[FOM] the ultimate aim of mathematics etc.

S. S. Kutateladze sskut at math.nsc.ru
Thu Nov 22 04:39:28 EST 2007

Dear Professor Stolzenberg:

11/22/2007, you wrote to me:

Gabriel Stolzenberg>    On Thu, 15 Nov 2007, in "Re: re re re the future of history,"
Gabriel Stolzenberg> S. S. Kutateladze replied to my posting, "re re re the future of
Gabriel Stolzenberg> history," also of 15 Nov.

Gabriel Stolzenberg>    He began with a quote from "re re re the future of history.".

>> > But don't we have to understand this ancient tradition of dichotomy
>> > of points and monads in order to be able to assess this claim of
>> > resurrection?  I also need a precise explanation of just what "in
>> > concordance with" means here.  This is crucial.

>> To understand is a big word,

Gabriel Stolzenberg>    I don't see how this addresses my question.
Many letters and many implications, that's what I mean.

Gabriel Stolzenberg>    So now you claim that resurrection is a fact.

Infinitesimals were expelled for a few decades from mathematics.
Since Robinson they are living here again. That's not a claim
to assess, but that a fact to be taken into consideration.

>> The concept of monad is explicit in Euclid's Elements  (Book VII,
>> Definition 1). The monad of Euclid is the primary concept of
>> counting. The point of Euclid is the primary concept of measurement.

Gabriel Stolzenberg>    If one must say something, why not say that the primary concept
Gabriel Stolzenberg> of measurement is that of a ratio?  Wouldn't Euclid have liked this?

The definitions of Euclid  are facts of history not to be neglected  in passing.

>> The dichotomy between point and monad is that basic and that old.

Gabriel Stolzenberg>   In arriving at this conclusion, how did you explore the possibility
Gabriel Stolzenberg> that you are, at least in part, projecting the present onto the past?
Gabriel Stolzenberg> ("Whiggish" history.)

The dichotomy is a fact as witnessed by Euclid's Elements and
it is definitely not a claim of a fact, so differing from any arbitrary
quibble or rebuttal.  We are both in the present, talking about the past.
This is not a possibility but  a fact.  You may call it projecting.

>> To count everything is the ultimate aim of mathematics.

This is just  an approximate thesis.  Mathematics belongs to the mankind.
Mathematics is a human endeavor.  It started with counting, and  it
deals with counting.  My thesis is abstract, and so it is a result of

Gabriel Stolzenberg>    As it stands, "to count everything" doesn't mean anything.  Also,
Gabriel Stolzenberg> I've never heard of an ultimate aim of mathematics.  Is it something
Gabriel Stolzenberg> that you discovered by pure thought?  Also, when the ultimate aim is
Gabriel Stolzenberg> achieved, is that the end of mathematics?  How
Gabriel Stolzenberg> not?

Sorry, but I'll stop here. "Polemics" is  shorter  than "understanding,"
whereas the implications of polemics are less rewarding.

                                           S. Kutateladze

Sobolev Institute of Mathematics
Novosibirsk State University
            mailto: sskut at math.nsc.ru
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