Plural Frege Arithmetic
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 impos...
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| Format: | Article |
| Language: | deu |
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Éditions Kimé
2022-02-01
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| Series: | Philosophia Scientiæ |
| Online Access: | http://journals.openedition.org/philosophiascientiae/3394 |
| _version_ | 1797402629769265152 |
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| author | Francesca Boccuni |
| author_facet | Francesca Boccuni |
| author_sort | Francesca Boccuni |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T02:27:39Z |
| format | Article |
| id | doaj.art-b3931fb214394a07976e642b60d93600 |
| institution | Directory Open Access Journal |
| issn | 1281-2463 1775-4283 |
| language | deu |
| last_indexed | 2024-03-09T02:27:39Z |
| publishDate | 2022-02-01 |
| publisher | Éditions Kimé |
| record_format | Article |
| series | Philosophia Scientiæ |
| spelling | doaj.art-b3931fb214394a07976e642b60d936002023-12-06T15:53:06ZdeuÉditions KiméPhilosophia Scientiæ1281-24631775-42832022-02-0126118920610.4000/philosophiascientiae.3394Plural Frege ArithmeticFrancesca BoccuniIn [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.http://journals.openedition.org/philosophiascientiae/3394 |
| spellingShingle | Francesca Boccuni Plural Frege Arithmetic Philosophia Scientiæ |
| title | Plural Frege Arithmetic |
| title_full | Plural Frege Arithmetic |
| title_fullStr | Plural Frege Arithmetic |
| title_full_unstemmed | Plural Frege Arithmetic |
| title_short | Plural Frege Arithmetic |
| title_sort | plural frege arithmetic |
| url | http://journals.openedition.org/philosophiascientiae/3394 |
| work_keys_str_mv | AT francescaboccuni pluralfregearithmetic |