Axiomathes 26 (1):1-40 (2016)

Authors
Wojciech Krysztofiak
Jagiellonian University
Abstract
In this paper, representational structures of arithmetical thinking, encoded in human minds, are described. On the basis of empirical research, it is possible to distinguish four types of mental number lines: the shortest mental number line, summation mental number lines, point-place mental number lines and mental lines of exact numbers. These structures may be treated as generative mechanisms of forming arithmetical representations underlying our numerical acts of reference towards cardinalities, ordinals and magnitudes. In the paper, the theoretical framework for a formal model of mental arithmetical representations is constructed. Many competitive conceptions of the mental system responsible for our arithmetical thinking may be unified within the presented framework. The paradigm underlying our research may be interpreted philosophically as a neo-Kantian approach to modeling the mind’s representational structures.
Keywords Cognitive arithmetic  Mental number line  Subitizing  SNARC effect  Distance effect  Size effect  Summation mental number axes  Point-place mental number axes
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DOI 10.1007/s10516-015-9271-1
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References found in this work BETA

The Mental Representation of Parity and Number Magnitude.Stanislas Dehaene, Serge Bossini & Pascal Giraux - 1993 - Journal of Experimental Psychology: General 122 (3):371.
Core Knowledge.Elizabeth S. Spelke - 2000 - American Psychologist 55 (11):1233-1243.

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Towards a Logic of Value and Disagreement Via Imprecise Measures.Federico L. G. Faroldi - 2021 - Bulletin of the Section of Logic 50 (2):131-149.

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