[FOM] the ultimate aim of mathematics etc.
gstolzen at math.bu.edu
Wed Nov 21 23:40:03 EST 2007
On Thu, 15 Nov 2007, in "Re: re re re the future of history,"
S. S. Kutateladze replied to my posting, "re re re the future of
history," also of 15 Nov.
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,
I don't see how this addresses my question.
> and the resurrection is not a claim but a fact.
So now you claim that resurrection is a fact. Is this new claim
stronger than the original one? The son of my friend, Deep Thought,
once made the following two-part observation. (1) You can write
anything on a piece of paper. (2) You can then add, "I mean it"
or "I'm not kidding." Your "is a fact" reads like his "I mean it."
(And your "claiming" something is like his "writing" it.)
> 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.
If one must say something, why not say that the primary concept
of measurement is that of a ratio? Wouldn't Euclid have liked this?
> The dichotomy between point and monad is that basic and that old.
In arriving at this conclusion, how did you explore the possibility
that you are, at least in part, projecting the present onto the past?
> To count everything is the ultimate aim of mathematics.
As it stands, "to count everything" doesn't mean anything. Also,
I've never heard of an ultimate aim of mathematics. Is it something
that you discovered by pure thought? Also, when the ultimate aim is
achieved, is that the end of mathematics? How not?
> To count the continuum is the first and foremost challenge of
I don't know what you mean either by "count the continuum" or
"the first and foremost challenge of mathematics." It seems odd
to me that there should be such a thing as the first and foremost
challenge of mathematics and I should never have heard of it. I
should think it would be a basic part of every mathematician's
education. (But maybe I was sick the day they covered this.)
Also, wouldn't you expect the first and foremost challenge of
mathematics as well as its ultimate aim to be discussed in the
collection, "What is Mathematics?" Is it? If not, how could they
have failed to include it?
> This is a "rough draft" of a possible explanation.
A possible explanation of "in concordance with"? I don't see
it. (I also don't see what work the word, "possible," is doing
> No source is beyond a doubt, and to decide objectively we must
> understand and evaluate facts.
"Understand" is a big word. (See above.) So is "objectively."
> The quotations of Nelson and Goedel
> are not ultimate truths or incontestable proofs of anything. Their
> views as expressed are listed among the instances of evidence by
> experts to be taken into account.
I don't think Goedel was an expert about this. To me, his remark
reads like wishful thinking. If somebody can produce evidence that
I am mistaken about this, I will happily eat crow because I will have
learned something very interesting. I have nothing against Goedel.
I used to play ping pong with him. (In a recurrent dream. He wasn't
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