The chapter discusses the concept of Turing-computability from the point of view of mathematical constructivism and with the help of Leibniz’s conception of computation. The author suggests that even within the domain of constructivist approaches to mathematics (as Bernard Bolzano and Karl Weierstrass defined them), the use of random choice produces computations that bypass the limitations of Turing-computability. Ever since its inception, ai has identified computation with Turing’s formalization of it, while the notion that mainstream computer science uses has been more flexible and more aware of its limitations. The close relationship between Turing-computability and the simulations of intelligent behavior that Artificial Intelligence attempts raises the possibility that a broader conception of computability may substantially renew the theoretical framework we use to model cognitive behavior.

Turing Computability and Leibniz Computability

MATTEUZZI, MAURIZIO
2011

Abstract

The chapter discusses the concept of Turing-computability from the point of view of mathematical constructivism and with the help of Leibniz’s conception of computation. The author suggests that even within the domain of constructivist approaches to mathematics (as Bernard Bolzano and Karl Weierstrass defined them), the use of random choice produces computations that bypass the limitations of Turing-computability. Ever since its inception, ai has identified computation with Turing’s formalization of it, while the notion that mainstream computer science uses has been more flexible and more aware of its limitations. The close relationship between Turing-computability and the simulations of intelligent behavior that Artificial Intelligence attempts raises the possibility that a broader conception of computability may substantially renew the theoretical framework we use to model cognitive behavior.
The Search for a Theory of Cognition.Early Mechanisms and New Ideas.
233
243
M. Matteuzzi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/108057
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