Logical structuralism and Benacerraf's problem

Synthese 171 (1):157 - 173 (2009)
Abstract
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
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References found in this work BETA
Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
Rudolf Carnap (1950). Empiricism, Semantics, and Ontology. Revue Internationale de Philosophie 4 (2):20--40.

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