Marxism and Mathematics
david.welch at SPAMst-edmund-hall.oxford.ac.uk
Mon Feb 12 07:05:09 MST 2001
On Sun, 11 Feb 2001, John Landon wrote:
> It is worth checking out a little book by Rudy Rucker
> called 'Infinity and the Mind'. There was a question
> about 0/0 in relation to differentials.
> Rucker's book contains a section and reference to the
> work by Abraham Robinson on the new demonstration of
> the real existence of differentials. The use of
> limiting concepts from the nineteenth century
> attempted to keep the subject out of paradox troubles,
> but now we can see that there really is a number
> smaller than any rational number 1/n as n increases,
> yet greater than zero.
IIRC Robinson showed there are interpretations of the
language of analysis where infinitesimals exist (a
similar method shows there are models of arithmetic
with a greatest element), but equally there are
interpretations without. I wouldn't say there
really are infinitesimals, only it is possible to
work with them in a consistent way if desirable.
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