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There are of course various ways in which "quantifier" can be
defined and in which one could set up subgroups.<br>
<br>
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:<br>
<br>
– adnominal quantifiers (many, all, two, etc.)<br>
– adverbial quantifiers (often, always, twice, etc.)<br>
<br>
And if we want to follow (or take into account) earlier
authoritative terminology, then I would take inspiration from these
three works:<br>
<br>
<div class="csl-bib-body" style="line-height: 1.35; margin-left:
2em; text-indent:-2em;">
<div class="csl-entry">Gil, David. 2001. Quantifiers. In
Haspelmath, Martin & König, Ekkehard & Oesterreicher,
Wulf & Raible, Wolfgang (eds.), <i>Language typology and
language universals: An international handbook (Volume 2)</i>,
1275–1294. Berlin: de Gruyter.</div>
<span class="Z3988"
title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzotero.org%3A2&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Quantifiers&rft.place=Berlin&rft.publisher=de%20Gruyter&rft.aufirst=David&rft.aulast=Gil&rft.au=David%20Gil&rft.au=Martin%20Haspelmath&rft.au=Ekkehard%20K%C3%B6nig&rft.au=Wulf%20Oesterreicher&rft.au=Wolfgang%20Raible&rft.date=2001&rft.pages=1275-1294&rft.spage=1275&rft.epage=1294"></span>
<div class="csl-entry">Keenan, Edward L. & Paperno, Denis
(eds.). 2012. <i>Handbook of quantifiers in natural language</i>.
Dordrecht: Springer.</div>
<span class="Z3988"
title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzotero.org%3A2&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook%20of%20quantifiers%20in%20natural%20language&rft.place=Dordrecht&rft.publisher=Springer&rft.aufirst=Edward%20L.&rft.aulast=Keenan&rft.au=Edward%20L.%20Keenan&rft.au=Denis%20Paperno&rft.date=2012&rft.language=English"></span>
<div class="csl-entry">Paperno, Denis & Keenan, Edward L.
(eds.). 2017. <i>Handbook of quantifiers in natural language:
Volume II</i>. Cham: Springer.</div>
<span class="Z3988"
title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzotero.org%3A2&rft_id=urn%3Aisbn%3A978-3-319-44330-0&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook%20of%20quantifiers%20in%20natural%20language%3A%20Volume%20II&rft.place=Cham&rft.publisher=Springer&rft.aufirst=Denis&rft.aulast=Paperno&rft.au=Denis%20Paperno&rft.au=Edward%20L.%20Keenan&rft.date=2017&rft.isbn=978-3-319-44330-0&rft.language=English"></span></div>
<br>
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.<br>
<br>
Incidentally, I did a Twitter poll last year on whether cardinal
numerals are considered a subtype on quantifiers, and two thirds
thought so:
<a class="moz-txt-link-freetext" href="https://twitter.com/haspelmath/status/1429061465332457478">https://twitter.com/haspelmath/status/1429061465332457478</a><br>
<br>
Best,<br>
Martin<br>
<br>
<div class="moz-cite-prefix">Am 04.03.22 um 14:00 schrieb Östen
Dahl:<br>
</div>
<blockquote type="cite"
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<p class="MsoNormal"><span lang="EN-US">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.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Östen<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<div style="border:none;border-top:solid #E1E1E1
1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span lang="SV">Från:</span></b><span
lang="SV"> Christian Lehmann
<a class="moz-txt-link-rfc2396E" href="mailto:christian.lehmann@uni-erfurt.de"><christian.lehmann@uni-erfurt.de></a>
<br>
<b>Skickat:</b> den 4 mars 2022 13:02<br>
<b>Till:</b> Östen Dahl <a class="moz-txt-link-rfc2396E" href="mailto:oesten@ling.su.se"><oesten@ling.su.se></a>;
<a class="moz-txt-link-abbreviated" href="mailto:lingtyp@listserv.linguistlist.org">lingtyp@listserv.linguistlist.org</a><br>
<b>Ämne:</b> Re: Sv: [Lingtyp] types of quantification<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p>Östen, what you mention is apparently a classification from a
logical point of view. Accepted.<o:p></o:p></p>
<p>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.)<o:p></o:p></p>
<p>----------------------------------------------------------<o:p></o:p></p>
<div>
<p class="MsoNormal">Am 04.03.2022 um 12:53 schrieb Östen
Dahl:<o:p></o:p></p>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<p class="MsoNormal"><span lang="EN-US">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.
<a
href="https://plato.stanford.edu/entries/generalized-quantifiers/"
moz-do-not-send="true" class="moz-txt-link-freetext">https://plato.stanford.edu/entries/generalized-quantifiers/</a>.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">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. </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<ol style="margin-top:0cm" type="1" start="1">
<li class="MsoListParagraph"
style="margin-left:0cm;mso-list:l3 level1 lfo1"><span
lang="EN-US">Östen</span><o:p></o:p></li>
</ol>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"> <o:p></o:p></p>
<div>
<div style="border:none;border-top:solid #E1E1E1
1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span lang="SV">Från:</span></b><span
lang="SV"> Lingtyp <a
href="mailto:lingtyp-bounces@listserv.linguistlist.org"
moz-do-not-send="true">
<lingtyp-bounces@listserv.linguistlist.org></a>
<b>För </b>Christian Lehmann<br>
<b>Skickat:</b> den 4 mars 2022 12:35<br>
<b>Till:</b> <a
href="mailto:lingtyp@listserv.linguistlist.org"
moz-do-not-send="true" class="moz-txt-link-freetext">lingtyp@listserv.linguistlist.org</a><br>
<b>Ämne:</b> [Lingtyp] types of quantification</span><o:p></o:p></p>
</div>
</div>
<p class="MsoNormal"> <o:p></o:p></p>
<p>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:<o:p></o:p></p>
<ol type="1" start="1">
<li class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0
level1 lfo2">
Numeral quantification: 'one', 'two' ...<o:p></o:p></li>
<li class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0
level1 lfo2">
Non-numeral quantification<o:p></o:p></li>
</ol>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<ol type="1" start="1">
<li class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1
level1 lfo3">
Universal: 'all', 'every'<o:p></o:p></li>
<li class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1
level1 lfo3">
Existential: 'some'<o:p></o:p></li>
<li class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1
level1 lfo3">
Sizing: 'many', 'several', '(a) few', ....<o:p></o:p></li>
</ol>
</blockquote>
<p>Two questions:<o:p></o:p></p>
<ol type="1" start="1">
<li class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l2
level1 lfo4">
Has anything concerning such a classification been
published which I should know?<o:p></o:p></li>
<li class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l2
level1 lfo4">
To the extent that the above is reasonable: Any
suggestions for a better terminology?<o:p></o:p></li>
</ol>
<p class="MsoNormal">-- <o:p></o:p></p>
<div>
<p><span style="font-size:10.0pt">Prof. em. Dr. Christian
Lehmann<br>
Rudolfstr. 4<br>
99092 Erfurt<br>
<span style="font-variant:small-caps">Deutschland</span></span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:9.0pt">Tel.:</span><o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt">+49/361/2113417</span><o:p></o:p></p>
</td>
</tr>
<tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt">E-Post:</span><o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt"><a
href="mailto:christianw_lehmann@arcor.de"
moz-do-not-send="true"
class="moz-txt-link-freetext">christianw_lehmann@arcor.de</a></span><o:p></o:p></p>
</td>
</tr>
<tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt">Web:</span><o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt"><a
href="https://www.christianlehmann.eu"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://www.christianlehmann.eu</a></span><o:p></o:p></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
</blockquote>
<div>
<p class="MsoNormal">-- <o:p></o:p></p>
<p><span style="font-size:10.0pt">Prof. em. Dr. Christian
Lehmann<br>
Rudolfstr. 4<br>
99092 Erfurt<br>
<span style="font-variant:small-caps">Deutschland</span><o:p></o:p></span></p>
<table class="MsoNormalTable" cellpadding="0" border="0">
<tbody>
<tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt">Tel.:<o:p></o:p></span></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt">+49/361/2113417<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt">E-Post:<o:p></o:p></span></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt"><a
href="mailto:christianw_lehmann@arcor.de"
moz-do-not-send="true"
class="moz-txt-link-freetext">christianw_lehmann@arcor.de</a><o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt">Web:<o:p></o:p></span></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoNormal"><span style="font-size:9.0pt"><a
href="https://www.christianlehmann.eu"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://www.christianlehmann.eu</a><o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
<pre class="moz-quote-pre" wrap="">_______________________________________________
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<br>
<pre class="moz-signature" cols="72">--
Martin Haspelmath
Max Planck Institute for Evolutionary Anthropology
Deutscher Platz 6
D-04103 Leipzig
<a class="moz-txt-link-freetext" href="https://www.eva.mpg.de/linguistic-and-cultural-evolution/staff/martin-haspelmath/">https://www.eva.mpg.de/linguistic-and-cultural-evolution/staff/martin-haspelmath/</a></pre>
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