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Gödel's DisjunctionThe scope and limits of mathematical knowledge$
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Leon Horsten and Philip Welch

Print publication date: 2016

Print ISBN-13: 9780198759591

Published to Oxford Scholarship Online: November 2016

DOI: 10.1093/acprof:oso/9780198759591.001.0001

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Algorithms and the Mathematical Foundations of Computer Science

Algorithms and the Mathematical Foundations of Computer Science

(p.19) 2 Algorithms and the Mathematical Foundations of Computer Science
Gödel's Disjunction

Walter Dean

Oxford University Press

The goal of this chapter is to bring to the attention of philosophers of mathematics the concept of algorithm as it is studied incontemporary theoretical computer science, and at the same time address several foundational questions about the role this notion plays in our practices. A view known as algorithmic realism will be described which maintains that individual algorithms are identical to mathematical objects. Upon considering several ways in which the details of algorithmic realism might be formulated, it will be argued (pace Moschovakis and Gurevich) that there are principled reasons to think that this view cannot be systematically developed in a manner which is compatible with the practice of computational complexity theory and algorithmic analysis.

Keywords:   algorithm, computability, Church’s Thesis

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