[Marxism] Reply to Les
Jurriaan Bendien
andromeda246 at hetnet.nl
Wed Apr 28 04:08:43 MDT 2004
The question of whether or not infinity is an integer is not meaningless,
anymore than whether zero is a natural number; it is simply a query about
whether a specific number is a member of a definable set of numbers, or not.
This means that the answer is ultimately dependent on a logically exhaustive
definition of the set.
If we cannot define the limits of a mathematical set, this undermines the
very notion of bijection, and thereby the concept of number. An astronomer
might well argue that the question "what is North of the North Pole" is
meaningful, in view of the specific orbit of the earth around the sun. Same
is suggested by an orienteering course I did in the New Zealand Air Training
Corps in 1976.
The proof provided by Tony to reduce my argument to absurdity, is not a
mathematical proof at all, in the absence of a definition of the second set,
i.e. countable or not, finite or infinite. The absurdity resides rather in
Fermat's claim of a mathematical impossibility, in the absence of any
specification of limits critical to establishing the validity of his claim.
If George Bush or Colin Powell argue that "we will stay in Iraq as long as
it takes, or as long as necessary", this is a statement not unlike Fermat's
last theorem, because it does not answer exactly the question of "as long as
it takes to accomplish what". Marx would call this an ideological maneouvre,
aiming to convey consistency and the existence of a specifiable purpose,
while the purpose itself is not specified (and the evidence we now have
suggests the real purpose was either unclear, or misrepresented to the
public). '
Attention focused on Fermat's Last Theorem to discover whether it could be
proved true, and nobody has. Why ? If it is false within its own terms, no
positive proof can be provided. If Fermat's Last Theorem is falsified by the
method I suggested, the positive benefit is, that we live with one less
illusion forming the basis for useless controversy, and can reframe relevant
problems and concentrate on a more appropriate use of mathematical
functions.
When I was 13, my family emigrated to New Zealand, where I went to private
school in 1973. I knew only a few words and sentences in English language,
plus some very basic grammar and syntax. I agreed with the English teacher
that to improve my language skills I had to start with a level of language
use appropriate to my situation, and I would read stories by Enid Blyton
about the "famous five". Some of my classmates joked about this, because
they were reading stories about world war 2 and so on. However, when I was
granted the class prize for academic performance that year and the next
year, it was clear that Enid Blyton had been a useful aid in mastering a new
language. It is one thing to deride someone for his communication, but quite
another thing to clearly reveal the practice that is its corollary.
In 1968, a revolutionary slogan in Paris was "Tout est possible". Everybody
knew that not everything is possible, that is obvious. However, the purpose
was to emphasise that previously existing limits could be overturned and
transcended. This slogan later mutated into its dialectical opposite: "There
is no alternative", and if that is true, nothing is possible beyond that
which we are already doing. In that case, we have placed a limit on what can
be done... but without any proof.
Jurriaan
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