Computability in Europe 2006
Logical Approaches to Computational Barriers
Logical Approaches to Computational Barriers
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Regular Talk:
Decidability of arithmetic through hypercomputation: logical objections
| THIS TALK HAS BEEN CANCELLED!!! | |
| Speaker: | Paolo Cotogno |
Abstract
The theory of hypercomputation aims to extend effective computability beyond Turing reducibility, in particular by means of supertasks; physical models are considered in Newtonian, relativistic and quantum contexts. Apart from implementation differences, all approaches take for granted that supertask computations would decide arithmetic; in logical terms, this amounts to assume that the undecidability of Peano Arithmetic can be bypassed by the omega-rule. We argue that this assumption is untenable, as long as the system is consistent: the conclusion follows from alternative versions of Gödel’s incompleteness, such as Rosser’s and Yablo’s, which are indifferent to infinite deductions.
| websites: Arnold Beckmann | 2006-06-30
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