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A Mathematical Science of Qualities: A Sequel

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Abstract

Following a previous article published in Biological Theory, in this study we present a mathematical theory for a science of qualities as directly perceived by living organisms, and based on morphological patterns. We address a range of qualitative phenomena as observables of a psychological system seen as an impredicative system. The starting point of our study is the notion that perceptual phenomena are projections of underlying invariants, objects that remain unchanged when transformations of a certain class under consideration are applied. The study develops with the observables, the entailed total order and metric, whence the algebra and the geometry of such a science, presenting a formal phenomenological model for phenomena that are not rigidly Euclidean. We show how non-Euclidean perception can have many useful (non-rigid) Euclidean formalizations, as well as locally-homeomorphic-to-Euclidean-space models. The mathematical models we provide are tested on the basis of results from experimental psychology, in particular from the field of color, time, and space perception.

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Acknowledgments

The authors thank the director and the scientific board of STIAS (Stellenbosch Institute for Advanced Study, Wallenberg Research Centre at Stellenbosch University, Stellenbosch, South Africa) for providing the perfect environment in which to write this paper during the authors’ visit in February to April 2016.

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Authors and Affiliations

  1. Center for Mind/Brain Sciences (CIMeC), and Department of Humanities, University of Trento, Trento, Italy

    Liliana Albertazzi

  2. Stellenbosch Institute for Advanced Study (STIAS), Stellenbosch, South Africa

    A. H. Louie

  3. Ottawa, ON, Canada

    A. H. Louie

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  1. Liliana Albertazzi
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Correspondence to Liliana Albertazzi.

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Albertazzi, L., Louie, A.H. A Mathematical Science of Qualities: A Sequel. Biol Theory 11, 192–206 (2016). https://doi.org/10.1007/s13752-016-0248-0

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