The Number Concept: Human Cognition and Philosophy of Mathematics
1 : Department of Philosophy, Lund University
In this paper is proposed a conceptual analysis of natural numbers. This analysis results in a plausible picture of number concept formation, proposing an explanation of the relationship between numbers as understood by cognitive scientists studying number concept in little children and natural numbers used by mathematicians in model-theoretical framework.
A designed picture is three-folded.
Firstly, research of cognitive scientists is reminded, and concepts of core knowledge and innate cognitive numerical systems are discussed.
Secondly, still with respect to cognitive scientists research, the necessity of ability to language use in order to apprehend number concept. Claims that "number words" and "counting routine" is necessary in order to "saturated" number concept to arise, are explored and an interpretation in mathematical language proposed.
Finally, descriptive methods used by mathematicians to define concept of number and concept of computability are explored.
A designed picture is three-folded.
Firstly, research of cognitive scientists is reminded, and concepts of core knowledge and innate cognitive numerical systems are discussed.
Secondly, still with respect to cognitive scientists research, the necessity of ability to language use in order to apprehend number concept. Claims that "number words" and "counting routine" is necessary in order to "saturated" number concept to arise, are explored and an interpretation in mathematical language proposed.
Finally, descriptive methods used by mathematicians to define concept of number and concept of computability are explored.
