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What is Shannon information?

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Abstract

Despite of its formal precision and its great many applications, Shannon’s theory still offers an active terrain of debate when the interpretation of its main concepts is the task at issue. In this article we try to analyze certain points that still remain obscure or matter of discussion, and whose elucidation contribute to the assessment of the different interpretative proposals about the concept of information. In particular, we argue for a pluralist position, according to which the different views about information are no longer rival, but different interpretations of a single formal concept.

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Notes

  1. Here we are considering the discrete case, but all the definitions can be extended to the continuous case (see, e.g., Cover and Thomas 1991).

  2. We are grateful to one of the anonymous referees for pointing out this interesting issue.

  3. We are grateful to one of the anonymous referees for urging us to consider the possible ways in which the strategy of defining Shannon information via the coding theorems can be retained.

  4. We are grateful to one of the anonymous referees for his suggestion of considering the relationship between Shannon entropy and algorithmic complexity.

  5. In his book of 2013, Timpson talks about information not being a “common-or-garden” referring term (p. 83). Perhaps here he tries to moderate his earlier claims about the non-referring nature of the term ‘information.’ We are grateful to one of the anonymous referees for making us notice this point.

  6. We are grateful to one of the anonymous referees for suggesting the discussion of this point.

  7. We want to thank again one of the anonymous referees for urging us to stress this point.

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Acknowledgments

We are grateful to the participants of the workshop What is quantum information?, Jeffrey Bub, Adán Cabello, Dennis Dieks, Armond Duwell, Christopher Fuchs, Robert Spekkens and Christopher Timpson, (Buenos Aires, May of 2015) for the stimulating and lively discussions about the concept of information. We are also grateful to the anonymous referees, who devoted considerable effort to discuss the previous version of this article. We also want to thank María José Ferreira Ruiz for her support regarding the question of information in biology. This paper was partially supported by a Large Grant of the Foundational Questions Institute (FQXi), and by a Grant of the National Council of Scientific and Technological Research (CONICET) of Argentina.

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  1. CONICET, Universidad de Buenos Aires, Buenos Aires, Argentina

    Olimpia Lombardi

  2. CONICET, Universidad Nacional de la Plata, Buenos Aires, Argentina

    Federico Holik

  3. Universidad de Buenos Aires, Buenos Aires, Argentina

    Leonardo Vanni

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  1. Olimpia Lombardi
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Correspondence to Olimpia Lombardi.

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Lombardi, O., Holik, F. & Vanni, L. What is Shannon information?. Synthese 193, 1983–2012 (2016). https://doi.org/10.1007/s11229-015-0824-z

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