BIBLIOS

Document type
Book chapters


Title
Zigzag and Fregean arithmetic

Participants in the publication
Fernando Ferreira (Author)
Dep. Matemática
CMAFcIO

Summary
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(s)
Hassan Tahiri


Institution
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA

Where published
Logic, Epistemology, and the Unity of Science

Publication Identifiers
ISBN - 9783319937328

Publisher
Springer International Publishing

Collection
Logic, Episyemology, and the Unity of Science



Document Identifiers
URL - http://dx.doi.org/10.1007/978-3-319-93733-5
DOI - https://doi.org/10.1007/978-3-319-93733-5

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