Hypercomputation and the Physical Church‐Turing Thesis
Bibliographic Data
| ID | 8397168 |
|---|---|
| Authors | Paolo Cotogno (corresponding author) |
| Year | 2003 |
| Volume | 54 |
| Issue | 2 |
| Pages | 181-223 |
| Publication date | 2003-06-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | The British Journal for the Philosophy of Science (JOURNAL) |
| Journal identifiers | ISSN: 0007-0882 • E-ISSN: 1464-3537 |
| Publisher | Oxford University Press (PUBLISHER • GB) |
| DOI | 10.1093/bjps/54.2.181 |
| OpenAlex | W2051481378 |
| Language | EN |
| Citations received | 9 |
| References cited | 62 |
A version of the Church‐Turing Thesis states that every effectively realizable physical system can be defined by Turing Machines (‘Thesis P’); in this formulation the Thesis appears an empirical, more than a logico‐mathematical, proposition. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non‐well‐founded, analog, quantum, and retrocausal computation. These models depend on infinite computation, explicitly or implicitly, and appear physically implausible; moreover, even if infinite computation were realizable, the Halting Problem would not be affected. Therefore, Thesis P is not essentially different from the standard Church‐Turing Thesis. 1Introduction 2Computability and incomputability 3The physical interpretation of the Church‐Turing Thesis 4Supertasks and infinite computation 5Computation on non‐well‐founded domains 6Analog computation 7Quantum computation 8Retrocausal computation 9Conclusions
Algebra over a field · Algorithm · Computation · Description number · Halting problem · Interpretation (philosophy) · Model of computation · Non-deterministic Turing machine · Probabilistic Turing machine · Programming language · Pure mathematics · Super-recursive algorithm · Turing · Turing machine · Universal Turing machine · Cellular Automata and Applications · Computability, Logic, AI Algorithms · Computer Science · Mathematics · Quantum Computing Algorithms and Architecture · Theoretical Computer Science
Computing Mechanisms
Technology and Mathematics
Rational analysis, intractability, and the prospects of ‘as if’-explanations
Computationalism, The Church–Turing Thesis, and the Church–Turing Fallacy
On Epistemically Useful Physical Computation
SAD Computers and Two Versions of the Church–Turing Thesis
The Physical Church–Turing Thesis
The Diagonal Method and Hypercomputation
On the Possibility, or Otherwise, of Hypercomputation
| Unique citing works | 9 |
|---|---|
| Citations per year | 0,41 |
| Citation span | 2004 - 2023 (20) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 8 |