In defence of Higher-Level Plural Logic: drawing conclusions from natural language

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F21%3A00520340" target="_blank" >RIV/67985556:_____/21:00520340 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s11229-019-02399-z" target="_blank" >https://link.springer.com/article/10.1007/s11229-019-02399-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11229-019-02399-z" target="_blank" >10.1007/s11229-019-02399-z</a>

Result language

angličtina

Original language name

In defence of Higher-Level Plural Logic: drawing conclusions from natural language

Original language description

Plural Logic is an extension of First-Order Logic which has, as well as singular terms and quantifiers, their plural counterparts. Analogously, Higher-Level Plural Logic is an extension of Plural Logic which has, as well as plural terms and quantifiers, higher-level plural ones. Roughly speaking, higher-level plurals stand to plurals like plurals stand to singulars, they are pluralised plurals. Allegedly, Higher-Level Plural Logic enjoys the expressive power of a simple type theory while committing us to nothing more than the austere ontology of First-Order Logic. Were this true, Higher-Level Plural Logic would be a useful tool, with various applications in philosophy and linguistics. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with a lot of scepticism. In this paper, I argue for the legitimacy of Higher-Level Plural Logic by providing evidence to the effect that natural languages contain higher-level plural expressions and showing that it is likely that they do so in an indispensable manner. Since the arguments I put forward are of the same sort advocates of Plural Logic have employed to defend their position, I conclude that the commonly held view that Plural Logic is legitimate, but not so its higher-level plural extensions is untenable.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GA18-00113S" target="_blank" >GA18-00113S: Reasoning with graded properties</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Synthese

ISSN

0039-7857

e-ISSN

1573-0964

Volume of the periodical

198

Issue of the periodical within the volume

6

Country of publishing house

US - UNITED STATES

Number of pages

28

Pages from-to

5253-5280

UT code for WoS article

000657791400015

EID of the result in the Scopus database

2-s2.0-85074008660