Computability, Notation, and de re Knowledge of Numbers

Philosophies 7 (20):20 (2022)
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Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of _which number_ is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of _notation_. The purpose of this article is to explore the relationship between the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects.



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Author Profiles

Stewart Shapiro
Ohio State University
Eric Snyder
Ashoka University
Richard Samuels
Ohio State University

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References found in this work

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.
Quantifying in.David Kaplan - 1968 - Synthese 19 (1-2):178-214.
Intensions revisited.W. V. Quine - 1977 - Midwest Studies in Philosophy 2 (1):5-11.
The Representational Foundations of Computation.Michael Rescorla - 2015 - Philosophia Mathematica 23 (3):338-366.

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