Descartes: A Biography

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 Descartes: A Biography

degree of certainty that was not feasible in natural science. These general

rules of method, outlined in Rule,were later summarized and reissued

in a very different context in theDiscourse on Methodin. The other

immediate reason for abandoning the project was Descartes’ inability to

construct a general problem-solving technique that would apply to all

problems, including mathematical ones.

The discussion of method in theRuleschanged suddenly at transitions

between different ideas that were competing for attention in Descartes’

still inchoate plans for a renewal of knowledge. One of those, already

mentioned, is the relegation of scholastic methods to the past. Another

version of this suggestion was that natural intelligence is a more reliable

guide to the truth than the convoluted systems of thought invented by

philosophers, and that the way to find the truth is to cultivate native

intelligence rather than to learn a method from someone else. However,

despite all these disclaimers, Descartes also had in mind a paradigm of

what success in his enterprise would mean. This was summarized in the

search for what he called a ‘mathesis universalis’, or a universal rigorous

method.

When these thoughts recalled me from the particular study of arithmetic and geometry

to searching for a certain general mathesis, I first inquired what precisely everyone

understood by that term, and why not only the disciplines already mentioned but

also astronomy, music, optics, mechanics and many others are also said to be part of

mathematics....since the word ‘mathesis’ means the same as ‘discipline’, the other dis-

ciplines have as much right as geometry itself to be called mathematics....Therefore,

there must be some general science, which explains everything that can be learned

about order and measure, which is not confined to any particular subject matter, and

which is called universal mathesis. (x.–)

TheRulespresents a very abstract version of the problems that seem to

have been bothering Descartes at the time of its composition. It is reason-

ably clear that he is still thinking of a way of integrating arithmetic and

geometry (or problems of discrete and continuous magnitude), and his

new emphasis on the role of the imagination suggests that all soluble prob-

lems could be mapped onto problems in geometry or spatial extension. Part

of the method envisaged is outlined in Part Two, which describes in gen-

eral terms how to translate mathematical problems into equations. How-

ever, the underlying philosophical and mathematical problems remained

unsolved – what methods of construction (apart from ruler and compass)

should be accepted as genuinely geometrical; how to construct higher