[Marxism] Fermat - response to Les
Jurriaan Bendien
andromeda246 at hetnet.nl
Tue Apr 27 09:56:35 MDT 2004
Hi Les,
I wrote:
>So even at this >very primitive level, things go wrong, because the authors
neither (a) respect the simplest requirements of measurement theory
Les replied:
>i dont see how your comments on fermat really lend any weight to this
argument Jurriaan. perhaps you can tighten and re-express your basic
argument?
Reply:
Argument about what ? As regards the transformation problem, the essence of
the thing is that the majority of products of human labour are at any given
moment not offered for sale in the market (withdrawn from the market), and
consequently they do not have any real prices. Nevertheless, those products
do have a value, whether it is a house, a car, or a piece of improved land,
an inventory of widgets, stock of unsold cars without license plates, a
stockpile of butter etc. Nobody says, that they do not have a value.
Everybody knows you can make capital gains out of assets.
But if I ask what that value is, people will refer me to a price which is
not an actual selling price, but a theoretical selling price, and this
theoretical selling price is based on current price relativities in the
market, the price system operating, and is arrived through comparing the
exchange-ratios of goods. It is the price it would sell for if you sold it,
but you don't know, until you have sold it and received payment. And then we
are back with Capital Vol. 1 chapter 1, and we have to agree with Kozo Uno
that Marx's method of presenting his theory wasn't very good, because Marx
creates important confusions about the central concepts of value and price
and does not show precisely why exactly the concept of value is necessary.
If labour-time is the substance of value and money-price is the form of
value, several important questions arise, such as (1) whether labour-time is
the measure of value or whether value is the measure of labour-time, (2)
whether money-price is the measure of value or whether value is a measure of
money-price and (3) why price cannot be a direct measure of labour-time
without the concept of value. This kind of thing is what you have to explain
in a non-dogmatic way and if you cannot do it you cannot solve the
transformation problem either. That is what my paper is about. Most of what
academics say about it is worthless, there are a few good books on it, but
most of it does not hit the spot in my way of thinking.
I agree, the solution to Fermat's problem that n=infinity is maybe not so
profound. In geometry it would express a triangle so large that it cannot be
known. My real point is that if infinity is an integer, then Fermat's last
theorem is false, and if infinity is not an integer, then Fermat's last
theorem is unproven and escapes from a general proof. It's a bit like
President Bush saying "we will stay in Iraq for as long as necessary" but
nobody knows how long that will be. At one level, it's sophistry, but at
another level it's a real problem. It's a bit like saying, we know there are
isosceles triangles, but we deny that there exists an isosceles right
triangle, or, we accept a Sunni Triangle, but we deny a Datsun Sunny exists.
Etymologically, the word "iso" derives from the Greek "iota-sigma (o}meaning
"equal" and it is not accidental that this is the name of the International
Organisation of Standardisation.
Fermat's problem has nothing directly to do with the transformation problem,
about which I posted my draft comments in answer to Paul Cockshott, except
that depending on how you define key terms affects the solution. Fermat's
explicit claim was, that no positive integers exist where x^n + y^n = z^n
for n>2. My explicit claim is that this is a false assertion, if infinity is
a positive integer. Those who wish to defend Fermats Last Theorem must deny
that infinity is a natural number or an integer, with the consequences that
has for mathematics.
The healthiest thing I can think of just now is to relax. I hope you get my
drift.
Jurriaan
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