Descartes: A Biography

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 Descartes: A Biography

long as he refused to disclose the fundamental theory of light on which

it depended.However, he also wished to persuade Descartes that he

should consider using scholastic distinctions to resolve some difficulties,

such as distinguishing between ‘act’ and ‘potency’ and thus recognizing

that light is a ‘faculty’ by which the Sun illuminates (ii.). This type

of resolution was fundamentally inconsistent with the Cartesian project.

Descartes replied that the substantial form of the Sun, insofar as it is

distinct from the qualities that are found in its matter, is ‘a philosophical

entity that is unknown to me.’Thus there were radical differences in

the type of entity that they were willing to include as contributing to an

explanation. Accordingly, Descartes resisted all the objections raised by

Morin, although their conversation was always polite and cordial, and he

eventually acknowledged to Mersenne that Morin’s views were ‘further

from mine than they were at the beginning, so that we will never agree.’

This might lead one to hope that, when discussing objections to Carte-

sian mathematics rather than physics, it would have been easier both to

identify the reasons why his critics objected and to resolve the resulting

disagreements. The evidence of his long-running disputes with Fermat,

Roberval, and Pascal shows the extent to which logic and mathematical

skill were relatively marginal considerations in those disputes also.

Pierre Fermat and the French Mathematicians

Like Descartes, Pierre Fermat (–) was effectively a self-taught

amateur in mathematics. He had become familiar with the analytical meth-

ods developed by Franc ̧ois Viete (` –) during a period spent in

Bordeaux, and had then embarked officially on a legal career, in,

in the Toulouse parliament. With such apparently unpromising edu-

cational resources, Fermat thought of linking indeterminate algebraic

equations in two unknowns with two-dimensional geometric curves,

an idea that Descartes seems to have stumbled on some years earlier.

Despite their subsequent fame, neither Fermat nor Descartes had ever

heard of each other during the years prior to publication of theEssays.

Fermatwas working in a remote corner of the kingdom of France, while

Descartes was hiding in an even more remote corner of Holland. The

contact point between the two mathematicians was their common friends

in Paris. Fermat sent the manuscript of hisIntroduction to Plane and

Solid Locito his mathematician friends in Paris, including Roberval and