Abstract (may include machine translation)
In this paper, I attempt to specify the relation between mathematical abilities as they have been studied by cognitive psychologists, and the history of mathematics. I present an epidemidemiological analysis of a mathematical notion: the notion of infnitely small quantities, or "infintesimals".
I will argue that the innate endowment of the human brain has determined the evolution of Mathematics in one direction, while social contingent factors were pulling in another direction. More precisely, while the social situation was favouring the development of the atomistic notion of infitesimals in the 18th century France, I suggest that the concept of limit was favoured by psychological factors related to human evolved cognitive capacities.
In the first section of this paper, I present the epidemiology of representation as a way to develop non-psychologistic enquiries into the cognitive bases of mathematics and its evolution. In the second section of the paper, I give a brief account of the psychological studies on the human abilities to perform arithmetic operation; in particular, the object-file representation system and the magnitude representation system. I argue that these abilities have had an effect on the history of the calculus. This effect is explained in terms of difference of relevance to the mathematicians of the 18th and 19th century of the Newtonian and the Leibnizian notions for the calculus. In the third section, I track down mathematical representations of the infiitesimal calculus, as they occurred at the turn of the 17th century France. I provide historical evidence in favour of the existence of a cultural attractor towards mathematical notions that resemble the notion of limit.
I will argue that the innate endowment of the human brain has determined the evolution of Mathematics in one direction, while social contingent factors were pulling in another direction. More precisely, while the social situation was favouring the development of the atomistic notion of infitesimals in the 18th century France, I suggest that the concept of limit was favoured by psychological factors related to human evolved cognitive capacities.
In the first section of this paper, I present the epidemiology of representation as a way to develop non-psychologistic enquiries into the cognitive bases of mathematics and its evolution. In the second section of the paper, I give a brief account of the psychological studies on the human abilities to perform arithmetic operation; in particular, the object-file representation system and the magnitude representation system. I argue that these abilities have had an effect on the history of the calculus. This effect is explained in terms of difference of relevance to the mathematicians of the 18th and 19th century of the Newtonian and the Leibnizian notions for the calculus. In the third section, I track down mathematical representations of the infiitesimal calculus, as they occurred at the turn of the 17th century France. I provide historical evidence in favour of the existence of a cultural attractor towards mathematical notions that resemble the notion of limit.
| Original language | English |
|---|---|
| Pages | 1-45 |
| State | Published - 2017 |