FOM: Robinson and Godel

[Akihiro Kanamori]

  This is in reference to recent remarks about Robinson, Godel, and the
development of non-standard analysis, 
  First, according to the preface of Robinson's Nonstandard Analysis,
he came to the concept in the fall of 1960 and first reported on it
at Princeton University in November 1960. He then gave an address
on it at an ASL meeting in January 1961, prior to the appearance 
of Robinson [1961]. Robinson and Godel knew each other by then,
so it is quite conceivable that Godel's 1961 remarks, alluded to
be Jon Barwise, were addressed to this new development. Perhaps the new
biography of Robinson by Dauben has more information.
  Second, Godel's greatly admired Robinson's work on non-standard
analysis throughout, and it is known that Godel wanted Robinson
to be Godel's successor at the IAS, this before Robinson's death
preceding Godel. Godel greated admired the philosophy of Liebniz,
and perhaps the rectification of the latter's use of infinitesimals 
was a resonating factor. Finally, it is significant to note that
Robinson propounded a decided formalist attitude to mathematics,
one ridiculed by Kreisel and quite antithetical to Godel's 
realist views. This being the case, it is intriguing consider
how Godel actually regarded the infusion of the infinitesimals into 
analysis through logic, as a formal device or as something more
actual.

--Aki Kanamori