Re: Das Kalenderblatt 090612

Am Fri, 12 Jun 2009 02:39:37 -0700 (PDT) schrieb WM:

[Antonio Leon Sanchez:
EXTENDING CANTOR’S PARADOX
A CRITIQUE OF INFINITY AND SELFREFERENCE]

Antonio Leon Sanchez: A Critique of Infinity

Synopsis

This book summarizes the results of a personal research on the formal
nature of the actual infinity developed along the last fourteen years.
Written by a naturalist (geologist and mathematician), and therefore from a
non-platonic perspective, the book consist of a collection of arguments
proving the inconsistency of w-order and then that of the actual infinity.

Ach so, ein zweiter Mückenheim also. Klar dass WM den gleich zitieren muss.
:-)

Das Kapitel 1 des Buchs ist schon mal sehr vielversptrechend:

Chapter 1

Cantor versus Cantor

Inexplicably, the possibilities for Cantor antidiagonal to be a rational
number have not been examined so far. Obviously, a rational antidiagonal
would prove that not only the set R of real numbers but
also, and for the same reasons, the set Q of rationals numbers, whose
denumerable nature was proved by Cantor, is non denumerable. So,
we would have a contradiction involving the foundations of Cantor
theory of transfinite numbers. Cantor's diagonal argument should be
therefore suspended until it be proved the impossibility of rational
antidiagonals in Cantor's argument. This paper gives, on the other
hand, a proof of the existence of such rational antidiagonals.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Source:
http://www.interciencia.es/PDF/Mathematics/ACritiqueOfInfinity.pdf


Aber der Mann hat noch andere bedeutende Arbeiten verfasst. Bemerkenswert
erscheint mir der 5-seitige (!) Aufsatz:

A syntactic critique of self-reference and of Godel incompleteness
theorems.


No comment.


Herbert
.

Relevant Pages

  • Re: Cantor and the binary tree
    ... According to Cantor ... > well-ordered and simultaneously ordered set < of all rationals, ... What you are doing is defining some sort of sequence of infinite sets. ... carried away and use sloppy wordings like 'at infinity' or 'after ...
    (sci.math)
  • Re: Uncountable many reals without Cantor
    ... Sorry this should read the reals are ... Where Cantor uses what you would probably call "actual infinity," is in ... with other sets, e.g. the rationals. ... "Actual infinity" compresses rather than distinguishes so-called ...
    (sci.logic)
  • Re: infinitely many nns = infinite nns?
    ... There are never two or more reals "in ... I meant that there must be a sequence of irrationals -- without ... Let a, b, c and d be naturals such that a/b < c/d as rationals, then ... point out that this proof uses the assumptions of potential infinity, ...
    (sci.logic)
  • Re: Side channels in theorems
    ... So why would doing these 4 operations an infinity ... the rationals are. ... If the assumption leads to a contradiction, then the assumption must be wrong, namely that I can order and enumerate all reals. ... "there is an algorithm that allows me to compute every digit" or, equivalently "as precise as I wish". ...
    (comp.compression)
  • Re: Side channels in theorems
    ... So why would doing these 4 operations an infinity ... rationals, just as happy for the reals. ... I have an algorithm that given n gives you the ...
    (comp.compression)