[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.
Sobolev Institute of Mathematics
Novosibirsk State University
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