# Hypercomputation and the Physical Church‐Turing Thesis

@article{Cotogno2003HypercomputationAT, title={Hypercomputation and the Physical Church‐Turing Thesis}, author={Paolo Cotogno}, journal={The British Journal for the Philosophy of Science}, year={2003}, volume={54}, pages={181 - 223} }

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…

## 51 Citations

SAD Computers and Two Versions of the Church–Turing Thesis

- Computer ScienceThe British Journal for the Philosophy of Science
- 2009

This paper first considers deterministic and probabilistic barriers to the physical possibility of SAD computation, and argues against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur.

How to Make a Meaningful Comparison of Models: The Church–Turing Thesis Over the Reals

- PhilosophyMinds and Machines
- 2016

It is argued that it is possible in both cases to defend an equivalent of the Church–Turing thesis over the reals, and some methodological caveats on the comparison of different computational models are learned.

A Brief Critique of Pure Hypercomputation

- Computer ScienceMinds and Machines
- 2009

Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just…

The Physical Church–Turing Thesis: Modest or Bold?

- PhilosophyThe British Journal for the Philosophy of Science
- 2011

It is proposed to explicate the notion of physical computability in terms of a usability constraint, according to which for a process to count as relevant to Physical CT, it must be usable by a finite observer to obtain the desired values of a function.

Are Gandy Machines Really Local

- Philosophy
- 2016

A precise definition of the realization of a Turing-computable algorithm into a physical situation is given and Gandy machines, intended in a physical sense, are analysed as a case study and an inaccuracy in Gandy’s analysis with respect to the locality notion is shown, showing the epistemological relevance of this realization concept.

On the Possibilities of Hypercomputing Supertasks

- Computer ScienceMinds and Machines
- 2011

It is concluded that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection or re-interpretation of the Church-Turing thesis in its traditional interpretation.

On the Possibility, or Otherwise, of Hypercomputation

- Mathematics, PhilosophyThe British Journal for the Philosophy of Science
- 2004

We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal…

Computationalism, The Church–Turing Thesis, and the Church–Turing Fallacy

- PhilosophySynthese
- 2005

This work scrutinizes the most prominent arguments for computationalism based on the Church–Turing Thesis in light of recent work on CTT and argues that they are unsound.

What is the Church-Turing Thesis?

- Computer Science
- 2020

We aim to put some order to the multiple interpretations of the ChurchTuring Thesis and to the different approaches taken to prove or disprove it. [Answer:] Rosser and its inventor proved that its…

## References

SHOWING 1-10 OF 178 REFERENCES

Physical Hypercomputation and the Church–Turing Thesis

- PhilosophyMinds and Machines
- 2004

It is argued that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy's thesis.

ARTIFICIAL SEMANTICALLY CLOSED OBJECTS

- Computer Science
- 1998

A model of a rate-dependent and memory empowered neuron is proposed in the construction of more complex Artificial Neural Networks, where neurons are temporal pattern recognition processors, rather than timeless and memoryless boolean switches.

Is the Church-Turing thesis true?

- PhilosophyMinds and Machines
- 2004

It is argued that mundane procedures can be said to be effective in the same sense in which Turing machine procedures can been said toBe effective, and that mundane Procedures differ from Turing machine Procedures in a fundamental way, viz., the former, but not the latter, generate causal processes.

Computation and Hypercomputation

- Computer ScienceMinds and Machines
- 2004

The meaning of physical computation is considered in some detail, and arguments in favour of physical hypercomputation are presented, and the relationship between versions of computability corresponding to different models of physics is considered.

Church's thesis and its relation to the concept of realizability in biology and physics.

- PhilosophyThe Bulletin of mathematical biophysics
- 1962

It is shown that the truth of Church’s Thesis in this, form is closely connected with the “effectiveness” of theoretical descriptions of physical systems, and the falsity of this form is related to a fundamental incompleteness in the possibility of describing physical systems.

Quantum Speed‐up of Computations

- Computer SciencePhilosophy of Science
- 2002

Wolfram’s thesis consists of two parts: (a) Any physical system can be simulated (to any degree of approximation) by a universal Turing machine (b) Complexity bounds on Turing machine simulations…

Non-Turing Computations Via Malament–Hogarth Space-Times

- Computer Science
- 2001

It is argued that there are several distinguished Church–Turing-type theses (not only one) and validity of some of these theses depend on the background physical theory the authors choose to use, and if they choose classical general relativity theory as their background theory, then certain forms of the Church-Turing thesis cease to be valid.

The Broad Conception of Computation

- Philosophy
- 1997

A myth has arisen concerning Turing's article of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine; this supposed principle is sometimes incorrectly termed the Church-Turing thesis.

History of \church's Theses" and a Manifesto on Converting Physics into a Rigorous Algorithmic Discipline

- Physics, Education
- 1999

| Church's thesis claims that any \reason-able computer" may be simulated by a Turing machine. The \strong" thesis says that the simulation may be performed with only polynomial slowdown. This…

Quantum theory, the Church–Turing principle and the universal quantum computer

- Physics, PhilosophyProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1985

It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible…