The Diagonal Method and Hypercomputation.
The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation which claim to be able to solve the ha...
| Published in: | British Journal for the Philosophy of Science Vol. 56; no. 1; pp. 147 - 157 |
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| Main Authors: | , |
| Format: | Article |
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University of Chicago Press
Mar2005
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=16571426&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 16571426 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00070882 BPL jtl: British Journal for the Philosophy of Science issn: 00070882 maglogo: N pubinfo: dt: Mar2005 vid: 56 iid: 1 pid: 415 pub: University of Chicago Press artinfo: ui: 16571426 10.1093/phisci/axi108 ppf: 147 ppct: 10 formats: tig: atl: The Diagonal Method and Hypercomputation. aug: au: Ord, Toby Kieu, Tien D. affil: Department of Philosophy University of Melbourne Parkville 3010 Australia Centre for Atom Optics and Ultrafast Spectroscopy Swinburne University of Technology Hawthorn 3122 Australia su: Turing machines High performance computing Supercomputers Machine theory Scientific method Mathematical models sug: subj: Turing machines High performance computing Supercomputers Machine theory Scientific method Mathematical models ab: The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation which claim to be able to solve the halting problem for Turing machines. We show that such arguments are flawed—a contradiction only occurs if a type of machine can compute its own diagonal function. We then demonstrate why such a situation does not occur for the methods of hypercomputation under attack, and why it is unlikely to occur for any other serious methods. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2005 holdings: @attributes: islocal: N |
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