[FOM] Alain Connes' approach to Analysis

[José Manuel Rodriguez Caballero]

Connes distinguishes between Newton's infinitesimals (his infinitesimals
variables) and Leibnitz' infinitesimals (the infinitesimals objects from
nonstandard analysis). Reference: between minute 11 and minute 16 in the
video https://www.youtube.com/watch?v=cmqeZJJgHWo

Connes criticizes Leibnitz's approach as follows (free translation from
French): Every nonstandard real number determines, in a canonical way, a
subset of [0,1] which is not Lebesgue measurable, hence such numbers do not
exist. Reference (page 6) in Kanovei-Katz-Mormann's paper:
https://arxiv.org/pdf/1211.0244.pdf

By the way, I am not sure if Connes criticism apply to Moerdijk's
intuitionistic approach to nonstandard analysis:
https://repository.ubn.ru.nl//bitstream/handle/2066/129065/129065.pdf?sequence=1

 Kind Regards,
Jose M.
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