Descartes: A Biography

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 Descartes: A Biography

Mersenne seems to have been embarrassed by the lapse of confiden-

tiality involved in this misunderstanding, and he delayed until the fol-

lowing September before forwarding the uncomplimentary comments to

Descartes. Fermat disputed Descartes’ assumption that a ‘tendency to

move’ obeys the same laws as a body that actually moves, ‘because there

is as much difference between them as between potency and act’ (i.).

More seriously, he questioned the geometrical analysis proposed in the

Dioptricsto support the laws of reflection and refraction, and he argued

that Descartes’ analysis (into two components at right angles) of what he

called the ‘determination’ of a ray of light presupposed the conclusion that

he was attempting to demonstrate. He summarized his objections with the

comment: ‘as far as I am concerned, I could not accept his reasoning as a

legitimate proof and demonstration’ (i.).

This unsolicited and obviously unwelcome intervention sparked a con-

troversy that continued to resonate long after Descartes’ death. Descartes

seems to have been as uninformed about Fermat as the Toulouse counsellor

was about him. Thus, without knowing the identity of his critic, Descartes

replied reasonably calmly in his first letter (October) and asked

Mersenne to forward his response to the critic identified simply as ‘one of

your friends’ (i.). Already, however, he antagonized Fermat by accus-

ing him of culpably misunderstanding what he read. Where Descartes

had written: ‘it would be easy to believe that the tendency to move should

follow the same laws as movement,’ the ‘Toulouse counsellor’ had taken

that to mean that it was probable – a reasonable interpretation, one might

have thought. The pedantic response from ‘north Holland’ must have

sounded like a cranky teacher rebuking a careless student. ‘I classify as

almost false everything that is merely probable. And when I say that some-

thing is easy to believe, I do not mean to say that it is merely proba-

ble,butthat it is so clear and distinct that there is no need for me to

take time to demonstrate it’ (i.). How was Fermat supposed to know

that?

The tone of the dispute became more acrimonious with each new letter.

This progression seems to have been facilitated by Mersenne, when he

shared confidential letters that he had been asked to reserve while failing,

atthe same time, to forward letters in a timely manner. It thus seemed to

each somewhat sensitive mathematician that he was being snubbed by the

silence or delayed response of the other correspondent.When Mersenne

sent Descartes a short mathematical text in Latin written by Fermat, which