Dean, Walter (2016) Algorithms and the mathematical foundations of computer science. In: Horsten, L. and Welch, P., (eds.) Gödel's disjunction : the scope and limits of mathematical knowledge. Oxford University Press, pp. 19-66. ISBN 9780198759591

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Abstract

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.

Item Type:	Book Item
Subjects:	B Philosophy. Psychology. Religion > BC Logic Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Social Sciences > Philosophy
Library of Congress Subject Headings (LCSH):	Algorithms, Computer algorithms, Computer science -- Mathematics, Logic
Publisher:	Oxford University Press
ISBN:	9780198759591
Book Title:	Gödel's disjunction : the scope and limits of mathematical knowledge
Editor:	Horsten, L. and Welch, P.
Official Date:	November 2016
Dates:	Date Event November 2016 Published
Page Range:	pp. 19-66
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Related URLs:	Publisher

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