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  1. Axiomathes
  2. Axiomathes : Volume 26
  3. Axiomathes : Volume 26, Issue 2, June 2016
  4. Algebraic Models of Mental Number Axes: Part II
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Axiomathes : Volume 27
Axiomathes : Volume 26
Axiomathes : Volume 26, Issue 4, December 2016
Axiomathes : Volume 26, Issue 3, September 2016
Axiomathes : Volume 26, Issue 2, June 2016
Against Mathematical Convenientism
Algebraic Models of Mental Number Axes: Part II
Abduction, Complex Inferences, and Emergent Heuristics of Scientific Inquiry
How Powers Emerge from Relations
Why be an Intellectually Humble Philosopher?
Axiomathes : Volume 26, Issue 1, March 2016
Axiomathes : Volume 25
Axiomathes : Volume 24
Axiomathes : Volume 23
Axiomathes : Volume 22
Axiomathes : Volume 21
Axiomathes : Volume 20
Axiomathes : Volume 19
Axiomathes : Volume 18
Axiomathes : Volume 17
Axiomathes : Volume 16
Axiomathes : Volume 15
Axiomathes : Volume 14
Axiomathes : Volume 13
Axiomathes : Volume 12
Axiomathes : Volume 11
Axiomathes : Volume 10
Axiomathes : Volume 9
Axiomathes : Volume 8

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Algebraic Models of Mental Number Axes: Part II

Content Provider Springer Nature Link
Author Krysztofiak, Wojciech
Copyright Year 2015
Abstract 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.
Starting Page 123
Ending Page 155
Page Count 33
File Format PDF
ISSN 11221151
Journal Axiomathes
Volume Number 26
Issue Number 2
e-ISSN 15728390
Language English
Publisher Springer Netherlands
Publisher Date 2015-04-18
Publisher Place Dordrecht
Access Restriction Subscribed
Subject Keyword 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 Philosophy Ontology Linguistics Cognitive Psychology Logic
Content Type Text
Resource Type Article
Subject Philosophy Mathematics
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