Logical structuralism and Benacerraf's problem

Synthese 171 (1):157 - 173 (2009)
There are two general questions which many views in the philosophy of mathematics can be seen as addressing: what are mathematical objects, and how do we have knowledge of them? Naturally, the answers given to these questions are linked, since whatever account we give of how we have knowledge of mathematical objects surely has to take into account what sorts of things we claim they are; conversely, whatever account we give of the nature of mathematical objects must be accompanied by a corresponding account of how it is that we acquire knowledge of those objects. The connection between these problems results in what is often called “Benacerraf’s Problem”, which is a dilemma that many philosophical views about mathematical objects face. It will be my goal here to present a view, attributed to Richard Dedekind, which approaches the initial questions in a different way than many other philosophical views do, and in doing so, avoids the dilemma given by Benacerraf’s problem.
Keywords Philosophy of mathematics  Structuralism  Dedekind  Benacerraf’s problem
Categories (categorize this paper)
DOI 10.1007/s11229-008-9383-x
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,841
Through your library
References found in this work BETA
Realism in Mathematics.Penelope Maddy - 1990 - Oxford University Prress.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Empiricism, Semantics, and Ontology.Rudolf Carnap - 1950 - Revue Internationale de Philosophie 4 (11):20--40.

View all 12 references / Add more references

Citations of this work BETA
Dedekind and Cassirer on Mathematical Concept Formation†.Audrey Yap - 2017 - Philosophia Mathematica 25 (3):369-389.
To Bridge Gödel’s Gap.Eileen S. Nutting - 2016 - Philosophical Studies 173 (8):2133-2150.

Add more citations

Similar books and articles
Added to PP index

Total downloads
83 ( #68,465 of 2,210,261 )

Recent downloads (6 months)
1 ( #387,753 of 2,210,261 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature