[Marxism] godel etc (was ...)
cbrown at michiganlegal.org
Thu Mar 17 08:38:02 MST 2005
Carlos A. Rivera
> In some fundamental sense human (mathematical) activity
> cannot be reduced to formalism alone, such formal systems are incomplete.
So we can say that Godel et al, do for Enlighment mathematics and logic what
Marx et al did to philosophy?
Cybernetics and digital fault protection as the mathematical realization of
Leninism, if you will.
Did this rant make sense?
Perhaps "incompleteness" is an expression of Engels and Lenin's dialectic of
absolute and relative truth, and their metaphor of the mathematical
asymptotic curve; relative truth as a curve progesses toward the "line" that
it absolute truth but never reaches it, is _incomplete_. As finite beings
our knowledge of the infinite universe is always incomplete. Materialist
mathematics should reflect that.
Now we come to the question, Engels writes in Anti-Dühring, in the
beginning of the chapter mentioned (Part I, Chap. IX), whether any, and if
so which, products of human knowledge ever can have sovereign validity and
an unconditional claim (Anspruch) to truth (5th German ed., p. 79). And
Engels answers the question thus:
The sovereignty of thought is realised in a number of extremely
unsovereignly-thinking human beings; the knowledge which has an
unconditional claim to truth is realised in a number of relative errors;
neither the one nor the other [i.e., neither absolutely true knowledge, nor
sovereign thought] can be fully realised except through an endless eternity
of human existence.
Here once again we find the same contradiction as we found above, between
the character of human thought, necessarily conceived as absolute, and its
reality in individual human beings with their extremely limited thought.
This is a contradiction which can only be solved in the infinite
progression, or what is for us, at least from a practical standpoint, the
endless succession, of generations of mankind. In this sense human thought
is just as much sovereign as not sovereign, and its capacity for knowledge
just as much un limited as limited. It is sovereign and unlimited in its
disposition (Anlage), its vocation, its possibilities and its historical
ultimate goal; it is not sovereign and it is limited in its individual
expression and in its realisation at each particular moment (p. 81).[Cf. V.
Chernov, loc. cit., p. 64, et seq. Chernov, the Machian, fully shares the
position of Bogdanov who does not wish to own himself a Machian. The
difference is that Bogdanov tries to cover up his disagreement with Engels,
to present it as a casual matter, etc., while Chernov feels that it is a
question of a struggle against both materialism and dialectics.]
It is just the same, Engels continues, with eternal truths.
This argument is extremely important for the question of relativism, i.e.,
the principle of the relativity of our knowledge, which is stressed by all
Machians. The Machians one and all insist that they are relativists, but the
Russian Machians, while repeating the words of the Germans, are afraid, or
unable to propound the question of the relation of relativism to dialectics
clearly and straightforwardly. For Bogdanov (as for all the Machians)
recognition of the relativity of our knowledge excludes even the least
admission of absolute truth. For Engels absolute truth is compounded from
relative truths. Bogdanov is a relativist; Engels is a dialectician. Here is
another, no less important, argument of Engels from the chapter of
Anti-Dühring already quoted:
Truth and error, like all thought-concepts which move in polar opposites,
have absolute validity only in an extremely limited field, as we have just
seen, and as even Herr Dühring would realise if he had any acquaintance with
the first elements of dialectics, which deal precisely with the inadequacy
of all polar opposites. As soon as we apply the antithesis between truth
and error outside of that narrow field which has been referred to above it
becomes relative and therefore unserviceable for exact scientific modes of
expression; and if we attempt to apply it as absolutely valid outside that
field we really find ourselves altogether beaten: both poles of the
antithesis become transformed into their opposites, truth becomes error and
error truth (p. 86). Here follows the example of Boyles law (the volume
of a gas is inversely proportional to its pressure). The grain of truth
contained in this law is only absolute truth within certain limits. The law,
it appears, is a truth only approximately
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