Minds and Machines

, Volume 7, Issue 3, pp 321-344

First online:

Two Dogmas of Computationalism

  • Oron ShagrirAffiliated withSidney M. Edelstein Center for History and Philosophy of Science, The Hebrew University

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This paper challenges two orthodox theses: (a) that computational processes must be algorithmic; and (b) that all computed functions must be Turing-computable. Section 2 advances the claim that the works in computability theory, including Turing's analysis of the effective computable functions, do not substantiate the two theses. It is then shown (Section 3) that we can describe a system that computes a number-theoretic function which is not Turing-computable. The argument against the first thesis proceeds in two stages. It is first shown (Section 4) that whether a process is algorithmic depends on the way we describe the process. It is then argued (Section 5) that systems compute even if their processes are not described as algorithmic. The paper concludes with a suggestion for a semantic approach to computation.

algorithm computability recursive function Turing-machine step-satisfaction analog and digital attractor neural nets