Magnitude and Number Sensitivity of the Approximate Number System in Conceptual Spaces

  • Aleksander GemelEmail author
  • Paula QuinonEmail author
Part of the Synthese Library book series (SYLI, volume 405)


In this paper, we propose a conceptual-spaces model of numerical cognition, and more precisely, of representations generated by Approximate Number System. The model is an extended and improved version of our earlier result (Gemel A, Quinon P: The approximate numbers system and the treatment of vagueness in conceptual spaces. In: Lukowski L, Gemel A, Zukowski B (eds) Cognition, meaning and action. Jagiellonian-Lodz University Press, Kraków, pp 87–108, 2015), where only purely quantitative information was accounted for. We focused on the idea that ANS evolved to detect numerosity in the input, and to abstract this information from all possible magnitude-related cues, such as size of compared objects, aggregate area of those objects, or density of their location. The idea is that when one sees a pile of apples, ANS acts as a “number sense”, informing one of the approximate quantity of apples. Consequently, the original model was very simplified, accounting only for one, uniform perceptual discrete visual input. With inspiration from computational models (ex. Dehaene S, Changeux JP: J Cogn Neurosci 5:390–407, 1993;, Lourenco SF, Longo MR: Psychol Sci 21(6):873–881, 2010) that can process more complex stimuli, we propose in this paper a conceptual-spaces model for non-uniform input. The improved version of the model accounts additionally for magnitude-related cues related to both “number sense” and “magnitude sense”.



We are very grateful to Peter Gärdenfors, as well as to the anonymous reviewers for the valuable comments and helpful remarks. Aleksander Gemel gratefully acknowledges financial support by the Approximate Number System in Conceptual Spaces project funded under the Grant of the Dean of the Faculty of Education Science University of Lodz (B1611800000228.01).


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Authors and Affiliations

  1. 1.Department of Cognitive Science, Institute of PsychologyUniversity of LodzLodzPoland
  2. 2.Department of Administration and Social SciencesWarsaw University of TechnologyWarsawPoland
  3. 3.Department of Philosophy and Cognitive SciencesLund UniversityLundSweden

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