, Volume 12, Issue 2, pp 221240
First online:
Effective Computation by Humans and Machines
 Oron ShagrirAffiliated withDepartment of Philosophy, The Hebrew University of Jerusalem
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There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. According to this account, to which I refer as the Gandy–Sieg account, Turing and Church aimed to characterize the functions that can be computed by a human computer. In addition, Turing provided a highly convincing argument for CTT by analyzing the processes carried out by a human computer. I then contend that if the Gandy–Sieg account is correct, then the notion of effective computability has changed after 1936. Today computer scientists view effective computability in terms of finite machine computation. My contention is supported by the current formulations of CTT, which always refer to machine computation, and by the current argumentation for CTT, which is different from the main arguments advanced by Turing and Church. I finally turn to discuss Robin Gandy's characterization of machine computation. I suggest that there is an ambiguity regarding the types of machines Gandy was postulating. I offer three interpretations, which differ in their scope and limitations, and conclude that none provides the basis for claiming that Gandy characterized finite machine computation.
 Title
 Effective Computation by Humans and Machines
 Journal

Minds and Machines
Volume 12, Issue 2 , pp 221240
 Cover Date
 200205
 DOI
 10.1023/A:1015694932257
 Print ISSN
 09246495
 Online ISSN
 15728641
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 effective computability
 Gandy machines
 human computation
 machine computation
 physical computation
 The Church–Turing Thesis
 Authors

 Oron Shagrir ^{(1)}
 Author Affiliations

 1. Department of Philosophy, The Hebrew University of Jerusalem, Jerusalem, 91905, Israel