[FOM] Answer to Friedman, Paulson, and Caballero

[Mikhail Katz]

I second Sam Sanders' choice of expressive register with regard to
Connes's expostulations concerning Robinson's framework.  Starting in
1994 when he first unveiled his own theory of infinitesimals, Connes
used to periodically comment at the expense of Robinson's theory.
Connes used to do this in articles, books, and interviews.  I
published two articles in 2013 analyzing Connes's expostulations.
Since then I haven't heard any comments from Connes on the subject of
Robinson.  In this sense my articles were successful.  This has now
held for 5 years.

Connes's former comments inscribe themselves in a long line of such
peeps by authors like Bishop and others, starting in 1974 shortly
after Robinson's death.  One discerns distinct profiles among such
critics:

(1) people opposed to Robinson's framework because they feel it
conflicts with a legitimate mathematical framework they favor on
philosophical grounds;

(2) people involved in a Cargo Cult Science (CCS) of their own without
necessarily any intrinsic or scholarly value, and hate Robinson's
theory because they perceive it as a valid competitor that
disqualifies their CCS.

Here Bishop would clearly fall under category (1), even though he may
have been factually wrong in thinking that there is actually a
conflict, as argued by Sam Sanders.

As far as Connes is concerned, he clearly has a system of his own
including a rudimentary notion of infinitesimal (viewed as compact
operators with a specific rate of decay of eigenvalues).  On the other
hand, some of the claims he makes, particularly about his so-called
"primordial mathematical reality" tend to place him into category (2).

Sergeyev is a shoo-in for category (2).

As far as Richard Arthur is concerned, his Leibniz scholarship
features a dose of obfuscation that conceals the triviality of his
ideas.  Given the volume of his output, he qualifies for category (2),
along with Sergeyev.

Paul Halmos seems to belong in category (1) even though some of his
stuff exhudes a visceral CCS-style platonist agenda.

The nonsequiturs found in papers by Ken Easwaran on realism, by
Ferraro on Euler, by Craig Fraser on Robinson, and by Judith Grabiner
on Cauchy would tend to place them into category (2).

Further details can be found at
http://u.math.biu.ac.il/~katzmik/infinitesimals.html

MK