In [Boccuni 2010], a predicative fragment of Frege’s BLV augmented with Boolos’ unrestricted plural quantification is shown to interpret PA2. The main disadvantage of that axiomatisation is that it does not recover Frege Arithmetic FA because of the restrictions imposed on the axioms. The aim of the present article is to show how [Boccuni 2010] can be consistently extended so as to interpret FA and consequently PA2 in a way that parallels Frege’s. In that way, the presented system will be compared with the system PE in [Ferreira 2018] and some relevant differences between the two will be highlighted.

Plural Frege Arithmetic / Boccuni, Francesca. - In: PHILOSOPHIA SCIENTIAE. - ISSN 1775-4283. - 26:1(2022), pp. 189-206. [10.4000/philosophiascientiae.3394]

Plural Frege Arithmetic

Francesca Boccuni
Primo
2022-01-01

Abstract

In [Boccuni 2010], a predicative fragment of Frege’s BLV augmented with Boolos’ unrestricted plural quantification is shown to interpret PA2. The main disadvantage of that axiomatisation is that it does not recover Frege Arithmetic FA because of the restrictions imposed on the axioms. The aim of the present article is to show how [Boccuni 2010] can be consistently extended so as to interpret FA and consequently PA2 in a way that parallels Frege’s. In that way, the presented system will be compared with the system PE in [Ferreira 2018] and some relevant differences between the two will be highlighted.
2022
Dans [Boccuni 2010], un fragment prédicatif du BLV de Frege augmenté de la quantification plurielle illimitée de Boolos interprète PA2. Le principal inconvénient de cette axiomatisation est qu’elle ne récupère pas Frege Arithmetic (FA), en raison des restrictions imposées aux axiomes. Le but du présent article est de montrer comment [Boccuni 2010] peut être étendu de manière cohérente afin d’interpréter FA et par conséquent PA2 d’une manière qui soit parallèle à celle de Frege. Ce faisant, le système présenté sera mis en comparaison avec le système PE dans [Ferreira 2018] et quelques différences pertinentes entre les deux seront mises en évidence.
Consistent subsystems of Frege’s Grundgesetze der Arithmetik; Frege Arithmetic; Frege’s Theorem
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11768/118913
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