Effective computation by humans and machines

Oron Shagrir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

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 Gancy-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.

Original languageAmerican English
Pages (from-to)221-240
Number of pages20
JournalMinds and Machines
Volume12
Issue number2
DOIs
StatePublished - May 2002

Bibliographical note

Funding Information:
I have been benefited from discussions with Eli Dresner, Paolo Mancosu, Gualtiero Piccinini, Itamar Pitowsky and Carl Posy, whose suggestions helped me to shape my arguments. I am grateful to Wilfried Sieg for detailed comments on an earlier draft of this paper. These comments contribute to the final version, which, I trust, is much improved. This research was supported by The Israel Academy of Sciences and Humanities.

Keywords

  • Effective computability
  • Gandy machines
  • Human computation
  • Machine computation
  • Physical computation
  • The Church-Turing thesis

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