[Lingtyp] types of quantification

[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:

  1.  Numeral quantification: 'one', 'two' ...
  2.  Non-numeral quantification

  1.  Universal: 'all', 'every'
  2.  Existential: 'some'
  3.  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?
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