From the section of "Smooth & Striated" in which he discuss mathematics in the context of multiplicities:
"...it might be thought that the Number would belong exclusively to the other multiplicities, that it would accord them the scientific status non-metric multiplicities lack ... the number is the correlate of the metric: magnatudes can striated space only by reference to the numbers, and conversely, numbers are used to express increasingly complex relations between magnatudes, thus giving rise to ideal spaces reinforcing the situation and making it coextensive with all of matter. There is therefor a correlation within metric multiplicities between geometry and arithmetic, geometry and algebra, which is constitutive of major science..."
Although he goes on to provide exceptions, he explains, in relatively clear terms, how numbers can define magnitudes which define space.
Friday, March 12, 2010
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