
> Dear all — First off, it is ironically precisely Barwise & Cooper’s (1981) generalized quantifier treatment that allows one to capture the meanings of quantificational expressions without reference to the logical quantifiers. In doing so, the GQ analysis also enables us to state what all kinds of quantificational expressions in natural languages have in common (which goes a ways toward answering Christian’s question which started this thread): i.e., subset formation.
>
> More broadly, I think Martin’s response (apologies in advance!) may be an example of what I perceive to be an unfortunate tendency in the descriptive and typological literature to dismiss theoretical innovations as irrelevant to one's work just because the proposers use some formalism or other to articulate their ideas.
>
> To be clear: this attitude is completely understandable. If the author used a formalism that is inaccessible to the reader, and the author didn’t offer any compelling arguments not couched in that formalism for why the reader should bother to engage with the ideas, then that’s on the author. Perhaps simplifying slightly.
>
> Still. One simple test of whether theoretical innovations are relevant to the descriptive and typological literature might be whether the ideas in question *can* be couched without the use of any formalism (or at least without the use of any more parochial, esoteric formalism; after all, there are some formalisms that are at this point pretty much part of the metalinguistic meme pool of the discipline).
>
> And I would argue that the GQ analysis meets that bar.
>
> Last point: on the topic of the relation between (ad)nominal and adverbial quantification, a recent formally couched but typologically insightful handbook piece is Hinterwimmer (2020).
>
> Best — Juergen
>
> Barwise, Jon and Robin Cooper, 1981, “Generalized Quantifiers and Natural Language”, Linguistics and Philosophy, 4(2): 159–219. doi:10.1007/BF00350139
> Hinterwimmer, S. (2020). Nominal vs. adverbial quantification. In D. Gutzmann, L. Matthewson, C. Meier, H. Rullmann, and T. Zimmermann (Eds.), The Wiley Blackwell Companion to Semantics.
>
>
>
>> On Mar 4, 2022, at 9:24 AM, Martin Haspelmath<martin_haspelmath at eva.mpg.de>  wrote:
>>
>> 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.
>>>   
>>> 	• Östen
>>>   
>>>   
>>> Från: Lingtyp<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:
>>>
>>> 	• Numeral quantification: 'one', 'two' ...
>>> 	• Non-numeral quantification
>>> 	• Universal: 'all', 'every'
>>> 	• Existential: 'some'
>>> 	• Sizing: 'many', 'several', '(a) few', ....
>>> Two questions:
>>>
>>> 	• Has anything concerning such a classification been published which I should know?
>>> 	• 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/
>> _______________________________________________
>> Lingtyp mailing list
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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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