[FOM] re re re the future of history
S. S. Kutateladze
sskut at math.nsc.ru
Wed Nov 14 20:50:06 EST 2007
11/15/2007, you wrote to FOM:
Gabriel Stolzenberg> But don't we have to understand
Gabriel Stolzenberg> this ancient tradition of dichotomy of points and monads in order to
Gabriel Stolzenberg> be able to assess this claim of resurrection? (Does everyone except
Gabriel Stolzenberg> me know what a monad is? I mean really know, not just kinda sorta.)
Gabriel Stolzenberg> I also need a precise explanation of just what "in concordance with"
Gabriel Stolzenberg> means here. This is crucial.
To understand is a big word, and the resurrection is not a claim but a
fact. The concept of monad is explicit in Euclid'd 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.
The dichotomy between point and monad is that basic and that old.
To count everything is the ultimate aim of mathematics.
To count the continuum is the first and foremost challenge of
mathematics. This is a "rough draft" of a possible explanation.
Gabriel Stolzenberg> Why must we think of Nelson's observation in order to understand
Gabriel Stolzenberg> Goedel's prediction?
Nelson was the first in the modern (postrobinsonian) era who demonstrated explicitly
that all infinitesimals and infinities are not (only) some imaginary "surds" or "hyperreals.''
They are or may be perceived on the same grounds as other reals.
They belong to the core of mathematics now, since they reside always reside in
Gabriel Stolzenberg> And why aren't we told what these allegedly
Gabriel Stolzenberg> good reasons are so we can decide for ourselves? (In my experience,
Gabriel Stolzenberg> Goedel was not always a reliable source.)
We are told to decide for ourselves. No source is beyond a doubt, and
to decide objectively we must understand and evaluate facts. 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.
Sobolev Institute of Mathematics
Novosibirsk State University
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