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Philosophies 2016, 1(1), 15-27; doi:10.3390/philosophies1010015

Should Computability Be Epistemic? a Logical and Physical Point of View

INSA Lyon, Humanities Department, 1 rue des Humanités, 69621, Lyon, IHPST (Paris 1, ENS, CNRS), 13 rue du four, 75006 Paris, France
Academic Editor: Vincent C. Müller
Received: 20 July 2015 / Revised: 23 October 2015 / Accepted: 23 October 2015 / Published: 29 October 2015
(This article belongs to the Special Issue Computing and Philosophy: Papers from IACAP 2014)
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Abstract

Although the formalizations of computability provided in the 1930s have proven to be equivalent, two different accounts of computability may be distinguished regarding computability as an epistemic concept. While computability, according to the epistemic account, should be based on epistemic constraints related to the capacities of human computers, the non-epistemic account considers computability as based on manipulations of symbols that require no human capacities other than the capacity of manipulating symbols according to a set of rules. In this paper, I shall evaluate, both from a logical and physical point of view, whether computability should be regarded as an epistemic concept, i.e., whether epistemic constraints should be added on (physical) computability for considering functions as (physically) computable. Specifically, I shall argue that the introduction of epistemic constraints have deep implications for the set of computable functions, for the logical and physical Church-Turing thesis—cornerstones of logical and physical computability respectively—might turn out to be false according to which epistemic constraints are accepted. View Full-Text
Keywords: computability; physical computability; Church-Turing thesis; physical Church-Turing thesis; physical process; usability computability; physical computability; Church-Turing thesis; physical Church-Turing thesis; physical process; usability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Franchette, F. Should Computability Be Epistemic? a Logical and Physical Point of View. Philosophies 2016, 1, 15-27.

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