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Descartes, Gödel and Kuhn: Epiphenomenalism Defines a Limit on Reductive Logic

Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

René Descartes’ enduring contribution to philosophy, natural science and mathematics includes the unresolved residue of Cartesian dualism, as well as a singular ‘bottom-up’ interpretation of reductive logic sustained within the modern structure of the reductive natural science paradigm. Application of strong reductive logic leads to the perplexing reductive epiphenomenalism proposition.

Kurt Gödel’s two famous incompleteness theorems provide an argument through analogy, demonstrating that reductive epiphenomenalism of consciousness is a logical and demonstrably true ‘bottom-up’ reductive proposition; characterized by conceptual paradox that cannot be resolved from inside the modern reductive science paradigm using sustained singular ‘bottom-up’ reductive logic. The argument by analogy concludes reductive epiphenomenalism is an undecidable reductive proposition declaring strong reductive logic to be fundamentally incomplete.

Thomas Kuhn’s historical conception of a scientific revolution and modern explorations of contextual paradigm adaptation do not include descriptions of a limit on reductive logic associated with reductive incompleteness. One analogous implication of reductive incompleteness is the potential for an unresolvable and undecidable reductive proposition, stated in the paradigm and strong logic of reductive science, to become a resolvable and decidable reductive proposition within a closely related meta-reductive paradigm, preserving strong reductive logic but employing slightly different assumptions and premises. This opens the door to exploring functional adaptation of the reductive paradigm with the creation of adjacent possible meta-reductive paradigms.

Adjacent possible meta-reductive paradigms responding to reductive incompleteness, may be able to more closely mimic Nature’s inherent evolutionary logic, provide novel solutions to unresolved or anomalous reductive scientific problems, and clarify the relationship formal reductive incompleteness might have with the natural logic of evolving systems.

Keywords

  • Descartes
  • Reductive logic
  • Reductive science
  • Reductionism
  • Reductive epiphenomenalism of consciousness
  • Unresolvable logical and conceptual paradox
  • Gödel
  • Incompleteness theorems
  • Undecidable reductive propositions
  • Reductive incompleteness
  • Kuhn
  • Reductive paradigm
  • Meta-reductive paradigm

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Acknowledgments

Dr. Norman Davies, Dr. Sol Levin, Dr. William Dewhurst, Dr. James McMullin, Dr. Jack Tuszynski, Dr. Don Page, and the steadfast support of Dr. Yakov Shapiro. Any errors or omissions in this paper are entirely my own responsibility.

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Rowan Scott, J. (2018). Descartes, Gödel and Kuhn: Epiphenomenalism Defines a Limit on Reductive Logic. In: Morales, A., Gershenson, C., Braha, D., Minai, A., Bar-Yam, Y. (eds) Unifying Themes in Complex Systems IX. ICCS 2018. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-96661-8_4

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