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Incomputability, Emergence and the Turing Universe

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Causality, Meaningful Complexity and Embodied Cognition

Part of the book series: Theory and Decision Library A: ((TDLA,volume 46))

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Abstract

Amongst the huge literature concerning emergence, reductionism and mechanism, there is a role for analysis of the underlying mathematical constraints. Much of the speculation, confusion, controversy and descriptive verbiage might be clarified via suitable modelling and theory. The key ingredients we bring to this project are the mathematical notions of definability and invariance, a computability theoretic framework in a real-world context, and within that, the modelling of basic causal environments via Turing’s 1939 notion of interactive computation over a structure described in terms of reals. Useful outcomes are: a refinement of what one understands to be a causal relationship, including non-mechanistic, irreversible causal relationships; an appreciation of how the mathematically simple origins of incomputability in definable hierarchies are materialised in the real world; and an understanding of the powerful explanatory role of current computability theoretic developments.

Research supported by a Royal Society International Joint Project Grant, and by EPSRC Research Grant No. EP/G000212, The computational structure of partial information: Definability in the local structure of the enumeration degrees.

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Authors and Affiliations

  1. University of Leeds, Leeds, LS2 9JT, U.K.

    S. Barry Cooper

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  1. S. Barry Cooper
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Correspondence to S. Barry Cooper .

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Editors and Affiliations

  1. FacoltĂ  di Lettere e Filosofia, UniversitĂ  di Roma - Tor Vergata, Via Columbia 1, Roma, 00133, Italy

    A. Carsetti

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Cooper, S.B. (2010). Incomputability, Emergence and the Turing Universe. In: Carsetti, A. (eds) Causality, Meaningful Complexity and Embodied Cognition. Theory and Decision Library A:, vol 46. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3529-5_8

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