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Detalhes Referência

Tipo
Capítulo em Livro


Título
Zigzag and Fregean arithmetic

Participantes na publicação
Fernando Ferreira (Author)
Dep. Matemática
CMAFcIO

Resumo
In Frege’s logicism, numbers are logical objects in the sense that they are extensions of certain concepts. Frege’s logical system is inconsistent, but Richard Heck showed that its restriction to predicative (second-order) quantification is consistent. This predicative fragment is, nevertheless, too weak to develop arithmetic. In this paper, I will consider an extension of Heck’s system with impredicative quantifiers. In this extended system, both predicative and impredicative quantifiers co-exist but it is only permissible to take extensions of concepts formulated in the predicative fragment of the language. This system is consistent. Moreover, it proves the principle of reducibility applied to concepts true of only finitely many objects. With the aid of this form of reducibility, it is possible to develop arithmetic in a thoroughly Fregean way.

Editor
Hassan Tahiri

Data de Publicação
2018

Instituição
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA

Suporte
Logic, Epistemology, and the Unity of Science

Identificadores da Publicação
ISBN - 9783319937328

Editora
Springer International Publishing

Coleção
Logic, Episyemology, and the Unity of Science

Edição
Springer International Publishing
Fascículo
43

Número de Páginas
20
Página Inicial
81
Página Final
100

Identificadores do Documento
URL - http://dx.doi.org/10.1007/978-3-319-93733-5
DOI - https://doi.org/10.1007/978-3-319-93733-5

Anotações
This is an international refereed contribution. The book is based on a conference in honour of Roshdi Rashed.


Exportar referência

APA
Fernando Ferreira, (2018). Zigzag and Fregean arithmetic. Logic, Epistemology, and the Unity of Science, 81-100

IEEE
Fernando Ferreira, "Zigzag and Fregean arithmetic" in Logic, Epistemology, and the Unity of Science, 2018, pp. 81-100

BIBTEX
@incollection{40326, author = {Fernando Ferreira}, title = {Zigzag and Fregean arithmetic}, booktitle = {Logic, Epistemology, and the Unity of Science}, year = 2018, pages = {81-100}, address = {}, publisher = {Springer International Publishing} }