----- Original Message ----- From: "Ted Winslow" <egwinslow at rogers.com> To: <lbo-talk at lists.panix.com> Sent: Sunday, December 30, 2001 3:17 PM Subject: Re: Marxism and "Science" (Was: Comic Book Marxism)
> Ian wrote:
>
> > Sorry, the question is whether Hegel's Logic is consistent. See
> > Bertrand Russell and the Brit rejection of Hegelianism on that
one.
> > Completeness is out for any system of logic that incorporates
simple
> > arithmetic.
>
> How will seeing "Russell and the Brit rejection of Hegelianism"
help?
============= The rejection of Idealism in the UK, Bradley, T.H. Green etc. excepted, and by the Pragmatists in the US was largely due to finding substantial contradictions within Hegel's work, given the evolution of logic by Frege, Russell et al and advances in physics, biology etc., no?
> The fundamental point at issue was Hegel's concept of "organic
unity" i.e.
> of "internal relations" (a concept which, by the way, Hegel is
elaborating
> in the passages from the Science of Logic you've quoted). G.E. Moore
claimed
> (e.g. Principia Ethica, , 2nd ed., pp. 84-5) the concept was
> self-contradictory. In this he was mistaken. The conclusion
depended on
> implicitly adopting an atomic ("ordinary language") meaning for the
concept
> of a "part" and then proceeding to demonstrate that this was
inconsistent
> with treating the part as internally related to the whole.
=============
And the controversies of mereology have been solved? I for one would hold that we have a far richer set of models of internal relations that have been arrived at without using Hegel's methods. Key to those developments has been the concept of recursion.
I can't make sense of what is meant by ordinary language, but perhaps that's because I showed up on the planet long after H & R and our theories of language, logic and theories themselves have changed substantially. At the same time that's not to denigrate H's insights on that topic. I would hold that they are less than what Leibniz, Russell, Whitehead, Church, Lewis etc have accomplished on the topic. No doubt many see Whitehead's scheme as preposterous as Hegel's but at least Whitehead respected the beauty and limitations of math and logic and pushed those limits in a way Hegel did not.
>
> The mistake in this argument was pointed out by Frank Ramsey in the
context
> of defending Whitehead's version of the idea of internal relations
from
> similar criticism by Russell and Johnson. He says of the criticism
that it
> mistakes "for a fundamental characteristic of reality what is merely
a
> characteristic of language." (Ramsey, Foundations of Mathematics, p.
117)
==========
Well that's a common problem in philosophy and science, given the multiple interdependencies of epistemology and ontology.
> That the claim of inconsistency was mistaken was eventually
acknowledged by
> Russell himself. He says he was persuaded of this by Whitehead who
also
> showed him how to disentangle "mathematical logic" from ontological
atomism.
> He was unable, however, to free himself from the atomism: "I am
persuaded
> that the world is made up of an immense number of bits, and that, so
far as
> logic can show, each bit might be exactly as it is even if other
bits did
> not exist."
==================
Well a modal argument based on STR and the relativity of simultaneity as well as other substantive breakthroughs in physics as well as transfinite mathematics
was largely responsible for Russell's clinging to the notion of OA, something Hegel could not have known about yet would have embraced as he would have embraced multivalued, fuzzy and paraconsistent logics all of which give us the opportunity to understand interdependencies, boundaries and identities in novel, fascinating and non-dialectical ways. Whitehead attempted a different model of relativity of simultaneity; whether this had to do with attempts at preserving his model of internal relations I don't know. As for the disentangling of mathematical logic from OA and physics, the last two paragraphs of the article below are quite interesting regarding the issue of internal relations especially as Russell and Whitehead's work gave rise to what Shannon accomplished.
[NYTimes] December 30, 2001 Bit Player By JAMES GLEICK Halfway through the last century, information became a thing. It became a commodity, a force -- a quantity to be measured and analyzed. It's what our world runs on. Information is the gold and the fuel. We measure it in bits. That's largely because of Claude Shannon.
Shannon is the father of information theory, an actual science devoted to messages and signals and communication and computing. The advent of information theory can be pretty well pinpointed: July 1948, the Bell System Technical Journal, his landmark paper titled simply ''A Mathematical Theory of Communication.'' Before that, no such theory existed. Suddenly, there it was, almost full grown.
To treat information scientifically, engineers needed to answer the kinds of questions they were asking about matter and energy: how much? How fast? For fundamental particles, an irreducible unit of measure, Shannon proposed the word ''bits'' -- as shorthand (suitably compressed) for ''binary digits.'' A bit is a choice. On or off. Yes or no. One or zero. Shannon saw that these pairs are all the same. Information is fungible: smoke signals and semaphores, telegraph and television, all channels carrying bits.
Back then, the main technologies for sending and storing information were analog, not digital, so this was far from obvious. Phonograph records embodied sound waves in vinyl, and Shannon's telephone-company employers trafficked mostly in wavy signals, too. Yet some interesting communications channels were not continuous but discrete: the telegraph and teletype.
Mainly, though, Shannon was thinking of electrical circuits. The marriage of on-off to yes-no meant that circuits could carry out something akin to logic. They could not only transmit bits; they could manipulate them. Not coincidentally, in that same year Bell Labs was preparing to announce a new invention: the transistor. ''It is almost certain,'' Scientific American declared bravely in 1952, ''that 'bit' will become common parlance in the field of information, as 'horsepower' is in the motor field.'' Sure enough, bits led to bytes and, inexorably, to kilobytes, megabytes, gigabytes and terabytes.
All that still rests on the theoretical foundation laid by this playful mathematician and electrical engineer. Shannon was born in rural Michigan in 1916, the son of a language teacher and a probate judge. He was an early and enthusiastic tinkerer in the new American style. Thomas Edison was his hero. Once he built a crude telegraph using a half-mile of barbed wire between his house and a friend's.
Nor did he stop playing just because he grew up. At Bell Labs, and then as a professor at the Massachusetts Institute of Technology, he amused colleagues by building juggling machines, unicycles, chess-playing computers and robotic turtles. He left a body of work comprising more than a hundred technical papers along the lines of ''Reliable Circuits Using Less Reliable Relays,'' as well as others, not quite so influential, like ''Scientific Aspects of Juggling'' and ''The Fourth-Dimensional Twist, or a Modest Proposal in Aid of the American Driver in England.'' He was also the author of ''A Rubric on Rubik Cubics,'' which can be sung to the tune of ''Ta-ra-ra-boom-de-ay.''
When modern theorists worry about compressing data, maximizing bandwidth and coping with noise, they use the tools Shannon provided. They also keep in mind a paradox he emphasized from the very beginning -- one that is either lovely or perverse, depending on your point of view. Information, in its new scientific sense, is utterly divorced from meaning. Chaotic systems, and strings of random numbers, altogether meaningless, are dense with information.
The medium, it turns out, is not the message. Words, sounds, pictures or gibberish -- it's still just bits
==========
Again, we see the modernist-materialist privileging of reductionism to the mathematical-formal. Are the bits more or less real than the meanings in words etc.? Would Hegel's doctrine of internal relations help resolve the issues? Or would a recursive model of emergence do the trick?
>
> "I began to develop a philosophy of my own during the year 1898,
when, with
> encouragement from my friend G.E. Moore, I threw over the doctrines
of
> Hegel. If you watch a bus approaching you during a bad London fog,
you see
> first a vague blur of extra darkness, and you only gradually become
aware of
> it as a vehicle with parts and passengers. According to Hegel, your
first
> view as a vague blur is more correct than your later impression,
which is
> inspired by the misleading impulses of the analytic intellect. This
point
> of view was temperamentally unpleasing to me. Like the philosophers
of
> ancient Greece, I prefer sharp outlines and definite separations
such as the
> landscapes of Greece afford. ...
> "It was Whitehead who was the serpent in this paradise of
Mediterranean
> clarity. He said to me once: 'You think the world is what it looks
like in
> fine weather at noon day; I think it is what it seems like in the
early
> morning when one first wakes from deep sleep.' I thought his remark
horrid,
> but could not see how to prove that my bias was any better than his.
At
> last he showed me how to apply the technique of mathematical logic
to his
> vague and higgledy-piggledy world, and dress it up in Sunday clothes
that
> the mathematician could view without being shocked. This technique
which I
> learned from him delighted me, and I no longer demanded that the
naked truth
> should be as good as the truth in its mathematical Sunday best.
> "Although I still think that this is scientifically the right
way to
> deal with the world, I have come to think that the mathematical and
logical
> wrappings in which the naked truth is dressed go to deeper layers
than I had
> supposed, and that things which I had thought to be skin are only
well-made
> garments. Take, for instance, numbers: when you count, you count
"things,"
> but "things" have been invented by human beings for their own
convenience.
> This is not obvious on the earth's surface because, owing to the low
> temperature, there is a certain degree of apparent stability. But
it would
> be obvious if one could live on the sun where there is nothing but
> perpetually changing whirlwinds of gas. If you lived on the sun,
you would
> never have thought of counting because there would be nothing to
count. In
> such an environment, Hegel's philosophy would seem to be common
sense, and
> what we consider common sense would appear as fantastic metaphysical
> speculation.
> "Such reflections have led me to think of mathematical exactness
as a
> human dream, and not as an attribute of an approximately knowable
reality.
> I used to think that of course there is exact truth about anything,
though
> it may be difficult and perhaps impossible to ascertain it.
Suppose, for
> example, that you have a rod which you know to be about a yard long.
In the
> happy days when I retained my mathematical faith, I should have said
that
> your rod certainly is longer than a yard or exactly a yard long.
Now I
> should admit that some rods can be known to be longer than a yard
and some
> can be known to be shorter than a yard, but none can be known to be
exactly
> a yard, and, indeed, the phrase 'exactly a yard' has no definite
meaning.
> Exactness, in fact, was a Hellenic myth which Plato located in
heaven. He
> was right in thinking that it can find no home on earth. To my
mathematical
> soul, which is attuned by nature to the visions of Pythagoras and
Plato,
> this is a sorrow. I try to console myself with the knowledge that
> mathematics is still the necessary implement for the manipulation of
nature.
> If you want to make a battleship or a bomb, if you want to develop a
kind of
> wheat which will ripen farther north than nay previous variety, it
is to
> mathematics that you must turn. You will kill a man with a
battle-ax or
> with a surgeon's knife; either is equally effective. Mathematics,
which had
> seemed like a surgeon's knife, is really more like the battle-ax.
But it is
> only in applications to the real world that mathematics has the
crudity of
> the battle-ax. Within its own sphere, it retains the neat exactness
of the
> surgeon's knife. The world of mathematics and logic remains, in its
own
> domain delightful; but it is the domain of imagination. Mathematics
must
> live, with music and poetry, in the region of man-made beauty, not
amid the
> dust and grime of the world.
> "I said a moment ago that, in revolt against Hegel, I came to
think of
> the world as more like a heap of shot than a pot of treacle. I
still think
> that, on the whole, this view is right; but I gradually discovered
that some
> things which I had taken to be solid shots in the heap did not
deserve this
> dignity. In the first flush of my belief in separate atoms, I
thought that
> every word that can be used significantly must signify something,
and I took
> this to mean that it must signify some thing. But the words that
most
> interest logicians are difficult from this point of view. They are
such
> words as 'if' and 'or' and 'not.' I tried to believe that in some
logicians'
> limbo there are things that these words mean, and that perhaps
virtuous
> logicians may meet them hereafter in a more logical cosmos. I felt
fairly
> satisfied about 'or' and 'if' and 'not,' but I [41] hesitated about
such
> words as 'nevertheless.' My queer zoo contained some very odd
monsters, such
> as the golden mountain and the present King of France - monsters
which,
> although they roamed by zoo at will, had the odd property of
nonexistence.
> There are still a number of philosophers who believe in this sort of
thing,
> and it is their beliefs which have become the philosophical basis of
> Existentialism. But, for my part, I came to think that many words
and
> phrases have no significance in isolation, but only contribute to
the
> significance of whole sentences. I have therefore ceased to hope to
meet
> 'if' and 'or' and 'not' in heaven. I was able, in fact, by the
roundabout
> road of a complicated technique, to return to views much nearer to
those of
> common sense than my previous speculations.
> "In spite of such changes, I have retained a very large part of
the
> logical beliefs that I had fifty-five years ago. I am persuaded
that the
> world is made up of an immense number of bits, and that, so far as
logic can
> show, each bit might be exactly as it is even if other bits did not
exist."
> (Russell, "Beliefs: Discarded and Retained" in Portraits from Memory
> pp. 38-42)
>
> Ted Winslow
>
===================
"1]The world can be resolved into digital bits, with each bit made of smaller bits.
"2]These bits form a fractal pattern in fact-space.
"3]The pattern behaves like a cellular automaton.
"4]The pattern is inconceivably large in size and dimensions.
"5]Although the world started very simply, its computation is irreducibly complex."
>From the mathematician Rudy Rucker's 'Mind Tools', Hegel's great,
great, great grandson.
Aufgehoben indeed!
Ian