Solutions to Puzzles of Existential Generalisation

RACLAVSKÝ, Jiří. Solutions to Puzzles of Existential Generalisation. In 10th Non-Classical Logic. Theory and Application (NCL'22). 2022.

Basic information

• Original name: Solutions to Puzzles of Existential Generalisation
• Authors: RACLAVSKÝ, Jiří.
• Edition: 10th Non-Classical Logic. Theory and Application (NCL'22), 2022.

Other information

• Original language: English
• Type of outcome: Presentations at conferences
• Field of Study: 60301 Philosophy, History and Philosophy of science and technology
• Country of publisher: Poland
• Confidentiality degree: is not subject to a state or trade secret
• Organization unit: Faculty of Arts
• Keywords in English: existential generalisation; quantifying in; explicit substitution;partial type logic; natural deduction

Abstract

The present paper addresses several puzzles related to the Rule of Existential Generalization, (EG). In solution to these puzzles, I clearly distinguish (EG) from a modified Rule of Existential Quantifier Introduction, which is derivable from (EG). Both these rules are often confused and both are considered as primitive. But I show that (EG) itself is derivable from the proper Rule of Existential Quantifier Introduction. The latter rule must be primitive in logical systems that treat both total and partial functions, for the universal and the existential quantifiers are not interdefinable in them. An appropriate natural deduction for such a system is deployed. It utilises an adequate definition of substitution which is capable of handling not only a higher-order quantification, but also (hyper)intensional contexts.

Links

• MUNI/A/1088/2021, interní kód MU: Name: Aspekty soudobé filozofie IV

Investor: Masaryk University