Re: misnomers

From: Eckard Blumschein (blumschein_at_et.uni-magdeburg.de)
Date: 10/20/04 

Date: Wed, 20 Oct 2004 08:27:31 +0200

On 10/19/2004 9:37 PM, Hibernatus wrote:

> These words are "labels", ...

Well, but my intention was to reveal the particular label "actual" as a
deliberately misleading one and to stress that semi-infinite is about
the same nonsense as semi-pregnant. There is just a seemingly tiny
difference between infinity as it was used from Aristoteles to Pierce
and Cantor's castrated "actual" infinity. Castor himself was not so
stupid as those who refer to him. I see his final madness some sort of
evidence for honest and clear selfjudgement making him indeed admirable.
The unsolved problem might be a rather fundamental one, not accessible
to a solution just by means of operating with numbers in the usual sense
and with axioms.

I am not a mathematician. Therefore I collected critical views
concerning that matter. Honest and prudent experts seem to regret that
mathematics is not based on a sound basis without contradictions, so
far. Abraham Robinson (born Robinsohn) introduced hyperreals. They seem
to make standard mathematics more complicated without providing a
complete solution. The same might be true for surreals. Maybe, it will
be best to accept that there is a cardinal difference between
representation in terms of sets of numbers and continuous or infinite
quantities. Cardinality is indeed a convincing concept except for
Cantor's basic assumption that infinity is countable by means of
bijection. Hilbert understood it quite clear: Infinity evades any
imagination in terms of numbers. Nonetheless, the two worlds are closely
linked with each other.

Well, this sounds too simple. However, I found a similar seemingly
trivial case: Because abstract time does obviously not adequately
represent reality, we need a trivial (in the original sense of the word)
time. Everybody already takes advantage of it except for those who
purified science. It is elapsed time, being trivial in a positive sense.

The most decisive things were clearly addressed from laymen.
A. Badiou. Theoretical Writings. The Athlone Press 2004, wrote:
The whole is the open.
The artist Diana Machulina wrote: The memory, like the imagination knows
no border between past and future but for "reality" in its materialistic
  sense, it is insurmountable.

E.B.

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