*Christopher G. Timpson*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199296460
- eISBN:
- 9780191741791
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296460.003.0006
- Subject:
- Philosophy, Philosophy of Science

Some of the philosophical questions raised by the theory of quantum computation are discussed. First it is considered whether the possibility of exponential speed-up in quantum computation provides ...
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Some of the philosophical questions raised by the theory of quantum computation are discussed. First it is considered whether the possibility of exponential speed-up in quantum computation provides an argument for a more substantive notion of quantum information than so far allowed. It is concluded that this is not so. Then some questions regarding the status of the Church-Turing hypothesis in the light of quantum computation are considered. In particular, Deutsch’s claim that a physical principle, the Turing Principle, underlies the Church-Turing hypothesis is rebutted. Finally, the question of whether the Church-Turing hypothesis might serve as a constraint on the laws of physics is briefly considered.Less

Some of the philosophical questions raised by the theory of quantum computation are discussed. First it is considered whether the possibility of exponential speed-up in quantum computation provides an argument for a more substantive notion of quantum information than so far allowed. It is concluded that this is not so. Then some questions regarding the status of the Church-Turing hypothesis in the light of quantum computation are considered. In particular, Deutsch’s claim that a physical principle, the Turing Principle, underlies the Church-Turing hypothesis is rebutted. Finally, the question of whether the Church-Turing hypothesis might serve as a constraint on the laws of physics is briefly considered.

*Gualtiero Piccinini*

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199658855
- eISBN:
- 9780191748158
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199658855.003.0016
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind

This chapter distinguishes between the Mathematical Church-Turing thesis—the thesis supported by the original arguments for the Church-Turing thesis—and the Physical Church-Turing thesis (Physical ...
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This chapter distinguishes between the Mathematical Church-Turing thesis—the thesis supported by the original arguments for the Church-Turing thesis—and the Physical Church-Turing thesis (Physical CT). It then distinguishes between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. It explicates 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. Finally, it argues that Bold Physical CT is not relevant to the epistemological concerns that motivate CT and hence not suitable as a physical analogue of Mathematical CT.Less

This chapter distinguishes between the Mathematical Church-Turing thesis—the thesis supported by the original arguments for the Church-Turing thesis—and the Physical Church-Turing thesis (Physical CT). It then distinguishes between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. It explicates 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. Finally, it argues that Bold Physical CT is not relevant to the epistemological concerns that motivate CT and hence not suitable as a physical analogue of Mathematical CT.

*Gualtiero Piccinini*

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199658855
- eISBN:
- 9780191748158
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199658855.003.0017
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind

This chapter discusses a modest version of the Physical Church-Turing thesis (roughly, that everything physically computable can be done by some Turing machine) and finds it plausible. A ...
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This chapter discusses a modest version of the Physical Church-Turing thesis (roughly, that everything physically computable can be done by some Turing machine) and finds it plausible. A hypercomputer is any system that yields the values of a Turing-uncomputable function. If a genuine hypercomputer is physically constructible and reliable, it would refute the modest Physical Church-Turing Thesis. Various proposals for hypercomputers, including relativistic hypercomputers and neural networks, are discussed, but such proposals are not now technologically practical or even physically possible. Proposed counterexamples to the Physical Church-Turing thesis are still far from falsifying it because they have not been shown to be physically constructible and reliable.Less

This chapter discusses a modest version of the Physical Church-Turing thesis (roughly, that everything physically computable can be done by some Turing machine) and finds it plausible. A *hypercomputer* is any system that yields the values of a Turing-uncomputable function. If a genuine hypercomputer is physically constructible and reliable, it would refute the modest Physical Church-Turing Thesis. Various proposals for hypercomputers, including relativistic hypercomputers and neural networks, are discussed, but such proposals are not now technologically practical or even physically possible. Proposed counterexamples to the Physical Church-Turing thesis are still far from falsifying it because they have not been shown to be physically constructible and reliable.

*Gualtiero Piccinini*

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199658855
- eISBN:
- 9780191748158
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199658855.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind

This book articulates and defends a mechanistic account of concrete, or physical, computation. A physical system is a computing system just in case it is a mechanism one of whose functions is to ...
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This book articulates and defends a mechanistic account of concrete, or physical, computation. A physical system is a computing system just in case it is a mechanism one of whose functions is to manipulate vehicles based solely on differences between different portions of the vehicles according to a rule defined over the vehicles. Six desiderata to be satisfied by an account of concrete computation are set out: 1) objectivity; 2) explanation; 3) the right things compute; 4) the wrong things don’t compute; 5) miscomputation is explained; and 6) taxonomy. The book discusses previous accounts of computation and argues that the mechanistic account satisfies the desiderata better than competing accounts. Many kinds of computation are explicated, such as digital vs. analog, serial vs. parallel, neural network computation, program-controlled computation, and more. The book argues that computation does not entail representation or information processing although information processing entails computation. Pancomputationalism, according to which every physical system is computational, is rejected as trivial insofar as true; false insofar as nontrivial. A modest version of the physical Church-Turing thesis, according to which any function that is physically computable is computable by Turing machines, is defended. A hypercomputer is a system that yields the values of a Turing-uncomputable function. If a genuine hypercomputer were physically constructible and reliable, it would refute the modest Physical Church-Turing Thesis. Proposed counterexamples to the Physical Church-Turing thesis are still far from falsifying it, however, because they have not been shown to be physically constructible and reliable.Less

This book articulates and defends a mechanistic account of concrete, or physical, computation. A physical system is a computing system just in case it is a mechanism one of whose functions is to manipulate vehicles based solely on differences between different portions of the vehicles according to a rule defined over the vehicles. Six desiderata to be satisfied by an account of concrete computation are set out: 1) objectivity; 2) explanation; 3) the right things compute; 4) the wrong things don’t compute; 5) miscomputation is explained; and 6) taxonomy. The book discusses previous accounts of computation and argues that the mechanistic account satisfies the desiderata better than competing accounts. Many kinds of computation are explicated, such as digital vs. analog, serial vs. parallel, neural network computation, program-controlled computation, and more. The book argues that computation does not entail representation or information processing although information processing entails computation. Pancomputationalism, according to which every physical system is computational, is rejected as trivial insofar as true; false insofar as nontrivial. A modest version of the physical Church-Turing thesis, according to which any function that is physically computable is computable by Turing machines, is defended. A *hypercomputer* is a system that yields the values of a Turing-uncomputable function. If a genuine hypercomputer were physically constructible and reliable, it would refute the modest Physical Church-Turing Thesis. Proposed counterexamples to the Physical Church-Turing thesis are still far from falsifying it, however, because they have not been shown to be physically constructible and reliable.