Scottish Neologicism aims to found arithmetic on full second-order logic and Hume's Principle, stating that the number of the Fs is identical with the number of the Gs if, and only if, there are as many Fs as Gs. However, Neologicism faces the problem of the logical ontology, according to which the underlying second-order logic involves ontological commitments. This paper addresses this issue by substituting second-order logic by Boolos' plural logic, augmented by the Plural Frege Quantifier $\mathcal F$ modelled on Antonelli's Frege Quantifier. The resulting theory (PHP) interprets second-order Peano arithmetic. Its ontological innocence is assessed: PHP offers an alternative that solves the problem of the logical ontology pervading Neologicism.

Arithmetic on the Cheap. Neologicism and the Problem of the Logical Ontology / Boccuni, Francesca. - In: THOUGHT. - ISSN 2161-2234. - (In corso di stampa), pp. 1-13. [Epub ahead of print]

Arithmetic on the Cheap. Neologicism and the Problem of the Logical Ontology

Francesca Boccuni
Primo
In corso di stampa

Abstract

Scottish Neologicism aims to found arithmetic on full second-order logic and Hume's Principle, stating that the number of the Fs is identical with the number of the Gs if, and only if, there are as many Fs as Gs. However, Neologicism faces the problem of the logical ontology, according to which the underlying second-order logic involves ontological commitments. This paper addresses this issue by substituting second-order logic by Boolos' plural logic, augmented by the Plural Frege Quantifier $\mathcal F$ modelled on Antonelli's Frege Quantifier. The resulting theory (PHP) interprets second-order Peano arithmetic. Its ontological innocence is assessed: PHP offers an alternative that solves the problem of the logical ontology pervading Neologicism.
In corso di stampa
Neologicism, ontological commitment, second-order logic, plural logic, Hume's Principle, second-order Peano arithmetic
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11768/175071
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