caa a22 4500 445838345 CHVBK 20180317145336.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s11023-011-9238-y doi (NATIONALLICENCE)springer-10.1007/s11023-011-9238-y Do Accelerating Turing Machines Compute the Uncomputable? [Elektronische Daten] [B. Jack Copeland, Oron Shagrir] Accelerating Turing machines have attracted much attention in the last decade or so. They have been described as "the work-horse of hypercomputation” (Potgieter and Rosinger 2010: 853). But do they really compute beyond the "Turing limit”—e.g., compute the halting function? We argue that the answer depends on what you mean by an accelerating Turing machine, on what you mean by computation, and even on what you mean by a Turing machine. We show first that in the current literature the term "accelerating Turing machine” is used to refer to two very different species of accelerating machine, which we call end-stage-in and end-stage-out machines, respectively. We argue that end-stage-in accelerating machines are not Turing machines at all. We then present two differing conceptions of computation, the internal and the external, and introduce the notion of an epistemic embedding of a computation. We argue that no accelerating Turing machine computes the halting function in the internal sense. Finally, we distinguish between two very different conceptions of the Turing machine, the purist conception and the realist conception; and we argue that Turing himself was no subscriber to the purist conception. We conclude that under the realist conception, but not under the purist conception, an accelerating Turing machine is able to compute the halting function in the external sense. We adopt a relatively informal approach throughout, since we take the key issues to be philosophical rather than mathematical. Springer Science+Business Media B.V., 2011 Accelerating Turing machine nationallicence Supertask nationallicence Halting problem nationallicence ATM paradox nationallicence Hypercomputation nationallicence External and internal computation nationallicence Epistemic embedding nationallicence Ontology of computing nationallicence Turing-machine purism nationallicence Turing-machine realism nationallicence Thompson lamp paradox nationallicence Jack Copeland B. University of Canterbury, Christchurch, New Zealand aut Shagrir Oron Hebrew University of Jerusalem, Jerusalem, Israel aut Minds and Machines Springer Netherlands 21/2(2011-05-01), 221-239 0924-6495 21:2<221 2011 21 11023 https://doi.org/10.1007/s11023-011-9238-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11023-011-9238-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jack Copeland B. University of Canterbury, Christchurch, New Zealand aut NATIONALLICENCE 700 1- Shagrir Oron Hebrew University of Jerusalem, Jerusalem, Israel aut NATIONALLICENCE 773 0- Minds and Machines Springer Netherlands 21/2(2011-05-01), 221-239 0924-6495 21:2<221 2011 21 11023 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer