Computing with Numbers and Other Non-syntactic Things: De re Knowledge of Abstract Objects

Philosophia Mathematica 25 (2):268-281 (2017)
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Abstract

ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.

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10.1093/philmat/nkx009

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Stewart Shapiro
Ohio State University

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References found in this work

What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
The ways of paradox, and other essays.Willard Van Orman Quine (ed.) - 1976 - Cambridge, Mass.: Harvard University Press.
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Foundations of mind.Tyler Burge - 2007 - New York: Oxford University Press.

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