FOM: hostility?

Josef Mattes mattes at
Fri Jan 16 23:13:03 EST 1998

>From: Stephen G Simpson <simpson at>
>Subject: FOM: Riemann surfaces; arithmetization of analysis; "list 2"
>The "list 2" people also want to consider a great deal of other pure
>mathematics as f.o.m.  For instance, McLarty and Marker say that
>Chow's lemma about projective analytic varieties is f.o.m.  

What happened was that I asked you (among other things) whether you 
would consider Chow's lemma a foundational result, adding 'You might say 
that this says something striking and basic about (an important type of) 
shapes, and their relations to functions.' 
Joe Shipman answered 
"I am beginning to see why some people are referring to others as 
having "blind spots". Obviously Chow's theorem is not foundational in 
anything like Steve's sense of the term." 
In response to this McLarty made several postings which at the very least
showed that there was nothing 'obvious' about Chow's theorem
not being foundational. In fact, he went quite a long way towards giving a 
foundational exposition of Chow's theorem, a goal which both you and 
Friedman seemed to value [see e.g. Friedman's posting of 4.Nov.].
(By the way, my original guess was that indeed would *not*  fit your
definition, but this did not seem *obvious* to me, for the  reason quoted 
above, which is why I was interested in your opinion.)

>says that Connes' "non-commutative geometry" (this is just C*-algebras
>and algebraic topology in disguise) 

Here we disagree. 
But whatever the technical details, again, Connes says: 
"[There are] many natural spaces for which
the classical set-theoretic tools ... loose their pertinence." 
Are you saying that this is obviously irrelevant to f.o.m.?
If not, why are you using this (without further argument)
as an example to support your claim that I (among others)
"don't give a damn about [. . .] which mathematical concepts are
truly basic, or any of the other issues that are, in my view, crucial
for f.o.m. " ?

>is f.o.m.  

>Date: Tue, 13 Jan 1998 13:29:45 -0500 (EST)
>From: Stephen G Simpson <simpson at>
>Subject: FOM: definition of f.o.m.; unity of human knowledge;

>Mattes, who has repeatedly exhibited extreme hostility toward f.o.m.

Not at all. For example, I asked you twice for clarification of  
your definition of f.o.m. (among other things, I asked whether you would 
consider certain things list-1 or list-2, in current terminology), clearly
not a sign of hostility.
This resulted in 
1.) the discussion of shapes [cf. your message of 
6.Nov.], that you seemed to appreciate: 
"[...] this could result in some important conceptual clarification and
research programs; There has already been some discussion of "shape" and
foundations of geometry; " [your posting of 12.Jan.98]; 
2.) the discussion of Chow's theorem referred to above; 
3.) my pointing out that you did not give a single
example of a theorem in set theory that is not foundational ("That's a
point well taken. Yes, I should have given such an example." [Simpson, 6.Nov.]).

The only thing I can think of that you might have had in mind in your 
claim of 'extreme hostility' is the quote from Serge Lang in my most
recent posting [12.Jan.98]. 
Again, no hostility here: I thought it might be worth pointing out what
such an eminent 
mathematician  has to say with regard to the role of axiomatization in
mathematics, in 
particular in relation with Harvey Friedman's posting that I refered to.
In regard to the 
language of the quote, I thought it was rather strongly worded but not
insulting  and in 
particular not stronger worded than some of Friedman's postings (Example:
8.Dec.: "I don't  hate  mathematicians,  or think they are stupid - at
least in the usual sense of the word.")

What I am not hostile to, but very sceptical about, is what seems a
de-facto identification of f.o.m. with set theory (by some people). For
reasons for this scepticism see my posting of 12.Jan.

>By the way, Mattes may be interested to know that when Alain Connes
>gave a series of four lectures here at Penn State a few years ago, the
>first lecture was devoted entirely to G"odel's incompleteness theorem.

Connes also discusses it for example in the book 
"Conversations on mind, matter and mathematics", but what is your point
(If it is to prove to me that the incompleteness  theorem is important
then I would like to 
remind you that I wrote on 10 Nov: 'It goes without saying that I have no
intention of denying the importance of Goedel's results.')

Josef Mattes

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