Axiomathes 26 (2):123-155 (2016)

Wojciech Krysztofiak
Jagiellonian University
The paper presents a formal model of the system of number representations as a multiplicity of mental number axes with a hierarchical structure. The hierarchy is determined by the mind as it acquires successive types of mental number axes generated by virtue of some algebraic mechanisms. Three types of algebraic structures, responsible for functioning these mechanisms, are distinguished: BASAN-structures, CASAN-structures and CAPPAN-structures. A foundational order holds between these structures. CAPPAN-structures are derivative from CASAN-structures which are extensions of BASAN-structures. The constructed formal model unifies two competitive conceptions of cognitive arithmetic: namely, the conception of the mental number line and the conception of parallel individuation. The paper is the continuation of a paper entitled Representational structures of arithmetical thinking, in which rich empirical evidence supporting the model is presented. The main result achieved in the present paper may be philosophically interpreted as an attempt to formalize the Kantian conception of the pure idea of time, understood as the a priori form of human arithmetical thinking. In this way, our theory may be comprehended as a result of applying the hard method of logical reconstruction of fundamental epistemological categories.
Keywords Cognitive arithmetic  Mental number line  Subitizing  SNARC effect  Distance effect  Size effect  Summation mental number axes  Point-place mental number axes  Exact mental number axes
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DOI 10.1007/s10516-015-9270-2
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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.
Reactions Toward the Source of Stimulation.J. Richard Simon - 1969 - Journal of Experimental Psychology 81 (1):174.

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