Fregean One-to-one Correspondence and Numbers as Object Properties
The paper critically examines an unpopular line of Frege’s view on numbers in the Foundations of Arithmetic. According to this view, which analyzes numbers in terms of properties and not in terms of extensions, numbers are properties of concepts vs. properties of objects. The latter view is held by...
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| Format: | Article |
| Language: | English |
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Universidade Federal de Santa Catarina
2009-12-01
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| Series: | Principia: An International Journal of Epistemology |
| Subjects: | |
| Online Access: | http://www.periodicos.ufsc.br/index.php/principia/article/view/19677/18039 |
| _version_ | 1818666163728547840 |
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| author | Boris Grozdanoff |
| author_facet | Boris Grozdanoff |
| author_sort | Boris Grozdanoff |
| collection | DOAJ |
| description | The paper critically examines an unpopular line of Frege’s view on numbers in the Foundations of Arithmetic. According to this view, which analyzes numbers in terms of properties and not in terms of extensions, numbers are properties of concepts vs. properties of objects. The latter view is held by Mill and is famously criticized in the Foundations. I argue that on the property account numbers cannot only be properties of concepts but they also have to be properties of objects. My main argument rests on purely metaphysical grounds. It stems from the motivation that were numbers only properties of concepts we would not have been able to explain mathematical truths about the physical world or those truths would have been miraculous. On pains that we do have mathematical truths about the physical world that are not miraculous we cannot agree with Frege’s property line about the metaphysical nature of numbers. |
| first_indexed | 2024-12-17T06:00:10Z |
| format | Article |
| id | doaj.art-741e236c740d452c8cee192ec092db53 |
| institution | Directory Open Access Journal |
| issn | 1414-4247 1808-1711 |
| language | English |
| last_indexed | 2024-12-17T06:00:10Z |
| publishDate | 2009-12-01 |
| publisher | Universidade Federal de Santa Catarina |
| record_format | Article |
| series | Principia: An International Journal of Epistemology |
| spelling | doaj.art-741e236c740d452c8cee192ec092db532022-12-21T22:00:55ZengUniversidade Federal de Santa CatarinaPrincipia: An International Journal of Epistemology1414-42471808-17112009-12-01133327338Fregean One-to-one Correspondence and Numbers as Object PropertiesBoris GrozdanoffThe paper critically examines an unpopular line of Frege’s view on numbers in the Foundations of Arithmetic. According to this view, which analyzes numbers in terms of properties and not in terms of extensions, numbers are properties of concepts vs. properties of objects. The latter view is held by Mill and is famously criticized in the Foundations. I argue that on the property account numbers cannot only be properties of concepts but they also have to be properties of objects. My main argument rests on purely metaphysical grounds. It stems from the motivation that were numbers only properties of concepts we would not have been able to explain mathematical truths about the physical world or those truths would have been miraculous. On pains that we do have mathematical truths about the physical world that are not miraculous we cannot agree with Frege’s property line about the metaphysical nature of numbers.http://www.periodicos.ufsc.br/index.php/principia/article/view/19677/18039Numberspropertiesone-to-one correspondenceFrege |
| spellingShingle | Boris Grozdanoff Fregean One-to-one Correspondence and Numbers as Object Properties Principia: An International Journal of Epistemology Numbers properties one-to-one correspondence Frege |
| title | Fregean One-to-one Correspondence and Numbers as Object Properties |
| title_full | Fregean One-to-one Correspondence and Numbers as Object Properties |
| title_fullStr | Fregean One-to-one Correspondence and Numbers as Object Properties |
| title_full_unstemmed | Fregean One-to-one Correspondence and Numbers as Object Properties |
| title_short | Fregean One-to-one Correspondence and Numbers as Object Properties |
| title_sort | fregean one to one correspondence and numbers as object properties |
| topic | Numbers properties one-to-one correspondence Frege |
| url | http://www.periodicos.ufsc.br/index.php/principia/article/view/19677/18039 |
| work_keys_str_mv | AT borisgrozdanoff fregeanonetoonecorrespondenceandnumbersasobjectproperties |