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Contextuality in the Integrated Information Theory

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Quantum Interaction (QI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10106))

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Abstract

Integrated Information Theory (IIT) is one of the most influential theories of consciousness, mainly due to its claim of mathematically formalizing consciousness in a measurable way. However, the theory, as it is formulated, does not account for contextual observations that are crucial for understanding consciousness. Here we put forth three possible difficulties for its current version, which could be interpreted as a trilemma. Either consciousness is contextual or not. If contextual, either IIT needs revisions to its axioms to include contextuality, or it is inconsistent. If consciousness is not contextual, then IIT faces an empirical challenge. Therefore, we argue that IIT in its current version is inadequate.

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Notes

  1. 1.

    This term was introduced by Pawel Kurzynski. See his contribution to this conference.

  2. 2.

    Because of our choice of \(\pm 1\)-valued random variables with zero expectation, their joint expectations coincide with their correlations.

  3. 3.

    This example is examined in detail in Specker’s Parable of the Over-Zealous Seer [cite], but was also discussed much earlier on by Boole [cite].

  4. 4.

    The indexing idea is also related to Stalnaker’s two-dimensional semantics; see [23].

  5. 5.

    In the works of Dzhafarov and Kujala, when we can assign contextuality because of direct influences between the measuring conditions of random variables, such variables are said to be inconsistently connected [8, 10,11,12, 14]. To those author’s, a system is contextual only if all context effects are not explainable by direct influences. So, for them the \(\mathbf {P}_{1}\), \(\mathbf {P}_{2}\), and \(\mathbf {P}_{3}\) perfectly anti-correlated example is contextual, whereas the Clinton/Gore one is not. However, we emphasize that this is a nomenclature issue.

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Acknowledgments

JAB and LPGA acknowledge support from the Patrick Suppes Gift Fund at Stanford University. Part of this work was developed at the Suppes Brain Lab in the Center for the Study of Language and Information, CSLI, and we thank CSLI and Professor John Perry for their hospitality.

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Authors and Affiliations

  1. School of Humanities and Liberal Studies, San Francisco State University, San Francisco, California, USA

    J. Acacio de Barros

  2. Department of Philosophy, San Francisco State University, San Francisco, California, USA

    Carlos Montemayor

  3. Suppes Brain Lab, Center for the Study of Language and Information, Stanford University, Stanford, California, USA

    J. Acacio de Barros & Leonardo P. G. De Assis

Authors
  1. J. Acacio de Barros
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  2. Carlos Montemayor
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  3. Leonardo P. G. De Assis
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Correspondence to J. Acacio de Barros .

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Editors and Affiliations

  1. San Francisco State University, San Francisco, California, USA

    Jose Acacio de Barros

  2. University of Oxford, Oxford, United Kingdom

    Bob Coecke

  3. City University of London, London, United Kingdom

    Emmanuel Pothos

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de Barros, J.A., Montemayor, C., De Assis, L.P.G. (2017). Contextuality in the Integrated Information Theory. In: de Barros, J., Coecke, B., Pothos, E. (eds) Quantum Interaction. QI 2016. Lecture Notes in Computer Science(), vol 10106. Springer, Cham. https://doi.org/10.1007/978-3-319-52289-0_5

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  • DOI: https://doi.org/10.1007/978-3-319-52289-0_5

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