*Paolo Mancosu*

- Published in print:
- 2010
- Published Online:
- May 2011
- ISBN:
- 9780199546534
- eISBN:
- 9780191594939
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546534.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind

The book contains innovative contributions to the history and the philosophy of logic and mathematics in the first half of the twentieth century. It is divided into five main sections: history of ...
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The book contains innovative contributions to the history and the philosophy of logic and mathematics in the first half of the twentieth century. It is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert’s program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). The treatment exploits extensively untapped archival sources thereby making available a wealth of new material that deepens in significant ways our understanding of the above-mentioned areas. At the same time, the book is a contribution to recent debates on, among other things, the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.Less

The book contains innovative contributions to the history and the philosophy of logic and mathematics in the first half of the twentieth century. It is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert’s program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). The treatment exploits extensively untapped archival sources thereby making available a wealth of new material that deepens in significant ways our understanding of the above-mentioned areas. At the same time, the book is a contribution to recent debates on, among other things, the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.

*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.