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Professor Henk J.M. Bos,
Mathematisch Instituut, Universiteit Utrecht :

Descartes' attempt to base the certainty of algebra on mental vision

In his unfinished (and at the time unpublished) 'Regulae ad Directionem Ingenii' ('Rules for the Direction of the Mind', composed during the 1620's) Descartes used examples from mathematics to illustrate how the human mind can attain certain knowledge. The crucial example was the certainty of the arithmetical operations. For adding, subtracting, multiplying and dividing he produced arguments which convinced him. However, the text which we have strongly suggests that he was not able to prove the certainty of root extraction (both square and higher-order roots) in a manner he found satisfactory. He later abandoned this line of approaching the problem of certainty in philosophy.

The criteria for certainty which Descartes used in the 'Regulae' were strongly visual; attaining certainty involved a process of `imagination' in which figures were created by the mind on a kind of mental screen, observable by some inner eye.

I shall discuss the background of his attempt and a conjecture about the reason why he abandoned the project.

tirsdag, den 30. november 2004
i auditorium 10, på H. C. Ørsted Instituttet,
Universitetsparken 5, København

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