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Vom Zahlen zu den Zahlen: On the Relation Between Computation and Arithmetical Structuralism
Philosophia Mathematica 20 (3):275-288 (2012)
Abstract
This paper sketches an answer to the question how we, in our arithmetical practice, succeed in singling out the natural-number structure as our intended interpretation. It is argued that we bring this about by a combination of what we assert about the natural-number structure on the one hand, and our computational capacities on the other handAuthor's Profile
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Citations of this work
The Representational Foundations of Computation.Michael Rescorla - 2015 - Philosophia Mathematica 23 (3):338-366.
Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of Mathematics.Tim Button & Sean Walsh - 2016 - Philosophia Mathematica 24 (3):283-307.
References found in this work
Wittgenstein on rules and private language: an elementary exposition.Saul A. Kripke - 1982 - Cambridge, Mass.: Harvard University Press.
Foundations without foundationalism: a case for second-order logic.Stewart Shapiro - 1991 - New York: Oxford University Press.
To be is to be a value of a variable (or to be some values of some variables).George Boolos - 1984 - Journal of Philosophy 81 (8):430-449.
Logicism and the ontological commitments of arithmetic.Harold T. Hodes - 1984 - Journal of Philosophy 81 (3):123-149.
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