Names and Quantifiers: Bringing Them Together in Classical Logic

Putting individual constants and quantifiers into the same syntactic category within first-order language promises to have far-reaching consequences: a syntax of this kind can reveal the potential of any such language, allowing us to realize that a vast class of noun phrases, including non-denoting...

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Bibliographic Details
Published inJournal of logic, language, and information Vol. 32; no. 3; pp. 473 - 487
Main Author Paśniczek, Jacek
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2023
Subjects
Education
Information Systems Applications (incl.Internet)
Logic
Philosophy
Semantics
(generalized) quantifiers
Individual constants
Modal logic
Particular objects
General objects
Existence
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Summary:Putting individual constants and quantifiers into the same syntactic category within first-order language promises to have far-reaching consequences: a syntax of this kind can reveal the potential of any such language, allowing us to realize that a vast class of noun phrases, including non-denoting terms, can be accommodated in the new syntax as expressions suited to being subjects of sentences. In the light of this, a formal system that is an extension of classical first-order logic is developed here, and is equipped with an appropriate semantics. An ontological interpretation of the new logic is then also provided, with several categories of object and notions of existence being distinguished. Last but not least, a modal version of the logic, with some interesting formal features, is proposed.
ISSN:0925-8531
1572-9583
DOI:10.1007/s10849-023-09395-0