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Oracle Hypermachines Faced with the Verification Problem

  • Florent Franchette
Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 7)

Abstract

One of the main current issues about hypercomputation concerns the claim of the possibility of building a physical device that hypercomputes. In order to prove this claim, one possible strategy could be to physically build an oracle hypermachine, namely a device which is be able to use some extern information from nature to go beyond Turing machines limits. However, there is an epistemological problem affecting this strategy, which may be called “verification problem”. This problem raises in presence of an oracle hypermachine and it may be set out as follows: even if we were able to build such a hypermachine we would not be able to claim that it hypercomputes because it would be impossible to verify that the machine can compute a non Turing-computable function. In this paper, I propose an analysis of the verification problem in order to know whether it is a genuine problem for oracle hypermachines.

Keywords

computability theory hypercomputation oracle hypermachine Turing machine verification problem randomness 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.IHPSTUniversity of Paris 1 Panthéon-SorbonneParisFrance

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