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
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.