Ports of Call

### The Method of Analysis

Descartes suggests in earlier works that in order to achieve results in the sciences we need to take things apart into their simplest elements, see how those elements are related to one another, and then recompose them. This is very much the resoluto-compositive method that Galileo used in analyzing motion. It is also a method which Descartes and other sixteenth and seventeenth century mathematicians believed the great mathematicians of antiquity, Euclid, Archimedes, and Apollonius for example, had used to make their discoveries, before these discoveries were presented in the synthetic form. Descartes developed his own version of this method. Many philosophers were impressed by the deductive form of Euclidean geometry. Descartes was not. His account of the method of analysis has to do with problem solving, with the method of discovering the truths which are then presented deductively. For a more detailed discussion of the method of analysis, you should look at Chapter 2 of John Cottingham's book The Rationalists. The point here is that what Descartes' analysis of dreams tells us is that we are moving both towards that which cannot be doubted on the strongest possible skeptical hypothesis and, at the same time, towards that which is most simple.

Under the pressure of the dream hypothesis, and adhering to the method of doubt, Descartes tries to determine which things can be doubted and which cannot. He remarks that "...while eyes, heads and hands may be imaginary, it must be granted that some simpler and more universal things are real -- the "real colors" from which the true and false images in our thoughts are framed." Besides these:

Things of this sort seem to include general bodily nature and its extension, the shape of extended things, their quantity (that is their size and number) the place in which they exist, the time through which they endure, and so on.
So, real colors, extension, shape, quantity, time and place all are immune to the doubts raised by the dream hypothesis. Just as he did for the senses, Descartes has neatly partitioned claims made on the basis of the imagination into two classes, one of which almost always turns out to be false, and the other which we find hard to doubt.

 Claims derived from the imagination Claims about the world about us derived from dreamsThese claims almost always turn out to be falseI am sitting by the fire (when in fact I am in bed asleep). Claims about the world which depend on truths of mathematics, and claims about time and space.These claims are almost all going to turn out to be true.

Descartes now shows his concern about the implications of these skeptical hypotheses for the sciences. He writes:

Perhaps we can correctly infer that, while physics, astronomy, medicine and other disciplines that study composites are dubious, disciplines like arithmetic and geometry, which deal only with completely simple and universal things without regard to whether they exist in the world, are somehow certain and indubitable. For whether we are awake or asleep, two plus three is always five, and the square never has more than four sides.
This passage makes it quite explicit that we are moving from the complex to the simple. This is good evidence that Descartes' method of analysis is being applied here. So, besides those general features of bodily nature, the truths of mathematics are largely immune to the doubts raised by the dream hypothesis. How then could one call such truths as that squares have four sides and that 2 +3 = 5 into question? Note just how difficult this is. If it seems mad to doubt things perceived near by, it is surely more difficult to genuinely call into question such truths as that squares have fours sides.

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